- A spaceship is sent to Mars. Once it has escaped the earth's
gravitation and not yet close to Mars, you do not have to keep burning
your rockets to keep up your speed; Newton's first law (N1) says that
with negligible force an object will move with constant speed in a
straight line.
- When you stand on a scale there are two forces on you, your own weight
(the force the entire earth exerts on you) and the force which the scale
exerts on you. Because of N1, the net force on you must be zero (you are at
rest), so the force the scale exerts on you must be equal in magnitude to
your weight but up. {To carry this a bit further, Newton's third law (N3)
says that the force you exert on the scale is equal and opposite the force
you exert on the scale and this is the force which the scale registers. A
scale does not measure your weight, rather it measures the force you exert
down on it which just happens in this case to be numerically the same. If
you are in an elevator accelerating upwards, the scale will read something
larger than your weight.}
- You are pulling a box across a level floor with constant speed. The
rope you are pulling on is horizontal. The force with which you must
pull is equal in magnitude to the force of friction the floor exerts on
the box.

**QUESTION: **

is it possible to increase gravitational force at a particular place or in a single room?

**ANSWER: **

The gravitational force depends on the mass located near that place, so
all you have to do is put a huge block of lead under the room to increase
the gravity. But the gravitational force is so weak that you would be hard
pressed to observe any change since the mass of the earth is so large. I
estimate roughly that if you put a 10x10x10 m^{3} block of lead
under your floor that the weight of something in the room would increase by
about 2x10^{-4}%!

**QUESTION: **

A ruler with length lo is at rest in a coordinate frame XY and tilt at an angle 45 degree. I know if paralell the length is not the same for both frame and if perpendicular it has the same length but what about the length of the ruler if it is at 45 degree? And how can i find the angle that i see between the ruler and the direction of motion?

**ANSWER: **

The component of the ruler along the direction of motion is shortened
from (*l*_{0}/√2) to
(*l*_{0}/√2)√[1-(*v*^{2}/*c*^{2})]
while the component perpendicular remains
(*l*_{0}/√2). You
should be able to do the trigonometry from here.

**QUESTION: **

I am a medical imaging student in PA. I asked this question in class and
was told not to worry about it, I wouldn't be tested on it, but I would
still like to clarify it in my mind. We were studying the difference
between characteristic and Bremsstrahlung X-rays. The text stated that
characteristic X-rays are dependent on the target material, tungsten for
most diagnostic X-ray machines and Mo or a combination of Rh and Mo for
mammography. The text further states that a characteristic X-ray occurs
when a K-shell electron is knocked out of it's shell and this requires
at least 70 KeV of energy and that no characteristic X-rays are produced
below 70 KeV and any less would produce only Bremsstrahlung. This makes
perfect sense to me when using a W anode, since the binding energy of
the K-shell electrons are 69 KeV. However, if the anode is made up of Mo
or Rh, the K-shell binding energy is around 20 KeV, so in a mammography
unit, wouldn't a 25 KeV setting produce characteristic X-rays? Or would
it only produce Bremsstrahlung X-rays?

**ANSWER: ** **(Thanks
to Dr. Mark Haidekker)**

I hope the following answer is helpful to you:
You are
"…correct in the assumption that characteristic X-rays are produced at lower energies as well.
Bremsstrahlung is emitted whenever a high-energy electron changes its momentum. This is when it decelerates and some of its energy is converted to
photonic energy. The spectrum of bremsstrahlung is broad. Conversely, when an electron or a X-ray photon of sufficient energy moves an electron out of its
shell into a neighboring shell (excitation) or removes it from the atom entirely (ionization), the vacancy gets filled eventually. This process frees energy that gets released as an X-ray photon of exactly the binding energy difference. The emitted spectrum is narrow, and it depends on the atom.
Therefore, it is referred to as characteristic X-ray radiation.
Characteristic X-ray radiation is not limited to the K shell, nor is it limited to molybdenum or tungsten. If a K-shell vacancy of ionized rhodium is filled, the characteristic X-ray energy will be 23 keV. An electron dropping
from the L- to the K-shell of rhodium would emit a 20 keV photon. A copper beam-hardening filter would produce scattered X-rays of about 10 keV.
However, any of these low-energy characteristic X-ray energies would be
absorbed: Either in the beam hardening filter that can usually be found in front of X-ray tubes, or in the tissue itself as the absorption coefficient of tissue is very high for low X-ray energies. This is why beam-hardening is
done in the first place: If low-energy X-rays get absorbed in the patient's body, they don't contribute to image formation, but they do cause ionization
in tissue. Therefore, low-energy X-rays get filtered out. In this context, characteristic X-rays from molybdenum or rhodium would not pass the beam-hardening filter, and low-energy emission would not be seen in the spectrum emitted from a typical X-ray unit."

**QUESTION: **

I left a bowl of water with three hard boiled eggs in the fridge and overnight the top 1/2 in of water froze. The fridge is only around 38 degree F, and nothing else in the fridge froze. Why did the water freeze? My fiancee says it has to do with evaporation because the fridge is really dry.

**ANSWER: **

I have answered questions
before which involve frost forming at temperatures above freezing. These
involve both evaporative cooling and radiative cooling, so your fiancйe has
a good idea. However, I really find it hard to believe that this could be
the answer to your question since a half inch of ice is a whole lot more
than a little frost and the temperature is so far above freezing. I suspect
a much more mundane reason: I have sometimes found ice on the top of a
bottle of milk but only if the bottle has been put in a particular place in
my refrigerator. Some locations of the refrigerator are colder than others
because of proximity to cooling coils, a duct to the freezer section, or for
other reasons having to do with how the refrigerator is engineered. And, the
temperature you suspect, 38^{0}, may be inaccurate so that the whole
refrigerator is set too low making it even more likely that somewhere will
be below freezing.

**QUESTION: **

we are trying to settle a debate at college. our questions regards the 4th dimension and its effects on ourselves in the 3rd dimension. the question is as follows. when you are watching television, are you watching something that happened at a different point in the 4th dimension?

**ANSWER: **

Normally, the 4^{th} dimension is regarded as time. Physicists
refer to "spacetime" indicating that time is on an equal footing with space
in relativity. So any two events which are not simultaneous can be regarded
as having happened at different "…point(s)
in the 4th dimension". It is interesting that different observers will not
agree on what is simultaneous, one of the important findings of special
relativity. Another way of saying this is that there is no such thing as
absolute time, a god-given clock right for everybody.

**QUESTION: **

In my physics class, we are only looking at one method of pendulum movement, which is an approximation method depending on the angle being very very small, but i was very curious about what its function would be when the angle is larger.
I tried figuring it out myself, but i came across a problem that i have no idea what to do about.
Lets say we had a pendulum mass M, Length L, and distance from 0 of X (0 is the middle, where angle Z= 0) If we let it go from a certain point, then the force upon it would be F= Mg[sinZ] (note, using Z instead of theta for the angle made by the pendulum and vertical in radians) Then Ma= Mg[sinZ] So a=g[sinZ] -- a=g[sin{X/L}] (radians arc/length) ANd because in calculus acceleration is the second derivative of the postion function (X) we get X''= g[sin{X/L}] Now here is where i get lost, because i cannot figure out any way to find the function X and i really need help for this...
You could rewrite this as f''(x) = sin[f(x)], to make things clearer as g and L are constants, but i have no idea at all how to find the integral to get f[x] (function x) and how to finish this to find a function that gives movement of pendulums.

**ANSWER: **

Well, you are treading on some pretty difficult stuff here. There are
certain aspects of this problem which can be solved using exotic
mathematical functions called elliptic integrals, but I suspect you don't
want to go there. So let us just say that this problem is one (as are most
of nature's real problems) which cannot be solved in closed form in terms of
standard mathematical functions. That is, *y*"+sin(*y*)=0 is not a
differential equation which can be exactly solved. But if we approximate
sin(*y*)≈*y*, as you have
learned in your physics class, it can be solved. But, now you want to do
better than that. So you have to use a better approximation for the sine
function. Where did the first approximation come from? It came from a series
expansion for the sine, sin(*y*)=*y-y*^{3}/3!+*y*^{5}/5!-…
So, if y is not so small a better approximation would be
sin(*y*)≈*y-y*^{3}/6.
Now you will find that the period is better approximated by *T=T*_{0}(1-(*A*^{2}/8))^{-1/2}
where *T*_{0} is the period in the small angle approximation
and *A* is the amplitude in radians. For example, if *A*=90^{0}=*π*/2,
*T*=1.2*T*_{0}, about 20% longer. I should warn you that,
unless you are pretty handy with differential equations, this is not trivial
to deduce. In this day and age, one can solve problems of this type
numerically on a computer.

**QUESTION: **

I try to move a very large boulder here on Earth. If I try to move the same boulder on the moon would it take more force, less force, or would it be the same force. I say same force, because it has the same mass. F = ma. Makes since to me, but my students don't buy it. Any other possible explainations?

**ANSWER: **

Perhaps what is bothering your students is that friction has not been
included in the discussion. In fact, why are you often unable to move a
boulder at all here on earth? It is because the static friction between the
ground and the boulder is larger than the force you are able to exert.
Indeed, the friction is approximately proportional to the normal force which
is in turn proportional to the weight, so you might very well be able to
move a boulder on the moon which you could not move on earth. However, the
lesson you are trying to teach is an important one. So, ask your students to
imagine the boulder being placed on a cart on a track with negligible
friction on both the earth and the moon; if you exerted a force the same on
each, each would move identically. In fact, if you went to the middle of
empty space where there was no gravity at all, the boulder would move just
the same. This confusion arising from having systems which are complicated
by many factors such as omnipresent friction was one of the major
impediments to progressing from the Aristotelean view to the Newtonian view
of nature.

**QUESTION: **

What is the relationship between an electromagnetic field or wave and a photon? What is the distinction between a wave and a field?

**ANSWER: **

Electromagnetic (EM) waves are time varying electric and magnetic
fields. An EM wave is normally characterized by a frequency *f*, a
wavelength *
λ*, a
speed *c*, and an amplitude usually specified by specifying the maximum
electric field value. It was discovered in the early 20th century that
sometimes an EM wave will behave like a stream of particles called photons.
(You might want to research the photoelectric effect and Compton scattering
to see the historical origins and verifications of this discovery.) This
type of duality turns out to be pervasive for all of nature, in particular a
thing we have always thought of as a particle (an electron, for example)
will behave like a wave if we design an experiment to look for wave
properties. It is a true feature of nature and physicists and philosophers
refer to it as the wave-particle duality. For EM waves, the amount of energy
which a photon has turns out to depend on the frequency of the radiation, *
E=hf* where *h* is Planck's constant. A photon is a special kind of
particle in that it has no mass.

An EM wave is, as I
said above, time varying electric and magnetic fields which propogate
through empty space (unlike most waves) and has a speed which is independent
of the speed of the source or observer, independent of the frequency or
wavelength or amplitude of the wave. So all EM waves are fields. However,
all fields are not waves. For example, there is an electric field around an
electric charge but it is not a wave if the charge is at rest or moving with
a constant speed; and, there is a magnetic field around a current carrying
wire which is not a wave if the current is steady.

**QUESTION: **

Some of my friends and I recently moved to St Louis, MO. We have all independently found that twist top bottles, no matter where they are originally from, are somewhat difficult to open. We have been told that the center of the continent and the center of mass of the continent are nearby and that St Louis or the surrounding area used to be a huge exporter of lead. Does any of this explain this weird phenomenon? Do nearby dense areas have an effect on torque? If so, would this translate into the tightening of a twist top bottle over time?

**ANSWER: **

You're jokiing, right?

**QUESTION: **

My students hear all the time that there is ZERO G. I tell them that astronauts are free falling, like someone jumping out of an airplane. But I hear professionals say zero G all the time and the kids are confused. How do explain that gravity exists everywhere, and then they hear of zero g on the space station ?

**ANSWER: **

First, let me say that your example (which I have not included here) is
not a good one. Let me attempt to give an answer to the question regarding
zero-g (sometimes referred to as weightlessness). Those terminologies are,
strictly speaking, incorrect. What is your weight? It is the force which the
earth exerts on you. It is not what is measured by a scale; a scale measures
the force you exert on it, not the force the earth exerts on you. Of course,
in every day life the force which you exert on the scale happens to equal
your weight, but if you are in an elevator accelerating up the scale will
read more than your weight. If you are in an elevator free falling down, the
scale reads zero but your weight is still the same. If you say zero-g you
imply that the gravitational field is zero but that is certainly not true
anywhere near the earth (except at that point where the earth's and moon's
gravity cancel). I presume that you have taught your students about
centripetal acceleration. Anything which moves in a circle of radius *R*
with speed *v* has an acceleration toward the center of the circle of
*v*^{2}*/R.* A satellite in a circular orbit has just the
right speed such that this acceleration is equal to *g* so, as you
correctly state, it is the same as the free falling elevator—you
feel like there is no gravity. All this is standard physics.

Here is another perspective: Einstein's
principle of
equivalence states that there is no experiment you can do to distinguish
whether you are in a gravitational field or in an accelerated frame of
reference (that is, the freely falling elevator and having zero gravity are
physically indistinguishable from inside). So, if it looks like a duck and
quacks like a duck, we might as well call it a duck!

(One final note:
Note that I have ignored the tiny correction that if you are orbiting with
your feet "down" your feet have a slightly different acceleration from your
head.)

**QUESTION: **

What exactly is in light that makes it be affcted by gravity?
please give me a thorough informtion about what light contains that is affected by gravity.

**ANSWER: **

See an earlier answer.

**QUESTION: **

Assume an electromagnetic wave in vacuo. From my reading, I infer: 1: that a photon is a single cycle os a wave
2: that each change in the orbital level of an electron produces one photon.
3: that the intensity of light emitted from a source is governed by the number of atoms in which electrons are changing orbital level
4: that the basic difference between "ordinary light" and lased light is that in lazsed light the photons are brought into tandem as a continuous stream (wave) of photons.
5: that the energy of the photon is equivanent to the energy lost by the electron during the orbital transition.

**ANSWER: **

- As in your question below, a photon is not a wave at all.
- true
- true (number/second decaying)
- essentially correct. The waves (think of waves, not photons) are
coherent, that is they are all in phase with all the others.
- true, but I would say energy lost by the atom rather than by the
electron.

**QUESTION: **

Is there a fixed relationship between the wavelength of a photon and its amplitude? Electromagnetice waves are usually graphed as two perpendicular sine waves. But I suspect that they must extend laterally to some extent. Is the shape if viewed longditudinally known? Can to direct me to a site that would dispaly such?

**ANSWER: **

A photon is a particle, not a wave. So it does not have a wavelength or
an amplitude in terms of electric and magnetic fields. A photon has fixed
energy so that if you think about the wave which is equivalent to the
photon, its amplitude will be determined by how spread out in space it is,
that is by the uncertainty as to where the photon is.

**QUESTION: **

I have read that according to Einstein's theory, if a person were able to travel at the speed of light, they could stop time completely, and slow time (from people on Earth's perspective) if they were to travel near the speed of light. Also, I read that the greater the gravitational force, the slower your biological clock would run. Why would scientists not utilize this theory in humans to slow their biological clocks and thus allow them to see a greater future? It is probably possible with certain machinery to elevate the force of gravity within a unit.

**ANSWER: **

You are breaking the rules! No questions about traveling the speed of
light! I can give you two reasons we don't accelerate humans to velocities
near the speed of light:

- The energy it would take get you going to 99% the speed of light is
huge.
- Even if we were willing to invest the energy is such an adventure, your
acceleration would have to be so enormous that your body would be crushed
beyond all recognition.
- Similarly, you body would not be able to remain uncrushed in a huge
gravitational field.

**QUESTION: **

If i have a superconductive wire and i attach a positive electrode to one end and a negative electrode to the other end there will be some measurable current through the wire. every time i recreate this circuit within the same parameters the same current will be read. not any current, only this current. if the wire were thicker (assuming that the cross sectional area of the electrodes were increased the same extent) , more electrons would be able to flow through the wire. thus the current would become greater. if were to replicate this circuit i would again read this same greater current, not any. to my understanding a potential difference is increased when the ratio of electrons to protons on the positive electrode increases or when the ratio of electrons to protons in the negative electrode decreases, thus the attractive force between the departing electrons in the positive electrode and the immovable protons in the negative electrode would in increase with increased potential difference. i acknowledge that my conceptualization of potential difference mat not be correct, but if it is why would placing a positive and negative electrode to either end of a superconductive wire result in a potential difference of zero? would the electrons not flow more quickly through a superconductive wire if the attractive force between them and the positive electrode is greater?

**ANSWER: **

By definition the potential difference across zero resistance must be
zero. When you connect a power source across it, the voltage across the
terminals must drop to zero or else the wire must go nonsuperconducting. I
have answered this question many times. You might be interested in searching
through previous answers for superconductor.

**QUESTION: **

I have a few unanswered questions about gyroscopic precession. I looked thought the archive but I haven’t found anything that directly answers my question. I understand if you spin up a gyroscope, put It down at an angle, its axis will precess around in a cone. I further understand (and correct me if I am wrong about this) that in a completely frictionless environment it will precess forever around its center of mass. This strikes me as similar to a spinning an object in space. Spin it once and it goes forever baring friction and outside influence. However in the case of the gyroscope where does the initial energy come from to start in precessing? Does it tilt slightly more upon release thereby lowering its center of mass and make use of some potential energy? Does the gyroscope itself reduce speed slightly?
If we assume one of these things is true than it would seem the energy would have to go somewhere once the gyroscope stops precessing. For instance say we built a half circular frictionless tack that is the correct height such that it supports the gyroscope once it gets to it, without lifting it. Now, when the gyroscope reaches the track it should stop precessing because there is no longer a tilting force applied to it. However if the gyrocope initially derived energy for precession from a slight drop or a decrease in rotation, does the reverse happen? It would seem that it could not rise back up because then it would then have a tilting force again. Does the gyroscope gain rotational speed?

**ANSWER: **

Your question comes close to violating the "single,
concise, well-focused questions" groundrule! Let's start out talking about
translation instead of rotation. Suppose you have a particle moving along
with some momentum and then you apply a force which is perpendicular to its
momentum; the result is that the momentum changes (its direction, not its
magnitude). This is because of Newton's second law which is often more
useful in the form of force equals rate of change of momentum than force
equals mass time acceleration. For rotational motion, Newton's second law
takes the form that torque equals the rate of change of angular momentum.
The gyroscope will not precess if there is no torque on it, that is, if it
were in empty space, it would not precess. Like in the case of the particle
above, the angular momentum changes its direction rather than its magnitude;
the spin rate stays the same but the spin axis changes its direction. If you
were to suspend the gyroscope so that there were no torque on it (as in
gyrocompasses, for example) it would not precess. Most of your questions are
sort of not answerable because you did not understand the basics which I
have tried to convey. The motion is actually more complicated than it
appears but is well-understood; it depends on the initial conditions but
usually includes small wiggles (called nutating) about the precession which
are usually damped out quickly by friction in real systems.

**QUESTION: **

if one has a circuit containing a superconductive wire with a certain cross section of area, there will exist some measurable current unique to this cross section of area. even though there exists no electrical resistance through the wire there is still a definite number of electrons which can fit within the wire's cross section of area, all traveling at some velocity. how does a definite number of electrons unique to a given cross section of area all traveling at the same velocity not result in some definite current unique to a superconductive wire with this cross section of area?

**ANSWER: **

What makes you think all the charge carriers would have the same
velocity? Your argument could equally well be made for a normal conductor.
In fact, all the charge carriers are in motion and the faster the average
motion the larger the current.

**QUESTION: **

If I sent you in a spaceship to Alpha Centauri or say, Vega, and
spun you in a circle, how would you reliably return to Earth? Since those
are relatively close, what about the center of the Milky Way?
I'm basically asking, since you would be at a different point in the universe, how would you reliably navigate back to Earth since the sky would look very different?
The difference might not be too great at Alpha Centauri, but at say, the center of the Milky Way, I can't imagine how you would know which direction you came from if you were "spun" around to face a random direction once you got there.

**ANSWER: **

You underestimate the power of computers in the current state of
celestial navigation. All you need to know is the position (say relative to
the sun or maybe relative to the center of the galaxy) of as many
recognizable stars as possible. Then any even modest computer could easily
calculate how those stars would appear to you as seen from anywhere.

**QUESTION: **

I understand that when an atom makes a transition from one state to another it emits a particle of light called a photon.. well now, is the photon in the atom ahead of time that it comes out? or is there no photon to start with? and if there is no photon to start with then where does it come from and how does it come out??

**ANSWER: **

Let's first discuss a radio station. The way we broadcast the radio
waves is that we cause electrons to move back and forth in the antenna.
These wiggling electrons cause the waves to be emitted from the antenna. Did
these waves exist before we started wiggling the electrons in the antenna?
Were they somehow sitting there waiting to be sent off? No, of couse not.
The wiggling electrons created them, not from nothing but using the
electrical power we put into the wiggling electrons in the antenna. For
example, if we put 50 kilowatts into the antenna, then 50 kilowatts of radio
waves will come out of it. Now to your question. The excited atom is like a
little antenna; when the atom drops to a lower energy state the electron has
to change the way it moves in the atom, sort of by wiggling into the new
state. But the atom lost energy equal to the difference between the two
states, so electromagnetic energy is radiated away, the photon which is the
smallest possible bundle of electromagnetic wave.

**QUESTION: **

What is meant by " Protons gyrating at very high magnetic fields"?

**ANSWER: **

I have not this expression before. It probably refers to the precession
of the proton's magnetic moment in the magnetic field. This is just the same
as a top which precesses in the earth's gravitational field. I can't say
more than that without knowing the context of the quote.

**QUESTION: **

i understand that all is always in motion & therefore changing/transforming/decaying.
My question is what does gold change to?

**ANSWER: **

I have no idea what you are talking about. Just because something is in
motion does not mean that it is "changing/transforming/decaying". A passing
car is in motion but not changing into something else. Gold is a stable
element and does not change into anything.

**QUESTION: **

Given a circuit comprised of superconductive material and a known voltage how could the current be calculated?

**ANSWER: **

I have answered this question a couple of times before. What it boils
down to is that if the resistance is zero the potential difference is zero.
You simply drain the power source by shorting it out. The current can be
anything and the voltage must be zero.

**QUESTION: **

We have just started a physics project and I was wondering if you could offer a little help. Our teacher hung a remote-controlled plane from the ceiling by a string. He turned it on and waited until it reached a constant velocity (it travelled in a circle). Then he timed how long it took for the plane to complete 15 revolutions. Our job is to find out how long it took for this to happen. We are allowed to take any measurement we want execpt for measuring the time. The mass of the plane is 29.6g. The length of the string is 2m 90cm. The radius of the circle in which the plane travelled is 2.37m. I'm not asking for an answer for this project but I was wondering if you could give me some ideas and inspire me. Heh heh. Every time I try to plug it into one of our distance, acceleration, momentum, etc. equations I hit a dead end. I have an idea about using the angle that the string was at to somehow play into this.

**ANSWER: **

This pretty much sounds like homework, so I cannot tell you how to do it. I
will give you a hint: the vertical component of the tension in the string
must be equal to the weight of the plane. Look up the analysis of the *
spherical pendulum*. Incidentally, you should not say that the plane has
constant velocity, it has constant speed. Velocity is a vector and since the
plane's direction is constantly changing its velocity is constantly
changing.

**QUESTION: **

My friend received a speeding ticket a long time ago on a motorcyle. He says it was for a speed much faster than he was ever going. He says a knowledgeable person told him that the false reading was due the the motorcyle wheel spokes going faster than the speed of the motorcyle, or the velocity of the spokes adding to the motorcyle speed.
Its been a while since I took a basic college physics class, but it seems to me that the if the bike is going speed X, the circumference of the tire - the part that contacts the road, has to be going the same X. If the tire tread is rolling out at a velocity of X, any spoke - being less far from the axle, has to be going less than X. EG, the spoke cant be going faster than the speed of the bike.
Is it physically possible parts of a motorcyle wheel can indicate on a radar, a speed that is faster than the actual speed over ground of the motorcyle?

**ANSWER: **

The axel of a wheel goes forward with the speed of the vehicle, the
bottom of the wheel is at rest, and the top goes forward with a speed twice
the speed of the vehicle. Any particular spoke might have a forward speed
anywhere from about zero to about twice the vehicle speed depending on where
you look. I would say that the likelihood of the radar reading the speed of
a spoke is virtually zero. Either your friend was mistaken about his actual
speed (likely) or the radar malfunctioned. The speed of the spoke argument
is not likely to be the explanation.

**QUESTION: **

My question is about light. If light is affected by gravity, what is in light that makes it be affected like any other matter? I know that light is affected by light because they are pulled into blackholes. Try to make two answers....one answers for a 6th grader (easy) and one for a teacher level (confusing).

**ANSWER: **

I have answered this
question previously. The answer has a part geared toward an 11 year old
and another from the perspective of warping spacetime.

**QUESTION: **

why does it become significantly easier to balance a bike the faster you are going (either pedaling it or say going down a hill)?
For instance, it would be very difficult to balance on your bike if it was standing still, less difficult when you first start to pedal away, and even less difficult when you get some speed. I can balance with no hands best when my bike is moving swiftly. Why is it that the additional speed results in easier balance? And is there a point of diminishing returns, like a point at which the additional speed doesn’t help you but hurts your balance? Let’s assume for all of this that we are on a “good road,” i.e. you aren’t trying to balance your bike on a rocky trail or something.

**ANSWER: **

This is actually a tricky question and one which requires more space
than I can give to a single answer. The glib answer would invoke the
gyroscopic behavior of the spinning wheels but, although this is often cited
in elementary physics classes as an explanation for steering a bike it turns
out to be a very small part of the explanation of bicycle stability. Here
are two sites where you can get a pretty lucid explanation:

http://en.wikipedia.org/wiki/Bicycle_and_motorcycle_dynamics

http://socrates.berkeley.edu/~fajans/Teaching/bicycles.html

Or, you can do a google search on *physics of bicycle*.

**QUESTION: **

Particle accelerators take up alot of space, would it be possible to make them take up less space by making them in a dense curled corkscrew shape?

**ANSWER: **

A particle with extremely high energy is extremely hard to deflect from
a straight path. Even using the strongest magnets available (superconducting
magnets) only a modest deflection of the passing beam of particles can be
achieved. So it is simply not possible to bend them around a closed path in
a very small space. An interesting detail is that once you get very close to
the speed of light, the magnetic field does not have to be adjusted to
compensate for the greater energies as the particles gain energy; a magnet
will bend a 500 GeV proton just about the same as a 1000 GeV proton, so you
can use the same path for the particle as it is accelerated. The accelerator
does not really accelerate the particle much at all as the energy increases
(like a proton traveling at 99.9999% the speed of light would have a much
higher energy than one with a speed 99.999% but almost the same speed). So
accelerators would be better named energizers than accelerators!

**QUESTION: **

how much percentage of light would be lost if light (say a flash light) was shot into a box with the dimensions of 1ft. by 1.ft by 1 ft., filled entirely with the best reflecting mirror found in the world?

**ANSWER: **

All of it, and very quickly. See an
earlier answer to get a
perspective on how fast the light would be lost. Incidentally, the light is
not really lost but is converted into thermal energy when it is absorbed by
the mirrors.

**QUESTION: **

What effects would we feel if a black hole approached the earth? What would happen to our orbit around the sun and the moon's orbit on us?

**ANSWER: **

That depends entirely on how massive the black hole is and how closely
it approaches. If the earth were inside the event horizon, it would be
swallowed up.

**QUESTION: **

As I understand the Quantum Mechanics double slit experiment an electron (or photon) is shot through a wall with two slits. If there's an observer (which I understand to mean any force that impacts on the experiment's system) then the electrons hit photoelectric paper as if the electrons were particles, in other words they hit in one and only one place. If there isn't an observer they hit as a probability wave. My question is, why isn't the photoelectric paper considered an "observer" since it clearly interferes with the system, in fact it's there to observe the behavior. Given my limited understanding of the Quantum Eraser experiment I don't see why time should have an impact on the recording of the electron's hitting the paper.

**ANSWER: **

You do not have it quite right. It is not "if there's an observer" but
rather whether the observation makes a measurement which tells you which
slit the electron (or photon) passed through. If you make this
determination, the interference pattern does not appear.

**QUESTION: **

a single photon of red light does not possess sufficient energy to remove an orbiting electron from its nucleus. in theory, if more than one photon were to contact one electron (of course quite an improbable scenario) could the combined energy of the photons potentially cause ejection of the electron?

**ANSWER: **

Yes, it is called multiphoton ionization. It is practicable with
high-intensity lasers.

**QUESTION: **

I am holding a 20 newton object at arms length a constant 1.5 meters above the ground. My body will clearly be expending energy to maintain the object at that height. How do I calculate the rate of energy expenditure (power) required to hold the object at the specified height?
This problem is vexing to me, because the same object could be placed on a stationary 1.5 meter platform to accomplish exactly the same thing, but the platform will obviously not have to expend any energy. I am having trouble understanding exactly how these scenarios differ.

**ANSWER: **

This energy which you perceive as being consumed is not going into the
object you are holding up. There is no work being done on it. I agree that
some chemical energy will be used by your body to achieve this, but there is
no way to calculate this since it depends on the individual's fitness,
metabolism, *etc*. The energy expended would end up in thermal energy
and would be used for the biochemical reactions necessary to maintain the
required tension in the muscles.

**QUESTION: **

When two objects come into contact (say my buttocks and a wooden chair) does an exchange of matter occur between the two? If so, what gets exchanged? Do they, for example, exchange electrons?

**ANSWER: **

Yes, of course. Untold millions of atoms go both ways. But millions is a
really small number compared to the total number of atoms in the objects
(like on the order of 10^{24}). But, ultimately this is why clothes
get dirty, clothes wear out, things have to be repainted now and then, *
etc*. Also, electrons can go one way or the other which is why you
sometimes have a static charge on you after rubbing on something.

**QUESTION: **

If a free electron interacted with a photon (in a vacuum if it helps), what would happen? For example, would the photon reflect off the electron, or does it depend on the motion of the electron?

**ANSWER: **

It depends on the energies of the electron and photon. If their combined
energies are high enough then production of elementary particles could
happen. For example, the photon could convert into an electon-positron pair.
I suspect that is not really what you are asking, though. Regardless of the
energies, the most likely interaction is simple elastic scattering, the
photon and electron have the same total energy and linear momentum as before
the scattering but move in different directions than before with different
shares of the energy. The best known example of such scattering is called
Compton scattering.
This is probably what you refer to as "reflect off the electron".

**QUESTION: **

1. Using a conversion factor such as (12inches/foot), the conversion factor is equal to what?
2. How to convert mm to meters?
3. How to convert ms to seconds?
4. How to convert cm to meters?

**ANSWER: **

The key is to multiply by 1 so the units come out the way you want them.
For example, suppose you wanted to convert 73 miles to centimeters: 73
~~
mi~~(5280
~~
ft~~/1
~~
mi~~)(12
~~
in~~/1
~~
ft~~)(2.54
cm/1 ~~
in~~)=73
x 1.61 x 10^{5} cm =1.175 x 10^{5} cm; note that each
quantity in parentheses is 1 even though it is numerically not 1. The ones
you ask for are easier: *N* ~~
mm~~(1
m/1000 ~~
mm~~)=*N*/1000
m; *N* ~~
ms~~(1
s/1000 ~~
ms~~)=*N*/1000
s; *N* ~~
cm~~(1
m/100 ~~cm~~)=*N*/100
m.

**QUESTION: **

I'm trying to see I have the right "image" in my mind of how photons work, specifically in the photoelectric effect. Suppose someone was trying to free electrons from a metal by using light. Would this mean that even though an individual photon can have a range of energies the amount of photons must be an integer number? The "image" in my mind is someone trying to break a window by throwing an (integer) amount of small projectiles, but he has the choice of rocks or ping pong balls. He could use a thousand times more energy throwing a million ping-pong balls at the window, than using a single rock, but the single rock will break the window (minimum frequency can release an electron) while throwing ping pong balls does nothing (does not release an electrons).

**ANSWER: **

I guess your visualization is ok. Your ping pong balls would represent
photons with energy smaller than the energy required to remove an electron.
Your rock would represent a photon which does have enough energy.

**QUESTION: **

I teach third grade and students have built a ramp and are using a toy car without mass and with mass to see if the distance increases with mass. The car should go further, correct? But why in third grade terms.

**ANSWER: **

I have addressed this question twice
before. If you read those
answers you will find that yours is not a simple question easily answered in
terms of basic physical laws. There are too many complicating factors and
friction is not nearly as clean a topic as it is often represented in
elementary physics textbooks. I am assuming your ramp takes the car down to
a flat surface. If there were no friction, the loaded and unloaded cars
would move exactly the same and would keep going forever. If the friction
were proportional to the weight, (which is what an elementary physics
textbook will tell you) the two cars would still move identically and go the
same distance before stopping. So, this experiment is a good example of an
experiment you can do to see if the simplest physics works. If not, tell
your kids that what scientists do all the time is test accepted theories and
when those theories fail the scientists try to figure out why. Since you are
using the same car for both tests, I would think they would go about the
same since the friction should roughly double if you double the weight.

**QUESTION: **

Doesn't a photon have to have a mass equal to its energy divided by the speed of light squared?

**ANSWER: **

The trouble with having a well-known equation like *E=mc*^{2}
is that it is often used when not appropriate. If you write *E=mc*^{2},
then this is the energy of a mass which is at rest; or else it means that
the mass has a different meaning from what you usually think of when it is
moving with speed *v*, namely *m*=*m*_{0}/√(1-(*v*^{2}/*c*^{2}))
where *m*_{0} is the mass of the particle at rest, what you
usually think of as inertial mass. As I have said in many
earlier answers, I
prefer to not think of mass as increasing with velocity, *m* to me just means
rest mass. The correct equation for energy is *E=**√*(*p*^{2}*c*^{2}*+m*^{2}*c*^{4})
where p is the linear momentum. So, if a particle is at rest, momentum is
zero and
*E=mc*^{2}; if the mass is zero (as is the case for a
photon), *E=pc.* So a photon has momentum even though it has no mass.
One thing to be careful of, as explained in my
earlier answers, is
that momentum is no longer *mv* but rather *mv*/√(1-(*v*^{2}/*c*^{2})).

**QUESTION: **

Has the superstrings theory been discarded?if yes why if not then what are these strings made of?

**ANSWER: **

String theory is still a very active area of research. However, many
physicists, including myself, are not attracted to a theory which cannot
make any predictions about nature which seems to be the case with string
theory. It is not an appropriate question to ask what the strings are made
of; supposedly everything else is made from them.

**QUESTION: **

A classic paradox in Greek philosophy is the paradox known as "Zeno's Paradox" which involves the race between Achilles and the Tortoise. According to this paradox, Achilles must traverse an infinite number of points to overtake the Tortoise, which is physically impossible and yet he does in fact overtake the tortoise. Hence the paradox. Most people have thought that the concept of "Limit" in calculus has solved this paradox, but apparently such solutions don't do justice to the paradox in it's original form. (See the entry on wikipedia on Zeno's paradox). It has been suggested that the correct solution comes from Physics directly. In other words it is better to consider that space-time is not infinitely divisible but is rather essentially discrete and that motion is actually a series of jumps from one quantum space-time coordinate to the next. This solves the Paradox since now Achilles actually traverses a finite series instead of an infinite one.

**ANSWER: **

I don't think any serious logician finds anything paradoxical about Zeno's
paradox. There is no need to discretize space to get a more satisfactory
explanation. If we assume space is continuous there is still no problem
understanding why the fast catches up with the slow. However, the question
of whether or not space is in fact continuous or discrete (as well as time)
is an open one and of interest to physicists, particularly those studying
quantum gravity. I have previously answered a question similar to yours.

**QUESTION: **

An ideal gas is inside an insulated container so heat can't escape. If the cas is compressed, according to the first law, internal energy is increased so temperature increases - am I right? If so, why does the temperature increase? The temperature relates to how fast molecules are moving. I am thinking that if they hit against a piston coming at them, they will rebound faster - am I right? This would explain the temperature decrease if the gas expands If I am right, I am thinking that if the piston is moved very slowly compared to very fast, I would expect a different final temperature - am I right? Also, why does gravity seem to have no effect on molecules. If gravity has any effect at all, I would expect all the molecules in the container to eventually end up at the bottom of the container if is left alone for a very, very long time.

**ANSWER: **

The first law is energy conservation. If you arrange so that no heat
goes in or out of the gas, then the work done on the gas must equal the
increase in energy of the gas. This is called an adiabatic compression (AC).
It may be shown that for AC the pressure and volume are related by *PV*^{γ}=constant
where *
γ*=*C*_{p}/*C*_{v
}and *C*_{p} and *C*_{v }are the specific
heats of the gas at constant pressure and volume respectively. The work done
on the gas when you go from *P*_{1}, *V*_{1 }to *
P*_{2}, *V*_{2 }is *W*=(*P*_{2}*V*_{2}-*P*_{1}*V*_{1})/(*γ-*1).
One can easily relate this to the temperature change because work may also
be written as *W=C*_{v}(*T*_{2}-*T*_{1}).
All the details can be found in any introductory physics textbook. Your
qualitative analysis of the moving piston speeding is the gas molecules is a
good one. There is no reference in my remarks above about how you get from 1
to 2, so your expectation that the temperature change depends on how rapidly
your compress the gas is not right; when you go slowly you give the
molecules many little kicks but when you go rapidly you give them a few big
kicks. In the real world we usually want the compression to be fast to
guarantee that it is adiabatic because it is hard to make a really well
insulated cylinder so if you compress slowly heat is more likely to leak out
as the gas heats up. But, if it is well insulated it should make no
difference. Regarding gravity, it does have an effect but, because the
molecules are restless (they can't all settle at the bottom because they
keep moving around if the temperature stays constant), the effect is smaller
than you expect. In fact, the density of gas at the top of a container is
very slightly smaller than at the bottom. You might find this difficult to
believe, but it happens for the same reason that the density (pressure) of
the air decreases with altitude.

**QUESTION: **

I just emailed you some very basic questions about thermodynamics. One of them was why gravity doesn't cause all ideal gas molecules to evetually settle at the bottom of the container. I am thinking now that this may be due to the temperature of the walls of the container. Since the walls are at the same temperature, maybe the motion of molecules in the walls excites the gas and keeps that from happening.
I feel like these are all dumb questions because they seem so basic - yet I don't remember these questions being answered in school, although it has been a long time.

**ANSWER: **

Your questions are not dumb. When we derive the ideal gas law we assume
that the collisions of the molecules with the wall are elastic, that is no
energy is lost or gained in a collision. This is not necessarily true for
any given collision but, if the gas and the walls are in thermal
equilibrium, it will be true on the average, just as many collisions gaining
energy from the walls as those losing energy. When you are dealing with
something like 10^{24} atoms, the average is what matters, not one
particular event.

**QUESTION: **

On Saturday I visited my sister in freezing eastern Pennsylvania and I noticed a strange ice formation in her outdoor birdbath, which is currently frozen due to subfreezing tempertures. This is a cheap 12 dollar birthbath, it is not heated. I would like to send you a photograph of the gravity-defying ice formation and hope a physicist can tell be what law of nature would cause water in a birdbath to freeze up into a small column.

**ANSWER: **

This question has been
previously answered.

**QUESTION: **

I've never quite fully understood the classic "bicycle wheel and spinning chair" demonstration. Specifically, I've never understood the middle stage, in which the wheel is rotated 90 degrees, rather than the full 180. At this stage, the student should be rotating around a vertical axis in the same direction in which the wheel was initially spinning (say, clockwise), with the wheel's initial angular momentum.
But the wheel is itself still rotating (around a horizontal axis) with its full initial momentum. There seems to be a new angular momentum vector, orthogonal to the system's initial angular momentum and equal to it in magnitude, that was not introduced by an external torque.
What am I missing?

**ANSWER: **

Imagine that you are in empty space where angular momentum must be
conserved. You start with angular momentum *L*_{0} which is
parallel to your spine, say. Later the wheel has angular momentum *L*_{0}
perpendicular to the original direction of your spine. So the change in
angular momentum of the wheel is in a direction 45^{0} relative to
the original direction of your spine so that is the axis along which your
angular momentum must have to conserve angular momentum. When you do this
experiment you should feel like something is trying to push you off the
stool but you can only rotate about an axis parallel to your spine so
angular momentum is not actually conserved; the friction between you and the
stool exerts an external torque.

**QUESTION: **

They say that the blackholes' gravitation is so massive that it devours light but the photon has no actual mass so how is he attracted to the hole?

**ANSWER: **

Light is affected by gravity just like mass. The reason it is not
evident is that light travels so fast. Imagine a baseball zipping by at near
the speed of light; you would be hard pressed to see at drop much as it
zipped by. It has been observed experimentally by observing the bending of
distant starlight as it passes close to a massive object, for example the
sun during a solar eclipse. This is all understood in the theory of general
relativity where the explanation of gravity is that massive objects actually
warp the space around them and when light is bent by gravity it is simply
following a "straight line" in this warped space.

**QUESTION: **

What is heat or thermal energy on the atomic or sub-atomic level? Is it the nucleus spinning or perhaps the nucleus is bouncing around relative to the electrons? Do we even know or have theories?

**ANSWER: **

First of all, heat is energy transfer, not energy content. For example,
heat flows from a hot object to a cold one but you do not say that the hot
object has more heat than the cold one. If we refer to the internal energy
of something, for example a gas, it is the average energy per constituent;
it is this average energy which temperature measures. In a gas this is the
average kinetic energy per molecule. So let us define thermal energy as
average energy per constituent. Then in a nucleus the average energy per
nucleon is the "thermal energy". A "hot" nucleus is a highly excited state.

**QUESTION: **

From a previous question a basketball zipping by at a substantial percentage of the speed of light will have its apparent shape change from sphere to an oblate spheroid because of the shrinking along the direction of motion. This will cause a decrease in its volume and surface area. If the basket ball is replaced by a black hole will the decrease in surface area cause a corresponding decrease in its entropy and mass?

**ANSWER: **

First, it is wrong to refer to its "apparent shape". Relativity tells us
how things __are__, not how things __appear to be__. Length
contraction says that a meter stick moving by (parallel to its own length)
is actually shorter than one meter if we make a measurement of its length.
(The operational definition of length is to measure the positions of the two
ends of something at the same time.) Regarding entropy, I believe the
article I referred you to in the earlier answer showed that entropy, like
temperature, is not a useful concept in relativity. The mass is also an
ambiguous thing; many people simply envision mass as increasing with
velocity, but in many
earlier answers I have argued that one may simply say that rest mass is
the useful concept and momentum is no longer defined as mass times velocity.

**QUESTION: **

If a basketball zips by at a substantial percentage of the speed of light will its shape still be a sphere or will the length contraction in the direction of motion cause the shape to change?
If the shape is different would the volume be the same or would it change and the pressure of the air inside change?

**ANSWER: **

The diameter of the ball along the direction of motion will get smaller
so the ball will not be a sphere. The volume therefore gets smaller as
measured by an observer seeing it zip by. The volume will be reduced by a
factor of
√(1-*v*^{2}/*c*^{2}). That is the easy part of
the question. The question concerning the pressure is a very difficult one
and I have not found anybody who can give me a definitive answer. I have
done a little research and have found more information about temperature
than pressure in special relativity. There is a what is called the
Planck-Einstein transformation for temperature: the temperature of the gas
in the passing ball is reduced by the same amount as the length, that is
√(1-*v*^{2}/*c*^{2}). So if we now assume that the
ideal gas law, *PV=NkT,* is correct in the moving system, then if *
V'=V*√(1-*v*^{2}/*c*^{2}) and *T'=T*√(1-*v*^{2}/*c*^{2}),
it follows that *P'=P*; the pressure is unchanged. That is all well and
good, but recent
research has shown that the Planck-Einstein transformation is incorrect.
In fact it appears that there is no Lorentz transformation for temperature
which essentially means that temperature as we define it is not a useful
variable in relativity. I suspect that the same could be said for pressure,
that is it is not a variable which we could transform into a moving system,
there would not be a way you could measure pressure in your moving ball.
That is the best I can do with this question. If you get a better answer
somewhere, I would be most interested in learning what you learn.

**QUESTION: **

My husband and I are having a disagreement on the energy used to air dry laundry indoors.
He argues that it is less energy efficient than, or at least the same as. running the gas dryer, to air dry laundry indoors in winter because then the house heating system has to work harder to convert the water molecules in the clothes to liquid and gas.
I don't have a good answer for him, but it just seems counter-intuitive. It seems like the air drying clothes are at the same temperature as the surrounding air, and don't need heat to "wam up" the water in the clothes. It also seems like the water in the clothes would evaporate due to the dry air (some mumbo jumpo about liquid/vapor equilibrium), not because of heat energy being transferred to the molecules. He doesn't deny that air drying provides moisture to the room, his argument is that the energy required to evaporate the water ultimately comes from the furnace so we might as well run the humidifier and the gas dryer.
What do you think?

**ANSWER: **

Your husband is not going to like this, but he is dead wrong. You could
turn your furnace off and your clothes would dry just about as fast.
Certainly air drying clothes takes energy from the environment, but the
amount is trivial compared with how much your furnace needs to put out to
keep your home warm. Believe me, your furnace will never notice. Yesterday
it was about 35 degrees at my house and I hung out clothes which dried in
about 2 hours. Clothes dryers are among the biggest energy hogs of all our
appliances because so much of the energy goes out the exhaust or heats up
the dryer drum or just leaks away in some other way. When I started hanging
out my clothes instead of putting them in the dryer my electric bills went
down about $20 per month. Here is another thing (ok, this is kinda off the
wall!): if you dry your clothes in the house it will humidify your house
which makes it feel warmer so you can actually turn the furnace down!

**QUESTION: **

How can Bob who lives in a 2 dimensional world (a) discover the 3rd dimension (b) imagine the 3rd dimension?

**ANSWER: **

This is a pretty open-ended question. Let me give one example. In some
respect you live in a two-dimensional world because you live mostly on the
surface of the earth. If you did not understand that your two dimensions
were embedded in a three-dimensional space you might be inclined to think
that you were on a big flat plane. But, if you started walking due west you
would eventually get back to where you started from and you would start
thinking maybe there were higher dimensions.

**QUESTION: **

Simple: All mass gives off a gravitational field. The more mass the stronger the field as well as the greater it's area of effect. Density is the amount of matter in a given space. So my question is: If you take all the matter in the Earth and increase it's density by two will the gravitational field effect space and matter the same as at normal density or will the area of effect half it's size while it's gravitational field strength doubles? This ratio is off the top of my head but an equation with explanation of the variables if ones exists will suffice.

**ANSWER: **

What you describe will double the mass of the earth. The result will be
that the gravitational field due to the earth will double everywhere. I do
not understand what you mean by "...the area of effect...". The
gravitational field extends to infinity regardless of its strength.

**QUESTION: **

What does it mean when a field is represented by 2nd-rank tensors (Einstein's gravity)? If a scalar (0-rank) is a numerical quantity representing magnitude, and a vector (1st-rank) is a magnitude that has a direction, then is a matrix (2nd-rank) a plane represented by orthogonal vectors (squared magnitude/perpendicular directions)? Have 3rd-rank tensors ever been used in any physical theories?

**ANSWER: **

This is really too technical a question for the purposes of this web
site. I can tell you that a physically observable quantity may be
characterized by how it transforms under certain tranformations; examples of
transformations are translations, rotations, space reflection. If you are
doing physics in an N-dimensional space then you need one number to specify
a scalar quantity, N numbers to specify a vector, N^{2 }to specify a
tensor (although symmetry proporties usually reduce this number, maybe
something like T_{ij}=T_{ji}), *etc*. I do not know how
to answer the question "what does it mean", it simply is what is
mathematically necessary to describe accurately something in nature. An
example more accessible than gravity is perhaps electromagnetism. Here we
may describe the electromagnetic field by specifying two 3-dimensional
vectors, the electric and magnetic field; this requires 6 numbers. However,
the field may be alternatively represented by a single quantity, the field
tensor, also containing six numbers but having the elegance of a single
quantity rather than two.

**QUESTION: **

I was reading the short article: Scientists Expose Light's Wierd Quantum Nature, #65, pg 56- Discover Magazine-The Year In Science-Jan 2008. Isn't Light's quantum nature fairly obvious taking the macro approach?
For instance...if two planets were one light year apart...and planet A flashed a bright light at planet B...wouldn't the guy on planet B be able to look through a (very powerful) telescope focused at 1/4 the distance in three months and see the same flash that he would be able to see three months later by focusing at 1/2 way point, and three months later focused at the 3/4 point?
In other words, the same event would not only exist in an infinate number of places at an infinate number of different times, but given the spray effect over that far a difference, would exist at an infinate number of focal points from an infinate number of points of view...wouldn't it?

**ANSWER: **

Your telescope does not allow you to observe someplace instantaneously
as you assume. When you focus your telescope at the 1/4 the distance point
you see light which started from there 9 months ago, not light coming from
there right now. If you focus your telescope there you will see your sought
pulse in your telescope in 9 months. And so forth.

**QUESTION: **

A middle-aged man typically has poorer hearing than a middle-aged woman. In one case a woman can just begin to hear a musical tone, while a man can just begin to hear the tone only when its intensity level is increased by 6.0dB relative to that for the woman. What is the ratio of the sound intensity just detected by the man to that just detected by the woman?

**ANSWER: **

Let *D* be the intensity in decibels and *I *be the intensity
in W/m^{2}. Then the definition of the decibel gives *D*_{woman}=*D*_{man}+10
log(*I*_{woman}/*I*_{man}). Then *D*_{woman}-*D*_{man}=6
dB=10 log(*I*_{woman}/*I*_{man}). So log(*I*_{woman}/*I*_{man}).=0.6
and solving I find *I*_{woman}/*I*_{man}=3.98 .

**QUESTION: **

If you could lump all of the atomic nucleuses in the human body into a ball, how big would it be? Smaller than the head of a pin? About the size of a pea?

**ANSWER: **

The size of an atom is on the order of 10^{-10} m and the size
of a nucleus is on the order of 10^{-15} m. So, if we say the size
of the body is on the order of 1 m, the size of the nuclear matter in the
body would be about 10^{-5} m, about 1/100 of a millimeter!

**QUESTION: **

In a nuclear reactor, what is the importance of particle speed in relation to cross-sectional area?

**ANSWER: **

I am not sure what you are talking about but have a rough idea, I think.
In a reactor, the fuel is induced to undergo fission by absorbing neutrons
which makes the nucleus unstable to fission. As luck would have it, when
fission occurs several neutrons are produced which may be used to induce
still more fissions (chain reaction). However, these neutrons are very fast
and unlikely to get absorbed before escaping from the reactor. Hence, to
enhance the probablility of these neutrons causing more fissions they must
be slowed down (moderation). Slow neutrons are likely to get captured and
maintain the chain reaction. So where does the cross section part come in?
It turns out that the probability of neutron capture is related to a
quantity called the *neutron absorption cross section* and, as should
be evident from the discussion above, the cross section increases as the
neutron gets slower. Essentially, cross section is a measure of how big the
nucleus looks to the neutron.

**QUESTION: **

Have you heard of "ball lightning?" If so, is it really lightning? Also, would you know of the microwave ball lightning demonstration, and, if so, what degree of danger it presents as an experiment?

**ANSWER: **

I have previously
answered this question. I don't know what the demonstration you refer to
is.

**QUESTION: **

Does the vapor generated by heating water in a container increase if the volume of water is increased? That is, would 2 cups of water create more steam than 1 cup at the same heating temperature?
To me that seems logical, but someone told me that the rate (water) vapor is generated might be limited by the surface area (the same in both cases above).

**ANSWER: **

The rate at which steam comes off is proportional to the net rate that heat
flows into the water and the surface of the water. So having two cups of
water in a particular pan on a particular burner does not generate steam at
a greater rate than one cup would. (Of course it will ultimately generate
more steam.)

**QUESTION: **

My question is, does the electromagnetic field have a dualistic property? Or is it better understood as a single entity?

**ANSWER: **

The most sophisticated way to think about it is as a single entity. However,
it is more comprehensible if we approach it from a historical perspective
(electric and magnetic fields). One reason this approach is easier to
understand is that the required mathematics are less demanding: electric and
magnetic fields are vectors but the electromagnetic field is a tensor. Also,
most devices fall rather neatly into electric and magnetic categories.

**QUESTION: **

Is hinge a simple machine?

**ANSWER: **

This is not something physicists really worry about, more often it is
important to fourth grade teachers teaching science! It depends on how you
define a simple machine. The hinge itself would have a mechanical advantage
of 1. The hinge-door system might be considered a lever I guess.

**QUESTION: **

Have we actualy measured the electromagnetic force of protons and electrons or are there values simply theory?

**ANSWER: **

Yes, of course we have. The measurements are amazingly accurate.

**QUESTION: **

I am a 5th grader in Texas and I am working on a science project concerning friction. Could you tell me how friction works?

**ANSWER: **

Friction is a very complicated thing microscopically and you should probably not, at your age, try to dig too deep since this is not a terribly well understood thing. I would recommend that you focus your project on something like the empirical observation that the force of friction when something slides is proportional to the normal force (the force a horizontal surface exerts upward on the sliding object). This normal force is just the the weight of the object and whatever is stacked on top of it if the surface is horizontal. Therefore, suppose you have a wooden block sliding on a wooden table top. If you measure a frictional force of 1 lb if the block weighs a half pound, then if you add another half pound to the block it should have twice the friction force,
2 lb.. Note that the surface area of the block does not matter, according to this empirical "law". I think it would be a good 5th grade project to test this.
I have judged many science fairs and have always found that the best
projects are those with a simple, well-focused, interesting, and achievable
objective.

**QUESTION: **

please explain briefly: cold is merely the absence of heat and darkness is simply the absence of light.

**ANSWER: **

Cold and dark are qualitative terms, not quantitative. If on object is
colder than another the energy per molecule is smaller. Dark usually refers
to absense of visible electromagnetic radiation but also sometimes can refer
to absense or low intensity of other wavelengths. Dark also does not
necessarily imply absense but may imply low intensity; when we say it is
dark out we certainly do not mean there is absolutely no light.

**QUESTION: **

To calculate the escape speed from the the earth's surface is straightforward with KE = PE.
How would I approach the same calculation if a hole were drilled to the earth's center and I wanted to launch from the earth's center?

**ANSWER: **

First you must make an assumption regarding the earth's mass
distribution. Although not true, most standard problems of the type you
present, assume a uniform mass density. In that case you will find that the
force on the object increases linearly from zero at the center until you
reach the surface. Therefore, the problem is simply a simple harmonic
oscillator problem (identical to a mass on a spring). This is a standard
problem you will find in many elementary physics textbooks. So you must
calculate the speed the particle would need at the center of the earth to
have the usual escape velocity at the surface.

**QUESTION: **

Can an object that is heated only get as hot as the flame that is heating it? I've thought about this question for a while and intuitively it seems that an object can only get as hot as the source. However, if we think of the source as having an infinite source of energy that is supplying heat to an object and that object can only dissipate heat at a certain rate due to radation, convection, etc...then at some point couldn't the object get hotter than the flame? At some point there will be equilibrium but that doesn't limit the object to the flame's temperature correct?

**ANSWER: **

The flame is not just some object at some temperature, it is a source of
energy. An object in a flame can, as you correctly conclude, become hotter
than the flame itself since heat will continually flow into the object from
the flame and, if heat leaves more slowly, will continue increasing its
temperature.

**QUESTION: **

my question concerns the hypothesized constant expansion of the universe. if the universe is growing exponentially as predicted, would not every object that we use as measurement also expand proportionally? thus it would be entirely impossible to measure such expansion? also, in what way does such an expansion change our view of the universe?

**ANSWER: **

It is the universe which is expanding, not the space in which it is
embedded (although that is changing also but differently). Imagine two cars
moving away from each other: would you measure, with a meter stick on one of
the cars, that they were not?

**QUESTION: **

When we drop water on tissue paper, why does it spread evenly ?

**ANSWER: **

Because of capillary action.

**QUESTION: **

If everyone in the world began to walk due east at a given time, would the rotation of the earth slow down (in order to conserve momentum)?

**ANSWER: **

Technically, yes (it is angular momentum conservation). However, the
mass of all the people on earth is so small compared to the total mass of
the earth that the effect would be too small to measure. (See following
question.)

**QUESTION: **

I wonder: in the event the north pole (artico) thaw completely and turn around the ice water, the balance of rotation of the earth suffer amendments? The masses of the planet will have to be redistribuidas to enter new balance? The axis of inclination of 23 degrees should be amended because of this?

**ANSWER: **

The total mass of all the water on earth compared to the total mass of
the earth is so small that the effect would be too small to measure. (See
preceding question.)

**QUESTION: **

I have question regarding conventional radar systems.
As you're aware, stealth technology is based on the notion of
reflecting, absorbing, scattering radio signals and cancelling them at
the source. Conventional radars look for a positive image of the sky.
Rather than looking for a positve image of the sky, what if we look for
a negative image instead. If we used naturally occuring or systhesized
background radiation, couldn't we passively look for holes at ground
sites? In other words, look for the absence of radiation rather than
it's presence. Track and triangulate on holes rather than positive
returns.
Also, if our background radiation source is broad, could we also
determine molecular composition of a target through the methods used in
spectroscopy?

**ANSWER: **

In principle you could do something like you suggest. But let me point
out a few difficulties:

- Background radiation is relatively weak and difficult to
receive reliably.
- Background radiation is a whole spectrum of wavelengths,
some of which would go through, some of which would diffract
efficiently around the aircraft.
- Because it is a whole spectrum, your detector would have
scan frequencies or lock in on one you like, which would further
enormously reduce the intensity.
- The radiation comes from all directions so you would need
very tight directional detection, again greatly reducing the already
tiny intensity.

Overall, it is not
practical.

**QUESTION: **

when you walk, do you do any work? The force I believe is perpendicular
to the motion (which means no work), but why do you move forward?

**ANSWER: **

I have previously
answered this question.

**QUESTION: **

How long will carbon dioxide take to disperse in a closed container
because of the Brownian effect? How does the Brownian effect work?

**ANSWER: **

Brownian motion refers to
particles suspended, not to other gases or liquids. The carbon dioxide
will diffuse into the rest of the gas. The rate of diffusion and the
time it takes depends on many things that you have not given
information about like temperature, volume, pressure, *etc*.

**QUESTION: **

according to Einstein's special theory of relativity the rate of time's
progression for any body is contingent upon its speed. Is it posssible
to express the rate of times's progression for a body without relating
it to other rates of progression (greater or less than another by some
factor)? is there some variable, indepedent of time, to which a rate
could be expressed with respect?

**ANSWER: **

In any frame of
reference, a clock runs at exactly the rate you would expect it to if
you are in that frame. All other clocks run slower than yours if not at
rest in your frame.

**QUESTION: **

There are two objects equal in mass and size and shape... identical
blocks of wood for example.
They are on a horizontal plane with no friction.
The first object moves at 10 mph and collides with the second which is
at rest.
The two masses merge together (unlike billiard balls,where one stops
and the other moves on), and continue as one mass.
How fast will the two be travelling after the collision?
It seems like it should be half of the speed of the original object,
but i was told by a physics instructor that it would be more like 90
percent of the speed of the original object, allowing an arbitrary 10
percent for heat loss in collision.
But, doesnt the first object give up some of its speed to the mass of
the second object, so that both now move with the same energy at a
lower speed?

**ANSWER: **

Wow, either you
misunderstood your instructor or else he has no business being a
physics instructor. What you describe is called a perfectly inelastic
collision but in any collision where there are no *external*
forces (the only relevant forces here are the forces the two blocks
exert on each other) the linear momentum must be conserved, that is
remain constant. The linear momentum is the mass times the velocity,
and it must be the same before and after the collision. Before the
collision the momentum is *mv*_{1} and afterwards it is *mv*_{2}+*mv*_{2}=2*mv*_{2}.
Therefore, *mv*_{1}=2*mv*_{2 }or *v*_{2}=*v*_{1}/2,
exactly like your intuition told you. What is not conserved is
the energy. Before the collision, *E*_{1}=½*mv*_{1}^{2
}and after the collision, *E*_{2}=½(2*mv*_{2}^{2})=¼*mv*_{1}^{2}.
So, you see, exactly half the energy was lost and most of this will
show up as thermal energy.

**QUESTION: **

Has anyone measured the amount of time it takes for electrons to jump
from one atomic orbital to another? For example, how long does it take
for a stimulated electron in a hydrogen atom to jump from a 99%
probability of being in the 2s orbital to a 99% probability of being in
the 1s orbital? And, when during the transition does the quantum of
energy get emitted?

**ANSWER: **

You could not make this
measurement on a single atom without disturbing the system. The only
way to do this is statistically with a large ensemble atoms and the
information you get is the transition rate or half life.

**QUESTION: **

Since water is incompressible, could a deep-diving "chamber" for an
aquanaut be built by means of a transparent balloon full of water in
which the aquanaut would float suspended without being subject to the
pressure of whatever depth the balloon assumed? This balloon would
submerge, surface and maneuver by means of machinery external to its
surface, controlled (perhaps) via fiber optics links.

**ANSWER: **

The pressure inside the
balloon would increase just like the water on the outside; just because
the volume remains constant does not mean the pressure does not
increase. Imagine a volume of water in a cylinder with a piston on top
and an aquanaut in the water. Now start piling weights on the piston;
the volume stays about the same (nothing is perfectly incompressible)
but the pressure will increase. Same idea.

**QUESTION: **

I am trying to figure out a simple puzzle, which is in my head a bit
confusing. The puzzle is this: If I mount a cannon on the posterior
surface of the earth, that is the rear of the planet as it circles the
sun, pointing the camera perpendicular to the plane tangent to the
surface, that is apparently straight up as seen from an observer on the
ground, and fire the cannon, then the earth should see a tiny increase
in speed equal to the momentum of the cannonball divided by the mass of
the earth. Then, as gravity slows the cannonball eventually to a stop
this increase in speed should be cancelled by the cannonball's pull on
the earth. I suppose I am wrong but this seems to be a zero sum
situation. Then as the cannonball comes back down and slams into the
earth, the original momentum is once again returned to the earth,
effectively once again adding speed to the earth. In all of this there
is an overall net gain in speed imparted to the earth without any mass
being ejected. Since this makes no sense to me I would like to know
where my conceptual error lies.

**ANSWER: **

The cannon fires and
momentum is conserved, that is the momentum of the earth plus the
cannonball are equal and opposite, adding to zero. Note, however, that
energy is not conserved because both the earth and cannonball have
kinetic energy; this energy came from the chemistry in the gunpowder.
During the whole flight of the cannonball momentum is conserved so that
the earth and the cannonball always have equal and opposite momenta. So
when they collide they are both moving, the earth "upwards" and the
cannonball "downwards". They now collide and stick together; momentum
is still conserved, so they must both end up at rest because the total
momentum must remain zero and both must have the same speed which must
be zero. Energy is not conserved since the kinetic energy disappears;
this energy shows up as thermal energy (ball and earth heat up a
little), energy of the sound produced, work it takes to squish the
earth, *etc*.

**QUESTION: **

I've read your answer about a theoretical mirrored room and whether or
not the room would remain lit after turning off the light source. My
wife has this crazy idea that due to light pollution, even if all the
lights in a city were turned off, the glow of the lights would remain
for some period of time. I've explained that the if the bulbs were
turned off, the existing photons of light would be absorbed, reflected
off into space, etc... nearly instantaneously and the entire city would
become dark. She insists that the atmostphere would still have light
bouncing around and would still give off light. She says that this
question won't be put to rest until somebody with serious Physical
knowledge gives a complete answer. Can you tell me wife she's being
silly and doesn't know what shes' talking about?

**ANSWER: **

Certainly energy is
conserved. However light is usually absorbed and then reemitted as
radiation which is outside the visible spectrum. For example, the
greenhouse effect is when visible light is absorbed and reemitted in
the infrared; the infrared does not effectively penetrate out of the
atmosphere so that energy is trapped. But you cannot see it. I agree
with you that visible light will almost instantly dissappear when the
source is extinguished. An exception would be if you had
phosphorescence, the phenomenon behind "glow-in-the-dark" materials,
but the air, clouds, and most of the world is not phosphorescent.

**QUESTION: **

I've read about the wigner effect where exposure to fast neutrons can
store energy in graphite that can later be released as heat. My
question is, if graphite is exposed to neutrons in a "clean"
environment (not contaminated by other radioactive elements) does
exposing the graphite to neutrons make it radioactive too?

**ANSWER: **

This effect is an atomic,
not nuclear phenomenon, where atoms of carbon are displaced from their
previous locations in the crystal lattice. It is essentially what is
called radiation damage and results in such things as electronic
components being ruined by exposure to radiation. There is no
radioactivity associated with it. That is not to say that there is no
radioactivity as a result of neutron activation but I would bet that it
would be vanishingly small because if carbon absorbs a neutron (for
which the probability is very small) it will simply make another stable
isotope of carbon. More exotic reactions could occur but these would be
rare. Neutron absorption by impurities in the carbon could also occur,
but you presumably would have a pretty pure graphite sample.

**QUESTION: **

An elementary problem in Newtonian physics is to show that the theory
predicts simple harmonic motion of a test object falling through the
center of a uniformly dense spherical mass. I've never seen, either in
the context of this problem per se or otherwise, any DIRECT empirical
evidence in support of the Newtonian prediction. Confidence in the
solution appears to be entirely based on observations of motions very
far from the centers or beyond the surfaces of gravitating bodies;
i.e., extrapolations. It seems to me that the oscillation -- or at
least a first approximation thereof -- would not be too difficult to
arrange with a suitably modified Cavendish balance. Has an experiment
like this ever been tried? If not, why not?

**ANSWER: **

And the point of this
experiment would be…? Gravity is one of the best understood of nature's
phenomena and there is really no need to verify each cute little
example which has been dreamed up. The idea of drilling a hole all the
way through the earth will obviously not work not to mention that the
earth is not really a uniform sphere. To do as you suggest is really
hard because the Eötvös experiment is one of the hardest
around to perform with precision (a group of renoun experimentalists at
the University of Washington has been working for years to measure *G*
with great precision this way). The main reason is that gravity is so
weak even for objects of mass of tens of thousands of kilograms which
you might be able to do an experiment with will experience forces so
weak that it might take years for one oscillation to occur. Similar
experiments are much easier with electric charges which are also 1/*r*^{2}
forces.

**QUESTION: **

In a home refrigerator freezer set to 0 degrees F, assuming all the
contents have enough space to give up their heat, will all the contents
eventually end up at 0 degrees F? I'm aware that not everything freezes
(which I read as "becomes solid") at 0 degree F, so some of the freezer
contents could still be liquid or flexible (as in sports gel paks). If
not all the contents go below 0 degree F, why not? And at the other end
of the thermometer, why can I pick up aluminum-wrapped bread just out
of the oven with my bare hand? Is the aluminum not as hot as the oven?
If not, why not? Thank you very much.

**ANSWER: **

In an isolated system,
which we assume the inside of the freezer approximates, everything will
eventually come to thermal equilibrium, that is everything will
eventually have the same temperature. Your other question, about the
foil, I answered
a long time ago.

**QUESTION: **

I am struggling to understand why it is easy to balance a basketball on
your finger when it spins but difficult when it is not spinning. I
consider the motion of the center of the ball, since it moves as though
all its mass is concentrated there and all external forces are applied
there. When the spinning ball tilts slightly so it its axis is at a
slight angle from vertical, gravity applies force at the center of mass
to pull it off your finger. There must be a countering torque when the
ball is spinning to balance the ball on your finger and keep it from
falling. Due to the torque from gravity, the ball precesses so its
center of mass moves in a circle around your finger. Since the center
of mass moves in a circle, there must be a net centripetal force
greater than zero acting on the center of mass of the ball. I believe
this centripital force provides the countering torque to balance the
ball. If the ball was not spinning there would be no countering torque
because the center of mass would not move in this circle.
The problem I have is that I know that the precess angular velocity
(which to my understanding is the angular velocity of the center of
mass of the ball as it moves in this circle) is inversely related to
the angular velocity of the ball. So the faster the ball spins, the
lower the precess angular velocity when it tilts at any angle, and
therefore the lower centripetal force and lower countering torque. This
seems backwards to me because it seems that there should be more
countering torque when the ball spins faster.

**ANSWER: **

The spinning ball has an
angular momentum which is a vector which points along the rotation
axis. I will suppose that this vector points vertically up (which means
that the spin is counterclockwise as seen from above}. The nonspinning
ball has no angular momentum. Now, if the ball starts to fall toward
the left as seen by you there will be a torque about your finger which
points toward you. Newton's second law states that torque is equal to
the time rate of change of the angular momentum, so if the ball is
initially not spinning it has no angular momentum so after a short time
it has a small angular momentum toward you which means that it is
falling to the left; but the torque gets bigger as it falls further so
the falling accelerates. Now, if the ball starts with an angular
momentum it will be changed also by a small amount toward you but since
it already had a lot, its angular momentum vector will change its
direction slightly toward you in a short time; this is precession. So,
you see that a small error in balance leads to falling for the
nonspinning ball but precession for the spinning ball. Now, you simply
keep correcting as precession starts which is easier to correct than if
falling starts.

**QUESTION: **

I have some questions regarding strength of an electromagnet

1) Does the size and the material of the core affect the strength of an
electromagnet?

2) Does the thickness of the coil affect the strength?

3) The electromagnets I've seen so far had only one layer of coils
wrapped around them. Would the electromagnets become stronger if I warp
a multiple layer of coils around them?

**ANSWER: **

- The field is proportional to the current around the core
and the number of turns per unit length. Therefore the strength is not
greater but there is more of it over a larger area. However, the
material certainly matters and a ferromagnetic material, usually iron,
works best.
- Answer 1 covers this.
- Again, answer 1 covers this because if you wrap two layers
around you are essentially doubling the current.

**QUESTION: **

What causes gravity? How can gravity be explained?
General Relativity, as I understand it, says that gravity is not a
force or interaction. Rather that spacetime is "curved" by the presence
of mass, and that this curve "tells" other matter ( a test mass?) how
to behave. Have I got that right? But the question remains does it not?
Accepting what GR says is one thing, but in reality the real question
is why or how does mass cause spacetime curvature? Am I thinking
correctly here? I teach astronomy at a local school, and some of those
kids come up with some tough (for me) questions.

**ANSWER: **

General relativity starts
with a simple premise, the equivalence principle: there is no
experiment you can perform which can distinguish whether you are in a
gravitational field or in an accelerating frame of reference. For
example, if you were in an elevator which was accelerating and a beam
of light entered through the side it would follow a curved trajectory
to the opposite wall; this is exactly what would happen if you were
sitting still in a gravitational field. This principle, coupled with
the principle of special relativity (the laws of physics are the same
in any inertial frame of reference) leads to the general principle of
relativity, the laws of physics are the same in any frame of reference.
One implication of this theory is that mass deforms spacetime which is,
as you state, how gravity works; mass deforming spacetime is simply a
consequence of the postulates of the theory. Is it the last word?
Probably not because gravity has not been reconciled with quantum
theory and the quest for a theory of quantum gravity is one of the holy
grails of physics. I would not say that gravity is not a force just
because we understand the mechanism for that force. Asking "why or how"
mass causes the curvature is essentially equivalent to asking what is
mass, why do objects possess it? The current well-publicized quest for
the Higgs boson is important because this is the particle which
physicists think is responsible for endowing the elementary particles
of nature with mass.

**QUESTION: **

Are metals more efficient as thermocouples or alloys?

**ANSWER: **

What does efficient mean
in this context? Most sensitive? All common types of thermocouples have
one or both metals being alloys.

**QUESTION: **

Two friends are standing on opposite ends of a canoe. The canoe
is initially at rest with respect to the lake. The person on the right
throws a very massive ball to the left, and the person on the left
catches
it. After the ball is caught, the canoe is (ignore friction between the
canoe and the water) moving in what direction?
A.) To the left.
B.) To the right.
C.) Stationary

**ANSWER: **

The linear momentum must
be conserved because there are no external forces on the system (boat,
ball, and two people). Since it starts out at rest it ends up at rest.
During the time the ball is in flight the canoe and passengers must
move in the opposite direction, so they do not end up in the same
place, but still at rest.

**QUESTION: **

Can energy exist only in certain quantities, or can it exist at any
level, but only be realesed at fixed amounts, or neither? If so what is
the minimum amount of energy possible?

**ANSWER: **

For a given system, *e.g*. an
isolated atom, a mass on a spring (harmonic oscillator), or a beam of
light of a given frequency, the energy may only have certain
discretized values. The simplest example, the photon, of which the
light of frequency *f* is composed, must have an energy of only *hf
*where *h* is Planck's constant. Therefore the energy of
a beam of that light may only have a total energy of some integer times
*hf*. However, there is no constraint on what the frequency
can be and so there is no constraint which says that the energy of a
beam of light must be discretized. Similarly, the energies of a
harmonic oscilator of a particular mass on a particular spring are
quantized; however, there is no constraint on the value which the
spring constant can have, so energy itself is not constrained to only
discrete values.

**QUESTION: **

I have a problem with making a contraconcave mirror. Please refer to
these links if my question is somewhat incomprehensible...I seem to be
having a hard time wording this question...

http://ec.hku.hk/schoolscience/Volumes/Vol_3/SSHK_Vol_3_03.pdf

http://www.wfu.edu/physics/demolabs/demos/6/6a/6A2035.html

http://www.i-am-bored.com/bored_link.cfm?link_id=17162

Anyways, it seems fairly simple enough to make this, however, I am
facing two major problems. These are:

1. How can one find out the focal length of any given concave mirror?
Is there a formula defined for this?

2. How would the size of the hole in the top mirror affect the mirage
produced? If the hole has to be of some exact size, how can one find
out what size should it be when making a contraconcave mirror?

**ANSWER: **

If it were a spherical mirror, the
focal point would be half the radius of curvature of the mirror. In the
case of a parabolic mirror, the focus is at the focus of the
paraboloid. However, It is realatively easy to directly measure the
focal length by focusing a distant object (the sun is good) to a point;
be careful, though, since the focused sunlight can burn what it is
focused on. The hole does not effect the quality of the image because
the mirror uses all points on its surface to form the image. Cutting a
hole anywhere will slightly reduce the brightness of the image, not its
quality.

**QUESTION: **

I work in an industrial plant and we have air diffusers which are round
and have small holes punched in them in a regular pattern. So think of
it as a tube about 2 feet in diameter standing on end. The small holes
(.125 inch or so) are regularly spaced about .375 inch or so apart.
When you stand back from the diffuser you see a pattern that changes
depending on your orientation to the diffuser, you see a pattern of
much larger light and dark areas that seem to match the pattern of
holes in the diffuser (tube) the patterm remains the same, but the size
of the pattern will change with distance from the object.
I've also seen this same effect when I lay one material with a pattern
on top of identical piece of material with the same pattern that is
back lit, as you change the orientation relative to each other you see
the pattern seem to shift and expand in size.
Is this just a complicated version of the interference pattern from the
famous 2 slit experiment that proves that light has the properties of
both a wave and a particle?

**ANSWER: **

I believe what you are seeing is a
moiré pattern which is what you see when you superimpose two or
more patterns on top of each other. It is a type of interference on a
macroscopic scale, that is, it is not the light which is interfering
but the patterns themselves. An example is shown at the right. The
fabric satin is pretty because of this kind of effect. You can download some software
where you can play around making your own moiré patterns. I
guess that I am a little surprised that you can actually see this in
this circumstance since I would expect that you would not be able to
see the air from the holes as being distinct from the ambient air;
maybe it is a different temperature, or contains a little dust, or…?
Have you tried to photograph it? I would be interested.

**QUESTION: **

I teach 5th grade science, and I desperately need a fifth grade answer
to this question. I have wonderful bright students who ask excellent
questions and I stuggle to answer accurately without completely
overwhelming them.
"If light is electromagnetic waves caused by the vibrations of atoms or
electrons, and if a vacuum is defined as the absence of all matter;
then how can light travel in a vacuum?"

**ANSWER: **

Imagine two magnets in a vacuum. Do
they exert forces on each other? The answer is yes as you could prove
in your classroom if you have a bell jar to create a vacuum in. What
about electric forces? Think about an atom: the nucleus exerts a force
on the electrons even though there is a vacuum between the nucleus and
electrons. So, both electric and magnetic forces can be transmitted
through a vacuum. Physicists often express the presence of forces
experienced at some point in space by the existence of something we
call a field. If a magnet feels a force it is because it is in a
magnetic field; if an electric charge experiences a force, it is
because it is in an electric field. Hence, fields can exist in a
vacuum. An electromagnetic (EM) wave (like light, radio waves,
microwaves, x-rays, *etc*.) is composed of electric and magnetic
fields which are oscillating and move through space with a speed of
186,000 miles/second. A picture of an EM wave is shown above. Think of
this as a snapshot; a little later the whole thing will have moved to
the right. This is why EM waves have no trouble propogating through a
vacuum.

**Extra material for the teacher if you think the kids can
get it:**

If there are fields in a wave, then where are the charges and magnets
which cause fields? It turns out that if a magnetic field changes it
can cause an electric field (which is how generators work) and if an
electric field changes it can cause a magnetic field (which is how
electromagnets work). Therefore, if you get a wave going (from an atom
or from an antenna), it will *keep itself going* as it propogates.

**QUESTION: **

On a sunny day when a sun angle shadow can be measured, and knowing the
time of day, how would you calculate the latitude for that position?
Also, it you note the sun angle rate of change, dy/dt, can you also
determine the longitude by angular displacement or by linear
translational velocity?
Lastly, if you look at a day/night view of the Earth, the curve appears
sinusoidal with respect to the equator. If that's true, then all sun
angles on the sunny side should also follow a similar curve. That being
said, how would you calculate the longitude/latitude fix of a given sun
angle with respect to some other know point along the sinusoidal path?

**ANSWER: **

In principle, it is simple, just a
problem in three-dimensional geometry; you need to know the two angles
which specify where the sun is in the sky, the angle of tilt of the
earth's axis, and the exact time of year. In practice it is a very
complicated process. Nowadays, you could program a computer to take the
input data and output the latitude, but I have never heard of this
being done since GPS systems make it all so simple. In traditional
celestial navigation you wait until the sun is at its highest point,
measure the angle, and look up your latitude in a table which is
appropriate for the date. Of course, the tables would be in a laptop
these days. I do not understand your second question at all. Your third
question, the "sinusoidal" day/night boundary, refers to an illusion;
the boundary on the globe is a simple circle around the earth and that
which you see on a flat map is an artifact of the projection from the
sphere.

**QUESTION: **

An object in motion has kinetic energy. Energy/mass warps spacetime. So
as you accelerate, let's say an electron, arbitrarily close to the
speed of light (hence its mass/energy increases without bound) ... at
what point does its kinetic energy cause gravitational collapse into a
blackhole? And couldn't two observers in relative motion each argue
with equal validity that its an electron (with respect to its rest
frame) or a blackhole (at 99.999 ... 999% c)?
Would this imply that were I to chase after and catch up to the
electron so that it is now at rest in my reference frame, it somehow
undoes its own blackhole formation before my very own relativistic eyes?

**ANSWER: **

As I have said many times in previous answers I
consider the interpretation of special relativity that mass increases
with speed to be a good qualitative crutch at best. Your question is
one of the best arguments I can think of to support this point of view.
Although there are lots of other reasons to consider an electron as an
impossible candidate for a black hole, how could it both be and not be
one? In its own rest frame the electron would not be a black hole.

**QUESTION: **

The whole of an electron is negatively charged, what stops the particle
blowing itself apart?

**ANSWER: **

Let's look at something else as an
example to put my answer in context. Why does a nucleus, positively
charged, not blow itself apart. Because the strong nuclear force, which
is attractive for protons/neutrons interacting with protons/neutrons,
holds it together. Why does one of the constituent protons not blow
itself apart, being positively charged? Because it is composed of
fractionally charged quarks which interact with each other via gluons
(which is ultimately, the origin of the strong nuclear force. Then why
do not the charged quarks blow themselves apart? Because we regard them
as fundamental, elementary particles which simply are as they are. I
know, that is a very unsatisfying answer, but eventually in science you
get down to a point where, until something better comes along, it is
simply the best answer. An electron, like a quark, is believed to be a
fundamental particle, and is simply indivisible.

**QUESTION: **

Gravity question. If a bowling ball and a tennis ball are dropped from
the same spot they will hit the ground at the same time. So why do I
(bowling ball) get to the bottom of a snow covered hill so much faster
than my daughter (tennis ball)? We are falling aren't we? Aren't the
factors of friction (weight and sliding) balancing with each other?

**ANSWER: **

This is not an easy question. See
my two previous
answers.

**QUESTION: **

Is it possible to describe the motion of a double pendulum as a
function of time alone? If so what would this function look like?

**ANSWER: **

Well, sure but not in terms of
mathematical functions you would be familiar with. Even the simple
pendulum is easily solvable only for small oscillations. The most
useful analytic solutions to such problems involve what are called normal modes;
choosing the initial conditions then determines a superposition of
these modes. However, the most useful solutions are often computer
simulations which are numerical computations of the function which
interests you; this is particularly true for large amplitudes of the
double pendulum which are chaotic.

**QUESTION: **

I was curious, if you plugged in the Rydberg Constant, into einstein's
equation e=mc2, could you get the smallest theoritical mass of a
particle?

**ANSWER: **

Where would you plug it? The
Rydberg constant has the dimensions of 1/length, SI units of m^{-1},
so it is neither an energy nor a mass. Also, why would you think that
there were some generalization here when the quantity is specific to
the hydrogen atom? You are also ripe for a physicist's reprimand:
physics is not about

**QUESTION: **

I was wondering about light falling into a black hole. If gravity is
pulling light in doest this imply that gravity can accelerate things
beyond the speed of light? Or that the force of acceleration of gravity
is faster than the speed of light? Have velocity calculations of the x
rays and other high energy states leaving black holes?
If one were to shine a light beam and an x ray out of a black hole and
the light falls bends back in while the x ray escapes, wouldn't this
mean that the x ray is technically moving faster than light in that
specific state?

**ANSWER: **

When light is acted on by gravity
it does not accelerate like matter does but it does have its energy
changed. Light falling into a black hole gains energy so its wavelength
gets shorter. But all electromagnetic radiation moves with the same
speed in vacuum. And x-rays are no different in this respect. No
radiation, regardless of energy, can escape a black hole. And no
electromagnetiic wave in a vacuum moves with a speed other than 3 x 10^{8}
m/s.

**QUESTION: **

Lets imagine i have a long stick(please continue reading) thats rounded
and as long as the galaxy itself, im holding one side of the stick and
the other side is near me, but the stick is a big halo that outlines
the galaxy, my question is, if i move the side im holding how long will
it take the "move" to reach the other side of the stick, lets say i
give 1 step with my stick, how long will it pass until i see the other
end moving.
I was wondering if that would be faster than the speed of light.
I'm here at earth with a stick as long as 4 years light, can i poke
instantly somebody by moving this imaginary stick.
For the purposes of this the stick wont brake and its light.

**ANSWER: **

The implications of your question
emphasize that it is really unphysical. Suppose we make the halo as
light as possible: I reckon that the number of atoms if the halo is a
single chain of atoms would be about 10^{31} and the mass would
be on the order of 1,000,000 kg. And this would not be very strong
would it? Anyhow, the motion at the other side cannot happen faster
than the speed of light and it would not even come close to the the
speed of light, more like the speed of sound in the halo. I have previously answered a similar
question.

**QUESTION: **

Is there any tangible evidence to Planet X and 2012? If so, why isn't
EVERYONE talking about this now? If this thing actually enters our
solar system, then we're all history. Is that correct?

**ANSWER: **

The first thing that comes up on a
google search is a site devoted to Nostradamus prophesies. Does this
tell you anything about tangible evidence?

**QUESTION: **

if one were to stand on an infinitely large plane and look off into the
distance there would be a horizon. how would one calculate the apparent
vertical distance between the lowest point visible and the horizon?
As an object moves away from a viewer its apparent size becomes smaller
and smaller. If an object were to move away from a viewer at constant
velocity what function would designate its apparent size with respect
to time?

**ANSWER: **

A horizon is the line beyond which
you cannot see the surface. There is no horizon on an infinitely large
plane. An object moving away at constant rate would shrink in apparent
size at a constant rate.

**QUESTION: **

I'm studying Specific Latent Heat at the moment, and I've taken an
interest in Plasma outside of school.
So I came up with a question, that my teacher couldn't answer.
Is there such thing as a Specific Latent Heat Of Plasmarisation? Or
something along those lines?

**ANSWER: **

It takes a certain minimum amount
of energy to ionize an atom. You could therefore define some sort of
specific heat but I have never heard of anybody doing it. One reason
not to do it is that atoms (except hydrogen) can become multiply
ionized so that some of the energy you put in would be used to remove
even more electrons from already ionized ions rather than to atoms not
yet ionized. Melting ice, on the other hand, you use all energy of your
latent specific heat to melt, you can't melt it further.

**QUESTION: **

I have a cylinder which has a piston inside it, 2 inches in diameter.
When the end of the cylinder is unrestricted, (a 2 inch opening) it is
very easy to draw material into the cylinder and to expell it from the
cylinder by moving the pison back and forth. But if the opening of the
cylinder is restricted down to 1/2 in diameter, it becomes much harder
to draw material in and out of the cylinder. What is the physics behind
this?

**ANSWER: **

Bernoulli's equation is ½ρ*v*^{2}+ρ*gh*+*P*=constant.
Here ρ is the density of the fluid, *h* the height above some
reference, and *P* the pressure. In this case *h* is about
the same for fluid inside and outside the piston. The pressure outside
is atmospheric regardless of what happens inside, so the constant is
the same regardless of which opening you use. The half inch opening has
an area 16 times smaller than the 2 inch opening, so the velocity will
be 16 times greater for the same rate of flow. Therefore ½ρ*v*^{2}+*P*_{2"}=½ρ(16*v*)^{2}+*P*_{½"}.
So *P*_{½"}=*P*_{2"}-½(255)ρ*v*^{2
} so the pressure for the smaller opening must be much lower
to move the fluid at the same rate which means you have to pull on the
piston much harder. This analysis neglects things like viscosity,
compressibility, *etc*. but gives a reasonable qualitative
explanation.

**QUESTION: **

I have a question relating to an aircraft in flight.
Since the total mechanical energy of an aircraft in flight is the sum
of it's potential energy and kinetic energy, is the total mechanical
energy of the aircraft derived from the fuel source?
In other words, does the BTU equivalent of the energy expended by the
power plant equate to the total energy of the aircraft?
If not, where does the additional energy come from?

**ANSWER: **

Suppose you suddenly acquired a
tailwind. The kinetic energy of your airplane would increase without
any additional expenditure of fuel. Also, nearly all the fuel you
consume is not used to give energy to the aircraft but rather to make
up for the energy lost to air resistance.

**QUESTION: **

Is there any definitive proof that the rate of radioactive decay of any
isotope is constant over the period of Earth's existance?

**ANSWER: **

The halflife of any particular
radioactive nucleus is determined only by the constants of nature.
There is absolutely no evidence that there has been any change in the
constants of nature over so short a time as the age of the earth.

**QUESTION: **

Is gravity a form of energy?

**ANSWER: **

To create energy you need to do
work and to do work you need to exert a force over a distance. Gravity
is a force so it can do work. For example, drop a ball and it acquires
kinetic energy as it falls because of gravity.

**QUESTION: **

If I have a reservoir filled with water that's 10m deep, 10m long, and
10m wide. And if I have a square hole on the bottom of the reservoir
that is 2mx2m in size. And this square hole extends downwards 1m and
runs under the reservoir 5m then up vertically 10m to exceed the
surface of the reservoir (10m+). What is the initial velocity of the
water at the start of the square hole (at -10m)? Also, will the water
reach the top (10m+)?

**ANSWER: **

I make the following assumptions: the fluid is ideal, *i.e.*
laminar flow, incompressible, no viscosity. Then the operative equation
is Bernoulli's equation, ½ρ*v*^{2}+ρ*gh*+*P*=constant.
Here, the pressure *P* is the same at both the surface of the
reservoir and the surface in the tube so we may use ½*v*^{2}+*gh*=constant;
I will choose *g* to be about 10 m/s^{2} to simplify my
arithmetic. Choose* h=*0* *at the bottom of the tank and
note that the velocity in the 2 m^{2} tube is 25 times the
velocity of the surface of the reservoir. Then ½*v*^{2}+10
x 10=*½(*25v)^{2} and so the speed *v* at the
surface of the reservoir is *v*=0.566 m/s and the speed at the
hole is 14.2 m/s. Now, for your second question, we are interested in
what the heights of the two surfaces are when the velocities of the
surfaces are zero. From the equation ½*v*^{2}+*gh*=constant
you can see that when the velocities are zero the heights must be
equal. The relative heights of the surfaces will depend on the details
of the shape of the tube below the reservoir (your descriptions are a
bit ambiguous). I estimate that the volume below the bottom of the
reservoir is about 31 m^{3} and so 100*h*+31+4*h*=1000,
so *h=*9.32 m. So the fluid will never rise even to the top of
the reservoir.

**QUESTION: **

If you have two tires on a vehicle
and they are the same size and ambient temp, is it possible with the
front tired at 0psi and the back tire at 35psi to achieve 20psi in the
front and 20psi in the rear if you use the 35psi tire to fill the front
0psi tire?

**ANSWER: **

Provided that the volumes start the
same and do not change the final pressure in each will be 17.5 psi.

**QUESTION: **

I found that the photon have zero
rest mass, but when we apply the formula E=m*cc if the rest mass is
zero then the E=0.
Is there another formula to calculate the energy of a photon?. or
E=mc*c only applies to macroscopic objects?

**ANSWER: **

*E=mc*^{2} applies
only to a particle of mass m at rest; a photon has no mass and is never
at rest. The general relation is *E=*√[*m*^{2}*c*^{4}*+p*^{2}*c*^{2}]
where *p* is the momentum. (See an earlier answer for
the definition of relativistic momentum.) So a massless particle has
energy * E=pc*. The energy of a photon is also related to the
frequency *f * of the corresponding electromagnetic wave by *E=hf*
where *h* is Planck's constant.

**QUESTION: **

In a vacuum photons travel at it's
maximum speed. Then why if they travel that fast based on the formula
E=mc*c, why photons don't convert into mass themselves?

**ANSWER: **

A photon is a stable particle and
will not change its identity spontaneously. However, you can induce a
photon to create mass. The most common process is called pair
production; here a photon, when passing close to a nucleus, will
spontaneously turn into an electron and a positron if the photon has
more than twice the electron rest mass energy. A positron is the
antiparticle of the electron and has the same mass and opposite charge.
(See the preceding question for discussion of energy of a photon.)

**QUESTION: ;**

I can not understand how Heisenberg
principle is valid in this case: an EM wave of wavelength L is faling
from direction z on a slit d. The photons have p(z)=h/L. So after the
slit maximum p(x) = p(y) as it was before the slit. So uncertainty in
p(x) is limited to Dp= p(y)-0=h/L. But the slit d can be made as small
as desired thus making Dp.d less then h (sufficient is d<L). What is
wrong here? Or photons just can't go thru apertures smaller than heir
wavelength?

Thank you very much. I am sorry you didnt understand the
question and the fault is mine.
I really commited an error in writing p(x) = p(y) instead p(x)=p(z).
PLEASE TAKE A LOOK AT THIS. I simply mean there is not enough p in the
incident beam to satisfy HUP in the case when its wavelength is smaller
than the slit. (If the photons dont take impluse from the walls.)
Indeed the photons spray after the slit and according HUP
[p(x).d>hbar] the component of the impulse parallel to the slit p(x)
of at least one photon must be greater than hbar/d. But the photons
which are falling have p=hbar/L (L>d wavelength bigger than the
slit).
What they can do after the slit is to turn to 90 degrees PI/2 maximum.
If a photon does so it would have maximum p(x) =p(z)=p=hbar/L Because
the impulse must be preserved p(x) can not be greater than p what it
had in z direction before the slit (e.g p=hbar/L). But this is smaller
than p(x)=hbar/D because L>D.

**ANSWER: **

The problem is that you are
treating a two-dimensional problem as a one-dimensional problem. A
vector may be uncertain with respect to either its magnitude or its
direction but in one dimension only the magnitude can vary. In the case
you describe, the narrower the slit becomes the more uncertain the __direction__
of the photon becomes because of uncertainty in the magnitude of the
x-component of the momentum. However, there is still the constraint
that the total momentum be unchanged, so the maximum value of *p*_{x}
is *p* when the angle with the* z*-axis is 90^{0}.
As the slit approaches zero width, the direction of the momentum
becomes completely uncertain as required by the uncertainty principle.

**QUESTION: **

Does a body in the universe at the
farthest distance away from the earth exert any real or even
theoretical gravitaional or other attractive effect on the earth and
vice versa?

**ANSWER: **

Such force would be so small as to
be unmeasurable

**FOLLOWUP QUESTION:**

Is that the same as non-existent or is it like thediference
between .999 repeating and 1.0?

**ANSWER: **

Theoretically, the force is
inversely proportional to the square of the distance, so the force is
not zero because the distance is not infinite. However, with distances
so vast, we can't really verify this theory by a measurement because of
the smallness of the force. Another way to say this is that the laws of
gravitation have never been really tested for such huge distances. No
good scientist would insist on the correctness of a theory which cannot
be tested.

**QUESTION: **

Compared to the buoyant force of
the atmosphere on a 1-liter helium-filled balloon, the buoyant force of
the atmosphere on a nearby 1-liter solid iron block is considerally
more, considerally less, or the same. My classmante thinks its more
because the baloon would displace more space, but i thought it was the
same because of the buoyant force law?

**ANSWER: **

The buoyant force is determined
only by the displaced air and a liter of iron displaces the same amount
of air as a liter baloon, so both have the same buoyant force on them.
But, the iron has much weight greater than the buoyant force so it
drops; the baloon has has weight less than the buoyant force so it
rises.

**QUESTION: **

A ship anchored at sea is rocked by waves whose crests are
14 m apart. The waves travel at 7 m/s. How often do the wave crests
reach the ship?
Using the formula speed=wavelength x frequency the answer would be .5
seconds. Conceptually it seems the answer should be 2 seconds. Can you
help explain?

**ANSWER: **

This sounds like homework, but you seem to already have
done the work; plus, you have commendably done one of the most
important things in solving a problem which is to ask yourself "does
this answer make sense?" You are confusing frequency and period.
Frequency is the number of crests per second, and 0.5 s^{-1} is
the right answer; check your answer for units, though, which should be
inverse seconds, not seconds. Period is number of seconds per crest,
and 2 s is the right answer. The period is the reciprocal of the
frequency, *T*=1/*f.*

**QUESTION: **

Does background microwave radiation or the higgs field
provide a means of averaging the energy measured coming from different
directions and establish a "special reference frame" that is "at rest"
with the background of space?

**ANSWER: **

First of all, the Higgs field is a hypothesis and never
observed, so let's dispense with that. The microwave background would
appear to present us with a preferred reference frame and, in fact, it
does. However, this is not a violation of the principle of relativity
which demands that the laws of physics are the same in all inertial
frames: the laws of physics are unchanged in a frame in which the
average velocity of the background photons is zero. You could also
argue that a preferred frame is one in which the average background
photon has a velocity of 20 mi/hr toward the North Star. All the
background does is provide a particular inertial frame.

**QUESTION: **

Why is the speed of light, seemingly arbitrarily limited
to 299,792,458 meters per second? More exactly, in being a finite
speed, is there anything particular about a photon that makes it travel
at this speed in a vacuum, and not another speed, faster or slower? It
just strikes me as odd that this has never been explained to me before.
I understand that it simply an observation, but is it explained?

**ANSWER: **

There is absolutely no mystery why the speed of light is a
universal constant. Electromagnetic theory predicts waves with a speed
determined only by the strengths of the electric and magnetic fields in
empty space. An earlier
question spells this out in detail. The fact that Maxwell's
equations (laws of electricity and magnetism) predict this and Einstein
felt strongly that the laws of physics should be the same in all
inertial frames is partly what led him to propose the theory of special
relativity. Incidentally, the speed of light is exactly the number you
quote because the meter is defined as the distance which light in a
vacuum travels in 1/299,792,458 seconds.

**QUESTION: **

If a projectile is shot at high speed from a non-rifled
barrel, from the air into the water at an angle, what path does the
bullet take through the water? Does any projectile experience a
"refraction-like" bending in the water the way a light ray would when
moving into an optically denser medium? This question arose when a
friend and I were discussing the refraction of light from the
perspective of individual photons. I guess the bigger question is: can
a strictly particle-view of light explain refraction?

**ANSWER: **

If you do experiments with particles, you get the wrong
result for refraction, that is if the particle slows down it is
deflected away from, not toward, the normal to the boundary. So,
presumably your bullet would be deflected so as to move more parallel
to the surface. If too large an angle of incidence is used, the bullet
will skip off the surface, "total internal reflection" except it is
really what we would call external reflection in optics. Also, a stream
of particles doesn't partly reflect and partly refract, it is either
one or the other. Nevertheless, you can still get the right answer if,
for photons, you impose the principle of least time: the path taken by
the particle (photon) will be that which minimizes the time of flight.

**QUESTION: **

To my understanding no object can exceed can exceed or
even acheive a velo. If an object starting from rest were to have a
force exterted on it which would cause it to exhibit an acceleration of
30 km/s*s, according to kinematics after 2.7 hours the object should be
traveling at light speed. what would actually happen at this point?
does the inertia of the object become infinitely great? continuing to
exert a force on this object could cause no change in acceleration. for
the action of exterting a force on this object there could be no equal
and opposite reaction. does this not violate newton's first law? does
this not also violate the law of conservation of energy? If the force
exterted on the object over a distance (energy) doesn't go into the
acceleration of the object, where does it go?

**ANSWER: **

(Your first sentence is a little difficult to read; I
assume you are referring to the velocity of light.) You cannot use
classical kinematics to do this problem because it is incorrect for
high speeds. Instead of writing *F=m*[d*v/*d*t*]* *you
must write *F=*d*p/*d*t *where the momentum is defined
as *p=mv*/√[1-(*v*^{2}/*c*^{2})] (__not__
*p=mv*) where *c* is the speed of light. If you now
exert a force of 3x10^{4} N as you propose (for a 1 kg object),
the time to reach speed v is given by *t*=*v*/√[1-(*v*^{2}/*c*^{2})]/3x10^{4}.
So, for example, to reach speed *c*/2, half the speed of light,
it would take, by my calculation, about five and a half years. It would
take infinite time to reach the speed of light. When the speed of the
particle is large, adding energy by doing work increases the energy of
the particle but it changes the speed by almost nothing. (I have always
thought that high energy particle accelerators should be called
energizers, not accelerators!) You might find the answer to an earlier question
interesting regarding why momentum has to be redefined in relativistic
mechanics.

**QUESTION: **

Inertia is a property of mass but is it necc. when moving
a mass from rest to apply force or energy exclusively to overcome
inertia? In other words, when I begin pushing on a boulder, regardless
of friction, won't it remain temporarily motionless in spite of my
effort until I overcome the interia? Can that energy be calculated?

**ANSWER: **

Any force you exert on the boulder will cause the boulder
to accelerate unless other forces on it prevent that. You use the
phrase "regardless of friction". Do you mean there is no friction? If
there is no friction, then that boulder begins accelerating the instant
you begin pushing on it; if the mass is very large and your force is
modest, the acceleration may be small enough for you to think that it
is not accelerating, but it is. However, friction here on earth is
never really zero. Here is what happens when you push on the boulder
(on level ground):

- There is no friction before you begin to push, but when you
start to push a little the (static) friction turns on, the net force is
zero and there is no acceleration.
- As you push harder, so does the friction, so still no
accereration.
- If you aren't strong enough, you will never be able to move
it; for example, maybe the boulder is Mount Everest which you will
never be able to budge.
- But there is a limit to how big friction can get, and if
you are strong enough or the floor is slippery enough eventually it
will accelerate since you will now be pushing with a force bigger than
the frictional force which is trying to slow it down.
- If you stop pushing, the frictional force will cause an
acceleration opposite the motion and it will slow down and stop.
- When it stops, friction dissappears again.

If the boulder does not
move you expend zero energy. If it does, the work you do on the boulder
(your force times the distance you push) is equal to the energy
expended. Don't forget that friction does work too, negative work since
it takes energy away from the boulder.

**QUESTION: **

WHAT MAKES SCIENTISTS THINK THAT THE FUNDAMENTAL PARTICLES
ARE ROUND SHAPED. AS THE STANDAR MODEL SHOW IN ITS GRAPHIC?.
WHAT SHAPE DO THEY REALLY HAVE?

**ANSWER: **

Just because a graphic shows something does not mean it
should be taken literally. Now, what do you mean by shape? Shape of the
mass distribution? the charge distribution? the current distribution?
Physicists measure things called moments which are used to quantify
shapes. For example, an electric dipole moment of a neutral particle
would imply that there was some positive charge on one side of the
particle and an equal amount of negative charge on the other. An
electric quadrupole moment of a charged particle would imply a
football-shaped (positive moment) or doorknob-shaped (negative moment)
charge distribution. The earth is known to have a large monopole moment
(it's mainly a sphere), a modest negative quadrupole moment (bulges at
the equator), and a small octupole moment (somewhat pear-shaped).
Extensive measurements of moments have been made for nuclei but little
is known about elementary particles. We really have no means of
measuring mass moments which is probably what you think about when you
think about the shape of something. It is often assumed, at least for
nuclei, that mass distribution usually follows pretty closely the
charge distribution.

**QUESTION: **

Assume that our sun is not a large gaseous sphere but a
solid of the same mass. It will attract and hold an atmosphere. What
would be the density of the pseudo solar atmosphere at the surface and
how thick would such an atmosphere be? Also, considering the refractive
index of air on earth, how would the refractive index on this pseudo
solar atmosphere vary with altitude?
**ANSWER: **

This is a pretty complicated question and the answer
depends on what assumptions you make in modeling the atmosphere. I will
assume that the density of the atmosphere is independent of temperature
and that the areal density (the mass above a given area of the
"planet") is the same as for the earth. You say that it "will attract
and hold an atmosphere". Hold an atmosphere, yes, but it wouldn't
attract an atmosphere since space is essentially empty so whatever it
has would have to have already been there or to get there somehow. It
is fairly easy to show, given the mass of the sun and its radius, that
the acceleration due to gravity at the surface would be about *g*_{S}=270
m/s^{2} compared to the earth's approximate *g*_{E}=10
m/s^{2}, about 27 times bigger. If we assume the density *ρ*
of the compressible atmosphere is proportional to the pressure *P*,
*ρ=ρ*_{0}*P*/*P*_{0 }where *P*_{0}
and *ρ*_{0 }are the pressure and density respectively at
the surface of the planet, we find that pressure as a function of
height *h* is *P*=*P*_{0}exp[(-*gρ*_{0}/*P*_{0})*h*].
Because the areal mass density is the same as on earth, one may now
show that the pressure and density at the surface are about 27 times
greater than on earth. Similarly, the height at which the density would
drop to some fraction of what it is on the surface would be 27 times
smaller than on earth. The question regarding index of refraction is
too technical for this site and depends on assumptions; clearly, the
index would be larger than for earth's for my model because the gas is
much more dense.

**QUESTION: **

Consider this scenario - there's a room full of mirrors
(for argument's sake let's say all surfaces in the room are 100%
reflective). There is a single light source in the ceiling which is
sending photons bouncing back and forth off the mirrors. If the light
source is switched off one assumes the room will go dark. Why is this
the case though? Why don't the photons already emitted from the light
source continue to be reflected around the room ad infinitum (i.e. why
doesn't the room stay bright)? Why would shutting off the light source
affect photons that have already been emitted?

**ANSWER: **

There is no such thing as a perfect mirror. If there were,
you had better not leave the light on too long since the light will
continue to increase because there is no loss. When you turn it off,
the light would remain bouncing around. Suppose that the mirrors were
99.99% efficient, far better than the best mirror, and the walls were 3
m apart. Then in one millisecond (10^{-3} s=0.001 s), the
intensity of the light would be reduced to about 1/22,000 of its
original intensity! So the real world can impose pretty big constraints
on ideal situations we can dream up.

**QUESTION: **

Why does the front and rear window of my car frost up
during winter while the side windows mostly get a bit moist?

**ANSWER: **

I am not really sure, but I believe that it may be because
the side windows are vertical whereas the front and back are not (but
the back is in SUVs and vans). This allows them to radiate toward the
sky more easily. I know that this is not clear, but I have answered
similar questions three times before and if you read those answers (click here and follow the links as you go) you can
follow my reasoning in my guess to your question.

**QUESTION: **

the speed of light is a constant. If i were in a spaceship
traveling at half the speed of light, one would think that a beam of
light passing by me would appear to me to be moving at half the speed
of light, but since the apparent speed of light is an inependent
constant time would dilate (slow down) for me in order to maintain an
apparent velocity of 300,000 km/s. In essence time has been manipulated
in order to maintain an apparent velocity equal to lights absolute
velocity. From this i conclude that the speed of light is such a
constant that time itself itself will be manipultaed in order to
maintain a constant velocity. I happen to know light travels fastest in
a vacuum and slower through a medium. do you happen to know how this
occurs and why time would not be manipulated (dilated) in order to
prevent light from maintaining a constant velocity?

**ANSWER: **

The constancy of the speed of light results in our having
to rethink our ideas of __both__ time and space, not just time as
you suggest. But that is not really relevant to your main question
concerning the speed of light in a material. The fact that the speed of
light is slower than in a vacuum has nothing to do with relativity. I
have previously answered
a similar question.

**QUESTION: **

Why are some object transparent? Why do some gases have
colour and some don't?

**ANSWER: **

It all depends on the atomic or molecular structure of the
object or gas. Let's take gases as the example. When light shines
through a gas it might interact with the atoms. If the energy of the
light is just right, a photon might be absorbed by an atom and excite
it to an excited state; then, quickly, that excited atom drops back to
the original atom and emits a photon of the same energy as the one
originally absorbed. But the new photon is radiated in a random
direction, so you would see it and the gas would appear to be that
color. For example, if yellow light could be absorbed then the gas
would look yellow in color. But suppose that there were no states in
the atom which could be excited by visible light; then all visible
light would pass right through and the gas would be colorless; we would
say that this gas is transparent.

**QUESTION: **

IF GRAVITY IS NEGLIGIBLE AT THE ATOMIC LEVEL, WHY THE
GRAVITATIONAL FIELD OF A STAR, FORCE LECTRONS TO FUSE WITH PROTONS,
CREATING NEUTRONS?
ISN'T THAT A BIG INFLUENCE OF GRAVITY UPON ATOMS?

**ANSWER: **

When people say that gravity is negligible on the atomic
level, they mean that, for example, the gravitational interaction
between an electron and a proton if negligible compared to their
electrical interaction. When in a sufficiently intense gravitational
field, any object with mass will respond. And any atom experiences
gravity; that is why the earth's atmosphere does not fly out into space.

**QUESTION: **

The speed of light moves @ constant velocity & hence
is not accelerating. This means that dv/dt = 0. This is the speed limit
that nature imposes & nothing can travel any faster.
For there to be an acceleration there must be a change in velocity, so
if I shoot fireworks into the night sky ( say a Roman candle) & at
a later time (dt), I see a flash, hence light. Before the flash
occurred, there is only the core material launched & the light
didn't exist because the explosion hadn't yet occurred.
To me this means the light had an initial velocity = 0. Did the light
not have to accerlate from v = 0 to v = constant? I had a change in
velocity, hence, the light had to accelerate initially?

**ANSWER: **

You say that the light did not exist before the explosion.
That is the key—it is created already having the speed *c*. In
terms of photons, they are created having a speed *c* and are
absorbed by being annihilated without slowing down. In terms of waves,
there is some kind of "antenna" (imagine a charge on a spring) which
has both electric and magnetic fields which are time varying and
propogate with speed *c*. (Imagine that a charge is created (as
in pair production); the electric field from that charge will appear to
an observer a distance * d* away after *t=d/c *seconds* *because
fields propogate with speed *c*.)

**QUESTION: **

Friends and I are discussing: If a ball is perfectly
elastic and it is released over a surface that is also perfectly
elastic, and there are no other sources of friction (like air) and no
other ways for the ball to lose energy, will the ball continue bouncing
forever? Of course these restrictions can never be realized. The
question evolved into: Does gravity alone, independent of any other
pathways of lost energy like friction, contribute to the successive
lower bounces of the ball and the ball's coming to rest? Some are
saying that gravity alone contributes to the successive lower bounces;
I think this cannot be true.

**ANSWER: **

Of course, this is a completely hypothetical question, as
you note. Let me start on a seemingly unrelated topic: some binary star
systems, two stars rotating around each other, are observed to be
gradually losing energy for no apparent reason. In the theory of
general relativity, accelerating masses will radiate energy much as
accelerating electric charges radiate energy in the form of
electromagnetic waves (it is how an antenna works). The gravitational
radiation is usually referred to as gravitational waves. Gravitational
waves have never been directly observed but there is an active program
to try to detect them. If you calculate the energy predicted to be
radiated by the binary stars referred to above you get a very good
match with measured rates, so this provides the best evidence we have
so far for gravitational waves (indirect evidence). Your hypothetical
ball is constantly accelerating and should therefore radiate energy
away and eventually stop bouncing. I don't know how to do the
calculation, but I suspect the time for the ball to lose its energy
would be extremely long (like you would probably notice no measureable
effect in your lifetime or the lifetimes of many generations to come).

**QUESTION: **

1)IF A PHOTON IS ABSORBED BY AN OBJECT, AND THAT OBJECT
EMITS ANOTHER ONE, BOTH PHOTONS WOULD HAVE THE SAME VELOCITY?
2)IF A PHOTON IS ABSORBED BY AN OBJECT AND THAT OBJECT EMITS ANOTHER
ONE IT WOULD STILL BE THE SAME PHOTON, OR WILL IT BE THE SAME PHOTON
WITH A DIFFRENT FRECUENCY?
3) WHEN ARE TWO PHOTONS THE SAME?

**ANSWER: **

It makes no sense to talk about a photon being the "same
photon" in quantum mechanics. If two photons exist in the same quantum
mechanical system, they are identical particles and cannot labeled
because their identity can be mixed, that is a particular photon might
be 10% of photon A and 90% of photon B. Essentially, your questions are
not meaningful in quantum mechanics.

**QUESTION: **

according to the laws of physics, friction does not depend
on surface area. Why then do Formula 1 cars not have narrow tyres and
wheels to save weight?

**ANSWER: **

The so-called "law of physics" is, presumably, *f=mN. *This* *is not a law of
physics, it is an empirical reltaionship which is approximately true
under restricted conditions. Friction is a very complicated thing, not
the simple thing normally presented in elementary physics courses. I
have previously answered your question, so have a look there.

**QUESTION: **

Has anyone ever suggested a place for tachyons in the
Standard Model or any other model of particle physics?

**ANSWER: **

I am not aware of any inclusion in the standard model. It
is apparently of interest in quantum field theory. See the Wikepedia entry on
tachyons.

**QUESTION: **

The speed of light and gravity. Is the speed of light
restricted to the speed at which gravity propergates, if so why? Or is
it the case that both gravity and the speed of light is restricted to
some other cause like say the speed of the expanding universe or
currently where we are in the universe. Further to my previous
question, is the speed restriction on the photon caused at the point of
where it is released from the atom or is it forced on it all the way
along it's journey through space by the fabric of space time itself, or
even both?

**ANSWER: **

The speed of light is a universal constant, it depends
neither on the source nor the receiver nor the "fabric of space." The
speed of gravity has never been measured but is widely assumed to be
equal to the speed of light. See my
earlier answer on this
question.

**QUESTION: **

what is RADAR,end howe did worked

**ANSWER: **

Radar is an acronym and stands for __ __**ra**dio **d**etection
**a**nd **r**anging. The basic idea is that
radio waves are transmitted and when they encounter something they are
reflected. If you then detect these reflected waves you can deduce the
distance of the reflector by the time of travel, the direction toward
the reflector using a directional receiving antenna, and the speed of
the reflector by observing the Doppler effect on the detected waves. I
would urge you to read the Wikepedia
entry on radar.

**QUESTION: **

what determines how long an electron stays in an excited
state?

**ANSWER: **

The lifetime of a state is determined by something called
the matrix element. Essentially this quantity includes the wave
functions of the initial and final states and a mathematical object
(called the transition operator) which describes the type of
transition. Various transitions are allowed for any pair of states
characterized by things called multipolarity like electric dipole,
magnetic quadrupole, * etc*. Hence the decay of one state to
another generally has many lifetimes corresponding to different
multipolarities; one is usually much more probable than all the others,
though, and will be the shortest lifetime. The larger the matrix
element is the shorter the lifetime.

**QUESTION: **

Why does a wave with a short wavelength not diffract as
much as a wave with a longer wavelength.

**ANSWER: **

How do you quantify diffraction? What does "diffract as
much" mean? Suppose we take, as an example, single-slit diffraction:
the longer the wavelength the more spread out is the first maximum in
the diffraction pattern. The equation for the location of the first
minimum is sin*θ=λ*/*W* where *λ *is the wavelength
and *W* is the width of the slit. So the angular width is
approximately 2*λ*/*W. *Since this is proportional to the
wavelength, longer wavelength is more spread out. You can see this at
this site.

**QUESTION: **

Based on the principal of binding energy when we burn
fossil fuels we are reducing the net mass of the earth. So how much
mass has the earth lost from burning fossil fuels (coal, oil, and
natural gas) in the last 100 hundred years.

**ANSWER: **

Assuming that the released energy does not escape from the
earth, the total mass of the earth does not change; this is because of
conservation of energy of an isolated system.

**QUESTION: **

My 8 year old asked me if gravity has the same effect on
water vapor as for everything else. I thought this an interesting
question and wondered about the effect of heat on gases and what about
mass? I thought that mass was not a factor in gravity's effect.

**ANSWER: **

Gravity has exactly the same effect on any object: the
object experiences a force which is proportional to its mass. This
force is called the weight of the object. So, yes, gravity affects
water vapor molecule by molecule. If there were no gravitational force
on water vapor, when water evaporated it would simply fly out into
space and all water would have been long gone by now. By the way, that
is why there is no evident water on the moon—the gravity there is not
strong enough to hold its atmosphere. Keep in mind that weight is
seldom the only force on an object. Consider a dust mote; it appears to
float around weightlessly but it is experiencing forces from the air it
is in which keep it from dropping the same way a bowling ball would.

**QUESTION: **

I want to know what is the force behind electrons in a
moving circuit. I want to know what makes them move. Explain what
potential difference is.

**ANSWER: **

The potential difference between the ends of the wire
causes there to be an electric field inside the wire. This field exerts
a force on the electrons which then move. If there is a potential
difference between two points in space this simply means that a charged
particle between those points will experience a force. Positive charges
will experience a force towards lower potential and electrons will
experience a force towards higher potential. Potential is related to
potential energy of a charge in a field. If the potential energy of a
charge *Q* is *U* then the potential at that point is *V=U*/*Q.*

**QUESTION: **

This is a question about why optical fibers are designed
the way they are. I know that an optical fiber has a center core of
glass with a high index of refraction which carries the light signal.
There is an outer cladding of transparent material around the core
which has a lower index of refraction than the core. The light signal
is confined to the core because it reflects off the interface between
the core and outer cladding due to the difference in index of
refraction. My question is this: why don't they simply use a single
glass fiber with a uniform index of refraction and coat the outside of
the fiber with mirror silvering so that the light signal is confined to
the inside to the fiber by mirror reflection? In other words, why is
the index of refraction interface better for confining the light than a
mirror surface?

**ANSWER: **

The kind of reflection which occurs in fiber optics is
100% efficient, that is no light is lost. It is called total
internal reflection and occurs when a boundary with another medium
with smaller index of refraction is encountered at an angle greater
than the critical
angle. In principle, one could just have a glass fiber in air which
has an index of refraction smaller than glass; the sheathing is just
for uniformity. A mirror, on the other hand, is not very efficient,
maybe only something like 90%. 90% sounds good, but when you think of
the millions of reflections the light undergoes, you quickly end up
with almost nothing—0.9^{1,000,000}≈0.

**QUESTION: **

is it considered possible that space has a structure ,
Iv;e read (popular magazines and science channel) that some physicists
believe that it is like a lattice , foam, or granular fluid and if so
could it flow like a fluid? what do they theorize it might be composed
of ?

**ANSWER: **

You are essentially asking whether space is quantized. I
have previously
answered this question; the answer involves what is called the
Planck length. It is certainly not possible with present knowledge to
prove that space is discretized.

**QUESTION: **

I would like to know what causes a charge at the atomic
level. I know that if you were to have more electrons than protons then
you would have a negative charge. Or even at a more basic level what
causes quarks to have fractions of a charge? What causes an electron to
have a negative charge?

**ANSWER: **

See the answer below.
Electrons and protons have equal but opposite charges. The electron's
charge being negative is a arbitrary; it simply must be opposite that
of the proton.

**QUESTION: **

If electromagnetism is conveyed by photons, why is
electricity considered a flow of electrons? Why isn't it a flow of
photons?

**ANSWER: **

The photon, as you correctly state, is the conveyer of the
force. Electric current, by definintion, is the flow of charge and
photons have no charge. Some signals are conveyed by flow of photons:
when pulses are sent down a fiber optic cable it is light which carries
the information much as electrons do in a copper cable. Come to think
of it, light from a light bulb is a flow of photons.

**QUESTION: **

Hello, I'm a high school student and I have a few
questions which are probably very annoying. For most of these things I
have only been able to get circular or abstract meanings which don't
explain HOW and WHY these things occur. Here's one of them:
1) What is charge actually? (not just when it's said that an atom is
charged because it has more positive/negative protons/neutrons etc.,
but also the charge that forms electric fields. In other words what
exactly are coulombs measuring, and what DOES and electric current
consist of?).
Thankyou!

**ANSWER: **

The problem often is that people don't know what physics
is. In many instances, particularly at the foundations, we are
compelled to be empirical, to simply acknowledge that some things are
because they are. We begin doing physics by looking around at forces in
nature. We feel our own weight, the force the earth exerts on us
because we have mass and, through many experiments and calculations, we
discover that two objects that have mass exert forces on each other.
But we don't really know what mass is, do we? It is a property that
most things in the universe have which allows them to exert and feel
gravitational forces. That may be unsatisfying to you, but sometimes it
is the best science can do. Armed with our experience studying gravity,
maybe we now look around for other kinds of forces in nature. One day
when combing our hair we notice that there seems to be a mysterious
force which attracts our hair to the comb, seemingly having nothing to
do with gravity. We start doing experiments and make a remarkable
discovery—some objects in the universe possess a new property which we
decide to call electric charge which allows them to cause and feel this
new force which we call the electromagnetic interaction. It is a force
much stronger than gravity and may be either attractive like gravity
always is or repulsive; hence we conclude that there are two different
kinds of charge whereas there is only one kind of mass. But what
actually is charge? We really don't know, we simply infer its existence
by observing nature.

**QUESTION: **

ordinarily, in order to find the electrical current
through a conductive medium one can utilize Ohm's equation and simply
divide the electric potential by the overall resistance of the medium
through which the electricity travels, but if one were to attempt to
find the electrical current through a superconductive medium by using
Ohm's law one would have to divide the electric potential by an overall
resiatnce of zero, making the electrical current, In theory, infinite.
I know in actuality this can't be the case. How would one find the
electrical current through a superconductive medium if Ohm's law is not
applicable?

**ANSWER: **

Ohm's law is not really what I would call a law because it
is something only approximately true for only some materials. So,
technically, Ohm's law will not tell exactly what the current is in
anything. In a super conductor imagine you get 10 amperes of current
flowing; it will continue to flow forever dependent on nothing and so
you would have to simply say the "law" is *I*=10 for this
situation. Now go in and increase the current to 20 amperes; now the
"law" is *I*=20. How can you cause a current to flow? Just
momentarily attach to a battery or use a changing magnetic field to
cause an induced current.

**QUESTION: **

I am a high school student, currently having a debate with
my friends about existence of "coldness"
As an active pursuer of philosophy, I was taught that there is no such
thing as "cold" - It is only the absence of heat.
However, as my knowledge extends only so far, I have no confidence nor
proper knowledge to effectively pursue my friends of this simple
concept when the debate turns into a science debate.
So I ask you, if, scientifically, "cold" is merely a word to describe
the absence of heat (or the movement of molecules, for that matter)

**ANSWER: **

Hot, cold, warm, cool, tepid, lukewarm, scalding, icy,…
These are all __qualitative__ words which give us __qualitative__
information about the temperature of something. So, the pertinent
question is: what does temperature measure. In physics, temperature is
a measure of the average kinetic energy per molecule of the object.
(Kinetic energy of a mass *m* with a speed *v* is ½*mv*^{2}.)
This is actually what temperature is for a gas; for a solid it is a
little more complicated but essentially comes down to average energy
per molecule. So, when we say one object is colder than another it does
not mean that it has more of something called coldness as suggested by
your friends; rather it means that it has less internal energy per
molecule, the molecules are jostling around with less speed than
something not so cold. Incidentally, your use of the word heat is
incorrect; but don't feel badly because lots of physicists use it
incorrectly too. Heat (*Q*) should be reserved for energy which is
transferred from one object to another whereas the temperature of
something is determined by its internal energy (*U*). The first
law of thermodynamics is essentially energy conservation. The change in
internal energy of a system equals the heat which flows *into*
the system plus the work *W* done *on* the system, ∆*U*=∆*Q*+*W.*

**QUESTION: **

Some 30 years ago I took an electronics course and there
was an ongoing debate over the amount of time it took from when power
was first applied to a circuit to when it was available throughout the
circuit. Some said it was instantaneous, while others argued the point.
I was never fully sure if what they really meant was "relatively
instantaneous" (as in the speed of light), because for all practical
purposes there would be no effective difference in most circuits. Do
you have an answer?

**ANSWER: **

Hell, I have an answer for anything; I might not be right
though, my wife tells me. When you switch on a light it comes on
instantaneously. Or, does it? As you probably know, the drift speed of
the electrons which flow in the circuit are very small, much smaller
than a millimeter per second. However, that which moves the electrons
is an electric field in the wire and when you turn on the switch, the
field appears in the wire at the speed of light, so it is not really
instantaneous, but since the speed is so large, it is for most
practical purposes. There are other effects which make more noticible
delays. When a current starts flowing in a loop, a magnetic field
starts building up and this changing field causes a back emf around the
circuit which opposes the increase of current; this is Lenz's law.
Another way of saying this is that the self inductance of the circuit
will keep the current from changing too fast. So if you had a simple
circuit with a resistor, a battery, and a switch and you watched the
voltage across the resistor with an oscilloscope when you closed the
switch, you would see a time much longer than the speed-of-light time.

**QUESTION: **

Is there any study or theory to explain the electrical
charge of an electron as a internal way of motion of the electron?

**ANSWER: **

No.

**QUESTION: **

If the rear wheel of a a 3/4 ton car, moving at 10mph,
drove over someone's ankle, would that person be able to get up and
walk away withiout a bruise, a mark or injury of any kind?

**ANSWER: **

I am not a forensic expert, so my opinion should hold no
sway from a legal perspective. This could certainly happen if either
the tire or the ground were soft. Also, if the victim were wearing a
shoe with a relatively strong sole which could support the weight of
the car momentarily.

**QUESTION: **

I did the following experiment:
I parked one car on my driveway. I parked the other car in the garage
but left the garage door WIDE OPEN. Overnight, the temperature dropped
below the dew point. The garage walls are insulated but the ceiling is
not. The garage is not heated.
Result: Frost formed on the windows of the car on the driveway but not
in the garage.
I assume that the temperature inside and outside both cars was the same
overnight so why did frost form on the windows of the car in the
driveway but NOT on the car in the garage?

**ANSWER: **

I have answered similar questions
twice before. There are two
important factors in frost formation at temperatures near the freezing
point, radiation cooling and evaporative cooling. My research has led
me to believe that radiation cooling is more important. If you read my
earlier answers, which are much more exhaustive than this answer, you
will see that all things radiate away energy and that tends to cool
them. However, there are also many things in the environment which are
also radiating energy and this energy will be absorbed by its
neighbors, and so everything will tend to be in thermal equilibrium.
So, look at the car in the garage: it, the walls, and the roof are all
at, say, 34^{0} and radiating but also absorbing so all stays
at 34^{0} and no frost forms. Now look at the car outside: its
environment is at 34^{0} and it is radiating accordingly but it
does not have the walls and roof from which to absorb energy and so it
cools to a lower temperature and frost forms. The second factor is
evaporative cooling. As you probably know, since it takes energy to
evaporate water, evaporation cools; just take a damp rag and twirl it
around and you will see that it gets cold. If there is a breeze which
would hasten evaporation and the car in the garage is sheltered from
the breeze, this would again give the outside car the cooling
advantage. I have noticed this effect even if one car is parked in the
vicinity of a house and the second is not.

**QUESTION: **

two walls stand opposite each other. The length between
them is L. one of the walls is moving toward the other at velocity V a
bird sits on that wall starts to fly back and forth at velocity 2V how
far will the bird travel before it gets crushed (assume the bird has no
dimension and that only when the walls meet will the bird be crushed)

**ANSWER: **

This is a trick question, much easier than it seems. The
walls will smash together at the time *T=L*/*v * and during
that time the bird will fly a distance *S=*2*vT=*2*L. *OK,
I will admit it—I spent some time trying to compute the infinite series
before I figured this out! But it was kind of cool because I was able
to use simple logic to find that the infinite series from n=1 to n=∞ of
(1/3)^{n} is 1/2 which I could not do mathematically because I
am not very good at evaluating infinite series.

**QUESTION: **

Are all coupling constants dimensionless and is this a
strict requirement?

**ANSWER: **

This is mainly a case of semantics. A coupling constant is
something which tells the strength of an interaction; for example,
electric charge could be thought of as a coupling constant for
electrostatics or mass as a coupling constant for gravitational forces.
However, field theorists prefer to work with quantities which do not
depend upon the system of measurement and so coupling constants are
usually defined in such a way that the constant is dimensionless.

**QUESTION: **

Thank you in being available for this type of thing. I
chat at physorg and I learn alot, but there are some cranks who state
things of opinion as fact. Please laugh at this question! A member of
physorg is adament that the neutron is the force carrier for gravity.
Myself and 2 or 3 others are trying to explain why and how that can't
be and why the graviton fits with our current knowledge, but he
continues to claim he is correct. Could you please come up with one
statement of why this is impossible so that I can quote it to him.
There must be a perfectly clear answer that even he has to recognize as
fact, yes?

**ANSWER: **

The current theory of gravity, general relativity,
attributes the gravitational force to geometric effects, the warping of
space-time by the presence of mass. There is no successful theory of
quantum gravity, that is the field has not been successfully quantized
thereby allowing identification of the "force carrier". There is no
such thing as a graviton, it is only a qualitative idea at this time.
So, your nemesis thinks maybe the neutron is the graviton, right? Here
is what is wrong with that:

- To the best of our knowledge, the gravitational force
propogates with the speed of light. The neutron, being a particle with
mass, cannot travel the speed of light. In fact neutrons, having no
charge, are quite difficult to accelerate and are usually relatively
slow in nature.
- The neutron is not a stable particle unless it is bound
inside a nucleus; a free neutron has a lifetime on the order of 15
minutes at which time it will decay into a proton, and electron, and an
antineutrino. This would not be very good for communication of the
gravitational force between, say, the sun and Jupitor would it?
- Forces which have carriers with mass, for example the
strong nuclear interaction with mesons as field quanta, are very short
ranged. Gravity is a long-range interaction like electromagnetism, that
is it falls off like 1/
*r*^{2}. The force carrier for
electromagnetism is the photon which is massless and one would
therefore expect the graviton to be massless.

**QUESTION: **

is energy quantized ?

**ANSWER: **

If a system is bound, its possible energy states are
discrete or quantized. If a system is unbound, its possible energy
states are continuous (not quantized).

**QUESTION: **

Sorry in advance for what may be a overly simple question;
but after watching various lectures on particle physics I was wondering
is there an actual proton, or is a 'proton' now verbal shorthand for
the two up & one down quarks which make up a proton? Or in other
words, after you remove (theoretically of course) the three quarks
which define a proton, is there anything left?

**ANSWER: **

This is just a matter of semantics, isn't it? Would you
say that there is no "actual" hydrogen atom because we know it to be
composed of an electron and a proton?

**QUESTION: **

Are power density and specific power the same thing? I
know power is work per unit time. Seems they would have different
units--power density--power per volume and specific power -power per
unit mass. The same for energy density and specific energy.

**ANSWER: **

I never heard of power density or specific power. It turns
out, according to Wikepedia,
that they are engineering terms and are apparently
synonymous, both meaning power per unit mass. In physics energy density
is energy per unit volume. Specific energy is apparently
energy per unit mass but I have not seen this quantity used in physics
except in the context of specific heat.

**QUESTION: **

Is there (potentially or actually) light in the universe
we cannot or potentially cannot DETECT (or see visually) on our color
spectrum systems? Does all light in the spectrum we know about/see,
travel at the same speed: light speed?

**ANSWER: **

By definition, light is the portion of the electromagnetic
spectrum to which our eyes are sensitive. It is a tiny part of the
whole spectrum which includes also radio waves, ultraviolet radiation,
xrays, gamma rays from nuclei, infrared waves, *etc*. All
electromagnetic radiation travels with the same speed in vacuum.

**QUESTION: **

how law of conservation of energy is not voilated in step
up & step down transformer

**ANSWER: **

Because it is not the law of conservation of voltage. You
may not draw more energy from a transformer than you put in. Since the
power is *VI*, the power input *VI* must equal the power
output *VI*. For example if you have a transformer which has a
step up factor of 10, you may only have a current 1/10 of the current
supplied to the primary. (Your email address is not valid.)

**QUESTION: **

Does a kernel of popped popcorn have the same number of
calories as it had before it was popped? Do not consider that it is
fried in butter, or that tiny particles of the popcorn fly off when it
is popped. My friend suggests that it uses energy (calories!) in the
popping process, I believe it simply is releasing energy it has
received in the heating process, which cause moisture in the kernel to
turn to steam, expanding, and creating the "popping". Do total calories
remain the same before and after?

**ANSWER: **

The first thing we should acknowledge is that what
"cooking" does is change the chemical composition of whatever you are
cooking, and changing the chemistry inevitably changes the caloric
content. That said, let's examine what happens when you "cook" popcorn.
The water inside the kernel becomes superheated and the hull cannot
contain the increased pressure and the kernel explodes. When this
happens the starch contained in the kernel expands rapidly which is
what the popcorn is. The rapid expansion causes cooling which tends to
keep the starch from undergoing a chemical change, and therefore
popping corn is, to a large extent, not really cooking. So, in my
judgment, you are correct: the caloric content is not much changed by
the popping.

**QUESTION: **

Can you please explain electron spin? It does not seem to
fit in with the model I have been taught of a cloud of electrons
'orbiting' a central nucleus.

**ANSWER: **

The earth orbits around the sun. Therefore the earth has
an angular momentum called *orbital* angular momentum. The earth
rotates about its own axis. Therefore the earth has an additional
angular momentum which we could call *spin* angular momuntum. The
spin angular momentum has nothing to do with the orbital angular
momentum.

An electron orbits around the nucleus (or, more sophiscatedly
has a wave function which contains the information about the electron
cloud). The electron has an angular momentum called *orbital*
angular momentum, the information about which is also contained in its
wave function. Like the earth, the electron has an additional *intrinsic*
angular momentum which we call *spin* angular momuntum. It is as
if the electron were spinning on its own axis (although that classical
idea has problems if taken too literally). The spin angular momentum
has nothing to do with the orbital angular momentum (or the electron
cloud).

**QUESTION: **

How to derive E=m.c.c?

**ANSWER: **

You should be able to easily find this in any physics
text. I have outlined the derivation in an
earlier answer. You basically
calculate the amount of work necessary to speed an object of mass *m*
up to a speed *v* and call that the kinetic energy.

**QUESTION: **

For a non-scientific person, what would be an explanation
of the term "array" when used in discussions regarding lasers? (i.e.
medical lasers or ipl)

**ANSWER: **

This simply means a bunch of something. Array usually
implies that they are arranged in an orderly way.

**QUESTION: **

the situation is this you use the elevator in the mall and
you put a weighing scale inside the elevator you measure your weight
and mass due to explain the second law of motion. is there changes in
your weight as you go up as you go down?. if there changes, what is the
reason of it changes. what is the scientific principle of it?

**ANSWER: **

Your mass is a measure of how much matter there is in you.
Being in an accelerating elevator cannot change that. Your weight is
the force which the earth exerts on you. Being in an accelerating
elevator cannot change that. What changes is your apparent weight, how
heavy you feel. You can determine this by looking at a scale on which
you are standing; this scale does not really measure your weight but
rather the force with which you push down on it. If you are
accelerating, Newton's second law says that the net force on you will
not be zero and the only forces on you are the scale (up) and you
weight (down). [Keep in mind that the force the scale exerts up on you
is equal and opposite to the force you exert down on it because of
Newton's third law.] If you are accelerating up (either going up
speeding up or going down slowing down) you will feel heavier. If you
are accelerating down (either going down speeding up or going up
slowing down) you will feel lighter.

**QUESTION: **

How close are scientist to developing a super laser
similar to the weapon used in the death star in star wars or is it even
possible to develop such a weapon. If it is no t possible to make a
laser like that then what is some of the weaknesses of this model and
please explain why it cannot be done if possible.

**ANSWER: **

Nobody is even considering trying to develop such a
weapon. The reason is very simple—we do not have access to the amount
of energy it would take to operate it. If you were to totally blow
apart an earth-sized planet the total energy you would have to supply
is about 10^{32} J; to calculate this, just use the magnitude
of the total gravitational potential energy of a uniform sphere is, 3*GM*^{2}/(5*R).
*Now*, *the death star took about one second to blow up
the planet, so the power had to be 10^{32} W=10^{26}
MW. The entire power output of the US is about 10^{6} MW, about
a million megawatts. So it takes a mere 10^{20} Americas
delivering all their energy in a second to fuel the death star laser.

**QUESTION: **

Eart pulls the yo-yo downward and the yo-yo pulls earth
upward.Which of Newtons laws explains this?

**ANSWER: **

The third.

**QUESTION: **

What happens tp particles at 0K?

**ANSWER: **

It cannot happen, quantum mechanics forbids it. You can
extrapolate from nonzero temperatures and conclude that all the
molecules would be at rest, but you can never really get there because
the Heisenberg uncertainty principle says that you cannot know the
velocity exactly if you have any knowledge at all of the position of
the particles.

**QUESTION: **

If light beams bend in the presence of mass, then, if we
view the entire universe as a pretty large mass, then all light beams
must be bending. That means that 2 light beams departing an object in
different directions might eventually cross each other's path (might
take a few billion years but might happen). Is it possible, therefore,
that, when we look up into the sky, we might be seeing the same object
more than once - as x light-years away in one direction and y
light-years away in another? If we see this object at very different
ages then there might be no way to determine that we are, in fact,
looking at the same thing.

**ANSWER: **

In fact this has been observed many times in an effect
called gravitational lensing. If, between us and a distant galaxy,
there is a very massive and compact object, light passing to the right
and to the left will both be bent, for example. In that case we will
see two images of the same galaxy. More commonly, one just sees blurs
or streaks of light from the source. Some nice images may be seen
here.
Your hypothesis that something could have images at very different
times because of very different path lengths is unlikely since the
intensity of the earlier image would be hugely reduced because of the
much longer distance the light had to travel.

**QUESTION: **

What is the definition of a megarod (pertaining to
radiation)?

**ANSWER: **

I think you must mean megarad. One rad is the amount of
radiation which will deposit 0.01 J of energy in 1 kg of material. So,
you see, a different amount of radiation will be 1 rad for steel than
for human flesh. A megarad would be 10^{6} rad. Incidentally,
the rad is an obsolete unit and radiation doses are now more often
quoted in Grays (Gy) where 1 Gy=100 rad.

**QUESTION: **

Does the orbital velocity of a meteoroid at the Earth's
distance from the Sun (in space) depend upon the eccentricity and size
of the meteoroid stream? Are the speeds of meteors from meteor showers
the result of two vectors: the Earth's orbital velocity and the
meteoroid's orbital velocity?

**ANSWER: **

I really do not understand what the first part of your
question is asking. Certainly the velocity of any object in orbit
around the sun depends on the orbit and where the object is on that
orbit. If we view the velocity of a meteoroid on the earth, then the
velocity we see will be the the velocity of the meteoroid relative to
the sun minus the velocity of the earth with respect to the sun, *v*_{ME}=*v*_{MS}+*v*_{SE}=*v*_{MS}-*v*_{ES}
where, for example, *v*_{MS} is the velocity of
the __M__eteoroid relative to the __E__arth. This ignores the
fact that we also have a velocity due to the earth's rotation about its
axis.

**QUESTION: **

is it possible to prove that there is a mimimum size X and
nothing can be smaller than X ? I seem to recall this may be Planks
constant. A similar analogy is there is a maximum speed ie C and
nothing can go faster than C

**ANSWER: **

You are essentially asking whether space is quantized. I
have previously
answered this question; the answer involves what is called the
Planck length. It is certainly not possible with present knowledge to
prove that space is discretized.

**QUESTION: **

What is gravity at the sub-atomic level

**ANSWER: **

Negligible.

**QUESTION: **

I assume the earth performs work in keeping the moon
within its orbit about the earth, otherwise the moon would just fly off
into space. As it performs work is expends energy.
Further I assume there is a minimum size that something can be as
everything is composed of waves. The smaller something is the smaller
the wave the shorter the wavelength. Wavelength is proportional to the
energy the wave contains. If a wave has infinitely small wavelength
then it has infinite energy within a finite volume and therefore
infinite energy density. As energy density is proportional to an
objects gravity infinite energy density means infinite gravity.
From the above I conclude that gravity does not expand out into space
for an infinite distance as the amount of work done by the earths
gravitational field on a planet billions of light years from earth
would be so small that it would be smaller than the minimum sized
object…is this right?

**ANSWER: **

Consider a book sitting on your desk; since it does not
fly off into space the earth must be doing work on it, right? Wrong.
Just because one object is bound to another does not mean work is being
done on it. So, first examine the moon situation: let's start out
making the approximations that the moon's mass is negligible compared
to the earth's and that the moon's orbit is circular; these are both
approximately true. Then, since the moon's velocity is always
perpendicular to the gravitational force it feels, no work is done.
Hence, to an excellent approximation, the earth does no work on the
moon. Now the more general case: If the moon's orbit is such that the
moon is getting closer to the earth, the earth is doing positive work
on the moon and if the moon is getting farther away, the earth is doing
negative work. But, the moon exerts a gravitational force on the earth
which is exactly the same magnitude as the force which the earth exerts
on the moon but in the opposite direction (Newton's third law);
therefore the moon is always doing work on the earth which is just the
negative of the work which the earth does on the moon, so the net work
done by the earth-moon system is zero, that is the total energy of the
system does not change.

Your statements regarding wavelengths of particles are
incorrect. A bowling ball going 100 mi/hr has a much shorter wavelength
than an electron going the same speed. Wavelength is not determined by
size of the particle.

I have no idea what you are trying to say about infinite
gravity etc., but it probably doesn't matter because it seems to be
based on your ideas of wavelength.

**QUESTION: **

If you are using a laser to cool an atom, the momentum of
a collection of photons is used to in a way counteract that of the
atom. So if you have an atom moving towards the right, it hits a photon
traveling towards the left, tuned to the resonance frequency of that
atom and hence is more likely to be absorbed. The tiny amount of
momentum that the photon has is transferred to the atom in the opposite
direction to the direction of travel and hence slows the atom down.
However what i would like to know, is that once the atom has absorbed
the photon, it cannot stay in that excited state forever, so surely
eventually it must emit another photon in a direction which is totally
random i believe. As the photon is emitted will it not give the atom a
slight kick in another direction? Considering the direction of emission
is totally random i would like to know why laser cooling is still so
effective at cooling atoms.

**ANSWER: **

A thousand small kicks opposite the direction the atom is
moving will make a significant change in the speed of the atom. A
thousand small kicks in random directions will average out to just
about zero change in the speed of the atom.

**QUESTION: **

Is gravity a byproduct of electromagnetism or somehow
related to it.

**ANSWER: **

Nobody has ever successfully unified electromagnetism and
gravity; there is no known relation between the two. Interestingly,
Einstein, after completing the theory of general relativity (which is
our best theory of gravity) in 1916, spent the rest of his life (he
died in 1955) trying to develop a unified field theory which would
unite the two forces but with no success.

**QUESTION: **

Hello, I would like to know how much time passes on earth,
doing one light year. The reason I'm asking this question, years ago, I
read an article about traveling to the Andromeda Galaxy from earth at
the speed of light and return. The article said the earth would 300
million years older when you return. I seen other articles on the
internet suggesting 2, 4, and even 20 million year would pass. So what
would be the correct time passage on earth? Could you also tell me in
layman terms, how you came up with the anwer, Thanks!

**ANSWER: **

For starters, your terminology needs some touching up: a
light year is a distance, not a time; it is the distance light will
travel in one year. Second, no material object may go the speed of
light, so your question technically has no answer. Now, Andromena
galaxy is about 2.5 million light years from earth. Now, let's assume
that the spaceship is going 0.99999 the speed of light. Then from
earth's perspective it will take almost exactly 5 million years for the
round trip so the earth will be that much older. The ship, however,
will see the distance to be only 2.5√(1-.99999^{2})=0.011
million light years=11,000 light years so the time for the trip as
measured by clocks on the ship would be about 22,000 years.

**QUESTION: **

If you had 2 trains traveling side by side Train A. at top
speed and Tran B. at half of that speed. As the two trains are
traveling along Train B. is ahead of Train A. but as Ta is about to
pass Tb at the exact moment they are exactly side by side lightning
strikes 1000meters ahead of them. Considering the fact that time slows
down the faster you travel, which Train driver would see the lightning
strike first? i believe if it was possibale to measure, the Train
driver travelling slower (Train B.) would see the light first.
This is similar to einsteins thought experiment.

**ANSWER: **

I believe the key here is length contraction. A train with
speed *v* will measure the distance to the light source not as
1000 m but as *L*=1000√(1-(*v*^{2}/*c*^{2}))
where *c* is the speed of light. He will see the light approach
him with speed *c* regardless of what *v* is (the basic
postulate of special relativity) and, while the light approaches him he
is approaching to meet it. So, calling *t* the time (measured by
the train) until the light is seen, we can write *ct=L-vt*. Doing
a little algebra, you will find that *t*=(1000/c)√[(*c-v*)/(*c+v*)].
Note that the larger *v* is, the smaller *t* is; so, as
measured by the clocks on the trains, the faster train sees the light
first.

**QUESTION: **

Please explain why a magnet does not drop straight through
a copper tube.

**ANSWER: **

The magnetic field of the magnet moves with it so the
magnetic field experienced by the copper is changing with time as the
magnet drops. However,
Faraday's Law states that a time varying magnetic field will induce
an electric field and this electric field will cause an electric
current to flow in the copper. This electric current will have an
associated magnetic field which will exert force on the magnet.

**QUESTION: **

Does gravity cause an elrctron to orbit

**ANSWER: **

No. The orbit is caused by the electric force. Gravity is
totally negligible on the atomic level. I have previously answered a similar question.

**QUESTION: **

how does the magnatism of the sun and the magnatism of the
earth affect the earths orbit ?

**ANSWER: **

In no measurable way. Magnetism is totally negligible here.

**QUESTION: **

does Atmospheric pressure effect ones weight on a plant.

**ANSWER: **

The atmosphere does not affect weight since weight is the
force of attraction to the earth. However, one's * apparent*
weight is affected because there is an upward buoyant force which adds
to the weight force to make the weight appear less; for example, a
helium balloon has a greater buoyant force than weight and so it
appears to have negative weight. A more thorough discussion of this may
be seen in an earlier answer.

**QUESTION: **

If an object is traveling east with a decreasing speed the
direction of the objects acceleration is: 1-North 2- south, 3 east. 4-
west? My grandson was given this question in a physics work book the
answer the teacher gave was 4-West. I believe the answer to be 3-east.
I believe the book for H.S. students is trying to give one familiarity
with the definition of acceleration which is a change in velocity and
or direction. Since the object is slowing down (constant speed) it is
accelerating ie its velocity changed ie in the negative. I know that
velocity and acceleration are vectors and that speed is not etc.amI
correct ie it accelerates in the direction it is going east but is
negative. I understand that Physicists do no like to use the word
decceleration.Kindly help since my grandson and I have differing
opinions.The teacher is a biologist who is also teaching physics. There
is no disrespect but simply I want to know since I am quite interested
in this.

**ANSWER: **

What you are saying is incorrect, the teacher's answer is
correct. An object speeding up has an acceleration vector in the
direction of the velocity vector; an object slowing down has an
acceleration vector opposite the direction of the velocity vector. The
negative sign which your argument deduces is correct and means that the
vector representing the change in velocity, which is tells the
direction of the acceleration, is opposite the velocity.

**QUESTION: **

I've used this: "all energy will go from high to low
spontaneously" as a rule-of-thumb definition when explaining events in
the context of the Second Law of Thermodynamics. I haven't found a
shorter or simpler explanation, but now I've been told that my
rule-of-thumb definition is wrong. I don't think it is wrong and the
person who told me it was wrong is not a physicist, but perhaps you
could show me where it is wrong? And, if it is wrong, could you give me
a short and simple rule-of-thumb definition that I could replace it
with?

**ANSWER: **

You have to be careful when you throw around the word
energy. Also, your definition does not state high or low what. If you
mean that "heat cannot spontaneously flow from a material at lower
temperature to a material at higher temperature", then your statement
of the second law is correct.

**QUESTION: **

As a non-scientist doing
primary science teaching - I have a problem and I can't work out the
answer. Doing stuff using a toy car on a ramp, it seems that the
heavier the vehicle, the faster it is going at the bottom and
consequently the farther it goes at the end of the ramp. My gut
reaction is that the heavier vehicles have better axle construction, so
less friction - and it is this not their mass that causes the
difference. I have done maths and know about KE and PE and I cannot see
how the extra mass would in fact increase the velocity, although the
momentum would be greater - am I correct or am I missing something?

**ANSWER: **

Well, this is very
interesting. A recent question was very
similar except that experiment had just the opposite result, the
lighter car went faster! I can only reiterate that, in simplest
physics, with no friction all cars will reach the bottom at the same
time. This is also the result if there is friction but the friction is
proportional to the weight (as in the usual * f=µN* for
sliding friction where * N *is usually proportional to* W*).
So, your gut reaction is right—the result of the experiment must
indicate that the friction of the winner is smaller (relative to the
weight).

**QUESTION: **

A ball rebounds one-half the
height from which it was dropped. The ball is dropping from a height of
160 feet and keeps on bouncing. What is the total vertical distance the
ball will travel from the moment it is dropped to the moment it hits
the floor for the fifth time?

**ANSWER: **

This is really not physics,
it is math. Until it hits the first time it goes 160 ft; until the
second time, 2x(1/2)x160 ft; until the third time 2x(1/4)x160 ft; *etc*.
So the total distance would be
160+2x(1/2)x160+2x(1/4)x160+2x(1/8)x160+2x(1/16)x160=160x[1+2x(1/2+1/4+1/8+1/16)]=460
ft.

**QUESTION: **

I'm wondering about the
distances between subatomic particals and that relationship to their
size. If the subatomic particals of all atoms on the Earth, for
example, were to collapse to the point of actually touching each other,
what would be its diameter?

**ANSWER: **

First of all, subatomic
particles do not have well-defined sizes (they are sort of smeared out
over space) so "touching" each other does not really have a definite
meaning. However, if we suppose the protons and neutrons in a nucleus
are just touching, we can compress the whole earth so that its density
becomes that of nuclear matter (the mass of a typical nucleus divided
by its volume) and see how big it is. The density of nuclear
matter is about 10^{18} kg/m^{3} and the mass of
the earth is about 6x10^{24} kg. So the volume of the earth
compressed to nuclear matter density would be about 6x10^{6} m^{3}.
This would correspond to a radius of about 113 m, pretty small!
Incidentally, this is what happens to a star when a neutron star forms
in stellar evolution.

**QUESTION: **

me and my friend have been
arguing about this for a week and he refuses to accept defeat unless i
get a "credible" source. So here goes: We were talking about mars has
approximately a third of the gravity that earth does, and he said that
is because the ATMOSPHERE is thinner there and it wouldnt be a third if
mars had an atmosphere similar to Earths. This turned into a debate
with him claiming that the atmosphere has everything to do with gravity
and your weight, how do I explain in a way that makes sense that
gravity is entirely about the mass of a planet and not atmosphere? He
says that even if i were right, if the earth all of a sudden had no
atmosphere whatsoever we would all weigh less because there would be
less total mass around our planet. Please help!

**ANSWER: **

You are correct that the
mass of the atmosphere is negligibly small compared to the mass of the
earth, however that is not the reason why gravity at the earth's
surface is independent of what the total mass of the atmosphere is. If
the atmosphere were as dense as lead and 5,000,000 miles thick the
gravitational force of something on the surface of the earth would be
the same as if there were no atmosphere at all. The reason is that for
a spherically symmetric mass distribution^{*}, the
gravitational force is determined only by how mass there is inside of
where you are. One way to convince yourself that this is true is that
if you are at the center of the earth you would experience no weight
because there is just as much mass no matter which direction you look.
Here is one technicality: because the atmosphere is not dense we
normally ignore the buoyant force (although you certainly can't for a
blimp, for example). However, there is a tiny buoyant force which makes
our weight __appear__ to be less (your weight is still the same,
there is just a different force up); hence, your friend is wrong on two
counts since if the atmosphere were less dense as it is on Mars, there
would be a smaller buoyant force so objects would appear to weigh more.

^{*}This means that the density depends only on
how far you are from the center, not on where you are angle-wise; so
everything looks the same at the north pole as at the south pole, for
example.

**QUESTION: **

I would like to know what
impact did Millikan's oil drop experiment have on science during and
before 1920?
Why is the electron charge so important? What is used for?

**ANSWER: **

This is a strange question!
I believe that understanding the world around us in as much detail as
we can is required by the human spirit. If you did not know the
electron charge you could have no atomic physics. Experiments like that
done by J. J. Thompson were able to measure the ratio of the charge to
the mass, but to get either you had to measure one independently which
is what Millikan's experient did. So you could say that knowing the
charge gives you the mass and knowing the mass of something is
important in physics. The electron charge is used, like many other
fundamental constants, for understanding the universe; what could be
more important than that?

**QUESTION: **

Where does the word "moment"
in "moment arm" come from? How do the two terms relate to one another
in analyzing torque?

**ANSWER: **

An alternative word for
torque is moment, so moment arm is the distance from the axis around
which torques (moments) are calculated. The torque is generally written
as the moment arm times the component of the force perpendicular to the
moment arm. A completely equivalent writing of torque is force times
the component of the moment arm perpendicular to the force; I call the
component of the moment arm perpendicular to the force the effective
moment arm.

**QUESTION: **

I am an 8th grade teacher
trying to teach Physics. When I make up word problems for force, am I
always using acceleration due to gravity.
For example: I can say a 15 kg object is being accelerated 9.8m/s^{2},
what is its force?
But can I say a 20 kg object is moved 2m/s^{2} what is its
force?
Are not all force problems using gravity as acceleration?

**ANSWER: **

The basic law is Newton's
second law, *F=ma *which relates the net force *F*
experienced by a particle of mass* m* which has an acceleration *a*.
When a 15 kg object is freely falling the only force on it is its own
weight (assuming no air resistance), so if we measure its acceleration
to be 9.8 m/s^{2} the weight must be 15x9.8 kg m/s^{2}=147
N (newtons)=33 lb. For the object of mass 20 kg which is measured to
have an acceleration of 2 m/s^{2}, the net force on it must be
40 N which is about 9 lb; since its weight is 20x9.8=196 N, there must
be other forces on this object. An object may certainly have an
acceleration different from 9.8 m/s^{2}. For example, a box
sliding across the floor might have an acceleration of magnitude 2 m/s^{2},
that is as each second ticks by the speed gets smaller by 2 m/s so if
it starts with a speed of 10 m/s it takes 5 s to stop. (We usually say
that the accerleration is, in such a case, negative, but the important
thing for 8th graders to understand, I think, is that acceleration
tells you how the speed changes, so you should think of an acceleration
of 9.8 m/s^{2} as 9.8 (m/s)/s so that if you drop something it
has a speed of 9.8 m/s one second later, 19.6 m/s two seconds laterr, *etc*.)
If you are in the US, it would probably be helpful for your students to
know that 1 N=0.225 lb since they probably think in terms of pounds; so
a newton is about a quarter of a pound.

**QUESTION: **

I'm interested in
understanding the interactions between subatomic particles. So I would
like to ask two questions. 1. Is there any thinking or explanation of
how the charges between the electron and proton are so evenly balanced,
despite the large difference in their respective masses? It seems like
there would logically be some underlying similarities that I don't see
discussed very much. 2. If these parcicles are really "smeared" like a
probability function, how can they exist for so long?

**ANSWER: **

Why would the relative
masses have any correlation with the relative electric charges? If
electrons and protons were not of identical charge, the universe would
be a very different place since atoms would not be electrically
neutral. Since the electric force is very strong, the lack of
neutrality of matter would cause there to be no objects as we know them
(the repulsive electric force would tend to keep objects from
coalescing. And, what does a particle being smeared have to do with its
existence?

**QUESTION: **

If two cars approach each
other from opposite directions, each traveling at a speed of 50 km/h,
each car one would perceive the other as approaching at a combined
speed of 50 + 50 = 100 km/h to a very high degree of accuracy.
But two spaceships approaching each other, each traveling at 90% the
speed of light relative to an outside observer, do not perceive each
other as approaching at 90% + 90% = 180% the speed of light; instead
they each perceive the other as approaching at slightly less than 99.5%
the speed of light. Why does this happen?

**ANSWER: **

Of course I cannot give you
a complete explanation since that would require that I do a complete
exposition of the theory of special relativity. Relativity is the
reason. Relativity is based on the postulate that all observers,
regardless or their motion or the motion of a source of light, will
measure exactly the same speed for light in a vacuum. So, if you
measure the speed of some particular beam of light to be *c,*
somebody moving with the speed of 95% the speed of light relative to
you will measure the speed of the beam to be *c* also. One of the
consequences of this postulate is that no object can move faster than
the speed of light relative to any other object. Hence, having two
objects have a relative speed of 180% violates this rule. The speed of
light is a universal speed limit. If you are truly interested, you
should learn the theory of special relativity; it requires only algebra
to understand it.

**QUESTION: **

I have a major question in
my mind and I have not found any website that helps me and so please
help me to answer my question: How is time affected by the amount of
mass? For example: if we put a cart on a slope which is 10.3 g, the
result will be 3 seconds... In addition, if we change the mass into 15
g, there will be an increase of time which will be 7 seconds...
( I have conducted an experiment exactly like the example above, and I
see that the more mass we put on the cart, the longer time we will get)

**ANSWER: **

Simple physics would say
that there should be no difference if there were no friction. Also, if
there were friction and it was proportional to the weight, the times
would be the same. However, if the friction were not proportional to
the weight, for example the lighter car had a frictional force 1/10 the
weight and the heavier car had a frictional force 2/10 the weight of
the car, the heavier car would have a smaller acceleration as you have
found. See earlier answer on this subject.

**QUESTION: **

My 8 year old son would like
to know if an object is moving faster than the speed of light, will it
cast a shadow.

**ANSWER: **

The groundrules of this site
clearly state that I no longer answer questions about going faster than
the speed of light. However, I want to encourage inquiring young minds,
so I will make an exception. No object may go faster than the speed of
light or even as fast as light. The reason is that the theory of
special relativity, which is extraordinarily well-verified
experimentally, shows that the energy required to accelerate an object
to the speed of light is infinite and, of course, there is not an
inifinte amount of energy in the universe.

**QUESTION: **

if you have a car in the air
and you fill the tires to 35 psi, when you put the car on the ground
the psi stays at 35 with the weight of the vehicle on the tires. why?

**ANSWER: **

I have previously answered
this question.

**QUESTION: **

How far would a golf ball
travel on the moon if hit at a 45 degree angle at 200 km/hour?

**ANSWER: **

I first checked and found
that the speed you indicate is far less than the escape velocity on the
moon. I then assume that the height attained and the distance traveled
will be small compared to the size of the moon so that I can assume
that the moon is flat, just as we do when we do such calculations on
earth. The acceleration due to gravity on the moon is about 1.6 m/s
(compared to 9.8 on the earth). Then I find (I presume you just want an
answer, not all the details) the ball will be in the air for about 49
s, travel a distance of about 1930 m, and achieve a height of about 483
m. Since these are very small compared to the radius of the moon, my
assumptions are fine.

**QUESTION: **

Does noise require energy to
happen?

**ANSWER: **

I presume you mean sound
noise. Sound is a wave and sound waves carry energy. Therefore, the
source of the noise must supply energy.

**QUESTION: **

Somewhat technical question,
so I don't know if it breaks the ground rules. I work in MRI and have
had some QM courses a long, long time ago. But this continues to puzzle
me. I don't mind at all looking it up in the QM books if only I knew
what to look under. Could you provide a reference or the correct
"topic" I could read up on? A charged spin-1/2 particle has a
gyromagnetic ratio.
For example, a proton has a QM spin-magnetic moment. When it is placed
in a constant and uniform magnetic field its magentic moment will be at
an angle (about 54.7 degrees) to the direction of the applied uniform
magentic field and it will precess around the direction of this
applied, external field.
The proton will radiate as it precesses in the magnetic field. This can
be detected by pickup coils. For example, this is how an MRI system
works. (But I am interested in a single particle case, not in an
ensemble of particles.)
Question: Where does the energy come from to drive the precession and
the associated radiating process as the particle precesses?
If from the magnetic field, then wouldn't this "drain", say, a
permanent magnet (system of magnets) generateing the magnetic field?
That doesn't seem right (but maybe).... Being in a uniform magentic
field, the gradient of B would be zero. So I guess there wouldn't be
any net translational force on the particle. I think this is because
there would not be any difference in energy between being at p1=(x, y,
z) and being at p2=(x+dx, y+dy, z+dz) so no net force to translate the
particle from p1 to p2. So does the particle just sit there radiating
as it precesses? That doesn't seem right. If it radiates it should be
loosing energy and going into a lower energy state. But there doesn't
seem to be a lower energy state to go into? Or, for every "bit" of
energy radiated it must be getting that amount of energy from someplace
else, but where/how? That is what is confussing to me.
If the magnetic field were not uniform I could see that the particle
would translate into a lower energy state and would convert some of the
potential energy into kinetic energy and radiation energy. But in a
constant uniform magnetic field?

**ANSWER: ** {this
answer is not complete yet, I have to go to a concert!}

Your question is closer to
breaking groundrules for not being concise and well-focused than being
too technical. However, I will answer it because it is interesting. If
you work with MRI, I am afraid I must tell you that you do not really
understand what is going on. If a classical magnetic moment is placed
in a uniform magnetic field it will align with the field. That is what
it wants to do. If it is a quantum mechanical particle (that is it has
a spin angular momentum) it cannot align with the field because the
component of the total angular momentum (which is *J=ħ*√[3/4])
along the field direction may be only ±½*ħ. *That
is where your angle comes from, cos(54.7)=½/√[3/4]. It is not
really correct to say that the proton precesses; it is more correct to
say that it is equally probable to be at any azimuthal angle and so
many texts describe this situation as precession. Go ahead and think of
it as precession, but it certainly does not radiate energy. Note that
the moment is "up", that is 54.7^{0} relative to the field
direction. Its other state, 54.7^{0} relative to the opposite
direction ("down") is at a higher energy because it takes work to take
the "up" aligned moment and turn it to a "down" moment. Let us say that
it takes an energy* E* (which depends on the field strength) to
flip the moment from up to down. In an MRI what happens now is that we
shine in some electromagnetic radiation. If the radiation is of just
the right frequency, that is *f=E/h*, there will be a high
likelihood that the radiation will be absorbed resonantly (hence the
"R" in MRI, magnetic resonance imaging). This absorption is what is
detected in MRI. This is a very simplified overview, but it gives the
basic physics principles. The details of how the whole imaging process
is very much more complicated because of the problem of locating where
the absorption is taking place.

**QUESTION: **

I was wondering if it is
possible you could explain to me the basic facts of how zero point
energy works. If you could explain in most basic form please as I am
not very physics or maths orientated. I have heard it could be used as
a prepulsion method. However I cannot find anywhere an explanation i
can really understand.

**ANSWER: **

The only meaning zero-point
energy has to me is the lowest possible total energy of a quantum
mechanical system. Take, for example, a mass hanging on a spring;
classically the lowest total energy of this system is zero
corresponding to when the system is at rest. However, a simple harmonic
oscillator (which is what a mass on a spring is called) is a classic
problem in quantum mechanics because it is a system which can be solved
analytically. It turns out that it is impossible for the mass to be
exactly at rest, it must have some very small motion and the energy of
the system in its lowest energy state is called the zero-point energy.
The reason you are not aware of it in everyday life is that the motion
is so incredibly small for a macroscopic size mass on a spring that you
could never hope to observe it. On a microscopic scale, however, it is
observable. For example a diatomic molecule may be modeled as two
masses connected by a tiny spring and the lowest state is not with the
molecule at rest. Obviously, this is nothing which you could use for
propulsion.

**QUESTION: **

if an object is falling at a
fixed rate of 500 feet per minute, what g-force will that object
experience upon impact on the earth's surface. If possible include the
formula so other rates could be used, since I would also like to
calculate the g-force for the forward motion at different velocities.
FYI: this is an attempt at calculating the best combination of
conditions for an off-airport landing in un-inviting terrain by an
aircraft experiencing complete power loss.

**QUESTION: **

I fell down the stairs two
years ago and am still wondering what effect the impact might have had
on my brain. I fell head-first from the top to the bottom, and hit the
wall where it meets the small landing at the bottom - with my head. My
body kind of crumpled to my left. I fell 11 steps of normal height,
with my body turning head first, without touching the wall or railing.
The landing at the bottom is about 3 feet from the stairs to a plaster
wall. The impact was at the top of my head. Please let me know the
fall's velocity and force of impact of my head - and if you can, how my
brain would have moved inside my skull after the impact.

**ANSWER: **

Both of these questions are
unanswerable because the force is proportional to the acceleration,
that is the time rate of change of velocity. So knowing the velocity
when an object hits and the fact that it is at rest afterward gives you
the change in velocity but you cannot compute the rate of change of
velocity without a time. So, if an object changes its speed by 500
ft/min =2.54 m/s, its mass is 100 kg, and it stops in 0.5 s, the
average acceleration is 2.54/0.5=5.08 m/s^{2} and the average
force experienced is *ma*=100x5.08=508 N=114 lb. Since the weight
of 100 kg is about 220 lb, the force of the ground must be 114+220=334
lb. So the force you would feel is larger than your weight by
334/220=1.5, so you would feel a 1.5 g-force. This is an example, but
if either of these questioners really wants an answer, more data are
needed.

**QUESTION: **

While working out I was
lifting dumbbells and had the following question...what percent of the
work is gravity doing when I curl a 20kg dumbbell?
For a specific example, here are some numbers that may help…say I have
a 20kg dumbbell and I’m doing curls with one hand. It takes me 5
seconds to raise the dumbbell and 5 seconds to lower it. My arm is
about 35 cm from the elbow to the hand and my elbow remains stationary
during the curl. When I lower the dumbbell it is much easier, so
gravity must be doing some of the work, right?
So what percentage of the work is gravity doing while LOWERING the
dumbbell in relation to the amount of work it takes me to RAISE the
dumbbell? For example, if it takes me 10 Joules of work to curl the
dumbbell and it takes me 5 Joules lower the dumbbell, then is gravity
doing 50% of the work when I lower the dumbbell?

**ANSWER: **

Assume that the dumbbell is
at rest at the bottom, then the top, then the bottom. The work that
gravity does on the way up is 20x9.8x(-0.35)=-68.6 J; work is negative
because the weight (20x9.8 N) is a force down and the vertical distance
(0.35 m) is up. The total work done is zero and so the work you do must
be 68.6 J. On the way down it is just the opposite, you doing negative
work and the weight doing positive work. The total work that you do is
zero as is the work done by gravity. Does this mean you have gotten
nothing from the exercise? Of course not. It is just that asking what
the work done on the dumbbell is is the wrong question. You should ask
a more biological question like how much energy is required by your
body to do this exercise. If you lift it very quickly you will still do
the same amount of work on the dumbbell, but it will require less
energy expenditure from your body than lifting it slowly.

**QUESTION: **

What would happen to an
object if it suddenly became immune to gravit (silly thoiught that idea
is)?
Oddly it would depend what time of day it is. Assuming it's midnight
when this immunitry strikes (ie it is on the outside of the earth's
orbit) it would continue on a tangent to the orbit of the earth while
the earth continues around the sun. I have worked out that the Earth
veers away from that tangential line by over 4,000 km an hour. Is this
right? If so the gravity iummune object would leave the earth's surface
with a huge acceleration. (If it was midday when immunitry struck the
object would suddenly appear to weigh a vast amount more). I realise
that gravity is simple the result of objects following curved space, is
not really a 'force' and so cannot have a anti-force (other than
curving space the other way?!) and that all anti-gravuty devices are
simply using magnetic or electrostatic forces. But this question has
bugged me since reading a book calles The Seach for Zero Point.

**ANSWER: **

Here is the problem with
trying to answer your question: for an object to be "immune" to
gravity, it would have to have zero *gravitational mass*. But for
it to behave as you expect, moving in a straight line with the constant
speed it had at the instant of its immunity, it must obey Newton's
first law which applies only to objects which have *inertial mass*.
However, inertial and gravitational mass are the same thing (a
long-held experimental fact and a cornerstone of general relativity
theory). So, I am afraid that your question would fall into the same
category as questions like "suppose we could go faster than the speed
of light"; it is "suppose an object had inertial but not gravitational
mass", an unphysical situation.

**QUESTION: **

Is there a way of
determining how temperature affects diffusion. For example, say I have
a jar filled with a foul odor and want to lower the temperature to the
point that none of the odor diffuses through the molecular pores in the
jar. Is there an equation or method for determining what the required
temperature would need to be?

**ANSWER: **

This is a quite technical
question. In order to calculate diffusion rate you must know the
diffusion constant. The temperature dependence of the diffusion
constant is
given in Wikepedia and is an exponential function. You can then put
this result into the diffusion
equation and solve. As you can see, this is a complicated problem.

**QUESTION: **

I understand Bohr's idea
about quantum amounts of energy and that a photon is emitted (or
absorbed) when a electron changes energy states. And I have read
several times that this idea explained the spectral lines of a hydorgen
atom. But what I have not been able to find (and has caused me to
bother you with this question) is how this expains the exact wavelength
produced. Related, can you direct me to something that explains how the
speed and/or frequency of an electron that is emitting electromagnetic
wave relates to the wavelength of the light produced. Math equation on
this last one is fine... I am sure the info is "out there" and/or in
one of my texts, but I can't find it.
Hints or help would be appreciated.

**ANSWER: **

The key is to understand the
relationship between the energy (*E*) of a photon and its
frequency (*f*). The photon is the quantum of light emitted when a
transition occurs. This is the famous relationship Einstein discovered
in his theory of the photo electric effect, *E=hf *where *h*
is Planck's constant, *h*=6.62×10^{-34} m^{2}kg/s.
Hence, if an atom makes a transition from a state with energy *E*_{1
}to a state with energy *E*_{2}, the frequency
of the emitted radiation is *f=*(*E*_{1}-*E*_{2})/*h.
*Then the wavelength (l) is just l=*c*/*f *where c is the speed of
light.

There is no well-defined energy
of the electron while it is emitting the photon, so your second
question has no answer. Anyhow, it is probably not a good idea to take
the idea of an electron crusing around in a well-defined orbit
too seriously.

**QUESTION: **

In the Movie "The Core" They
travel to the center of the Earth. Now if you were down there wouldnt
gravity not effect you as much, or what because almost half of the
earth is above you?

**ANSWER: **

The gravitational force is
only caused by mass not outside you. Therefore if you go down to half
the radius of the earth your weight will only be ⅛ of what it is at the
surface. If you get to the center your weight will be zero. You might
be interested in an answer to an earlier question.

**QUESTION: **

If you started with a
lightbulb. Surrounded the lightbulb with a perfect glass sphere, which
was coated on the inside, with a first-surface reflective mirror.
Removed the air from inside creating a vacuum within... and turned the
light on, then off...
In theory, would the light inside the sphere bounce around within the
sphere indefinitely?

**ANSWER: **

I have previously answered this
question.

PS there is no such thing as a perfect vacuum either.

**QUESTION: **

Okay, let's say that the
wind is blowing at a constant velocity of 30 km/hr from the south. If a
person were travelling at the same constant velocity, would that person
feel wind? Since the air around the person is moving exactly as fast as
the person is, would it be safe to say it would be the equivalent of
someone standing still when there is no wind outside?

**ANSWER: **

You are correct, you would
be at rest relative to the air and therefore would feel no wind. An
example of this is a hot air balloon or a helium filled balloon. One of
the problems with using such vehicles to move around is that they can't
be steered, they are totally at the mercy of the winds and go where
they are blown. An airplane can only steer because of the air moving
past its surfaces.

**QUESTION: **

If there were a civilization
on a planet orbiting Alpha Centauri 4.37 light years away, how big
would the diameter of their radio telescope have to be to clearly
receive a TV signal from Earth? I asked the people at SETI the same
question once and never got an answer.

**ANSWER: **

OK, I will take a stab at
this. But, I am not an engineer and do not really know for sure how
much information one must receive to be able to put together a tv
picture. I will assume that, since the wave nature of the radio waves
carries the information, we will need at least one million photons per
cycle of the wave. My thinking is more in line with AM radio waves
where there is one constant frequency of carrier waves and the
information is carried by the amplitude of the wave; I realize that
this is not really what tv is but it should give an order of magnitude
estimate. The typical power of a tv station is about 100 kW=10^{5}
J/s. The energy of a single photon is *hf=*6.6x10^{-34}x10^{8}=6.6x10^{-26}
J/photon so for our power source we have *N*=10^{5}/6.6x10^{-26}=1.5x10^{30}
photons per second. The frequency of a tv station is about 100 MHz= 10^{8}
s^{-1}. To get 10^{6} photons per cycle we therefore
need 10^{6}x10^{8}=10^{14} photons per second.
4.7 ly=4.4x10^{16} m so the intensity (in photons/second/square
meter) at Alpha Centauri will be about 1.5x10^{30}/[4p(4.4x10^{16})^{2}]=6x10^{-5}_{
}photons/s/m^{2}. We therefore need an area of 10^{14}/6x10^{-5}=1.7x10^{18}
m^{2}. That is about an 800,000 mile square. This hinges mainly
on my assumption of needing 10^{6} photons per cycle of the
wave which might be wrong by several orders of magnitude.

**QUESTION: **

Can beef melt? This will
help me settle a long-standing debate with a coworker.

**ANSWER: **

There is no definitive
answer to this question because beef is not a homogenous substance like
iron or water or salt or oxygen or whatever. It is a mélange of
many different things. It has lots of water in it and we wouldn't argue
that water can melt; thaw a frozen steak and the ice in the steak melts
and becomes water. It has fat and we wouldn't argue that fat melts; put
it on a fire and watch the melted fat drip onto the coals. But it also
has lots of organic molecules which, when heated, change their
molecular identity, that is heat causes a chemical change rather than a
phase change (which is what melting or evaporating are). When you cook
something, that is what you do—cause the food to undergo a change into
something different from the uncooked food. So regardless of which side
of this argument you are on, you both win and lose!

**QUESTION: **

an arrow is shot up from the
ground at 30 m/s one second later, another arrow is shot up from the
ground at 40m/s what is their displacement from the ground when they
collide? (This was the most difficult question on a test that i had 2
days ago. The top 5 students of the class all got different answers. My
answer was around 170, i don't remember exactly, i just want to know
the answer.)

**ANSWER: **

I only need the kinematic
equations *y=y*_{0}*+v*_{0}*t-½gt*^{2}
and v*=v*_{0}*-gt *and I use g≈10 m/s^{2}
for calculational ease. First, find out where the first arrow is and
how fast it is going after 1 s. *y*(1)=30x1-5x1^{2}=25 m
and *v*(1)=30-10x1=20 m/s; the purpose of this step is to find
the initial conditions for arrow #1 to use in the next step of the
problem. Now write the *y* equations, choosing *t*=0 when
the second arrow is shot, for each arrow. *y*_{2}*=*40*t-*5*t*^{2}
and *y*_{1}=25+20*t*-5*t*^{2} (we don't
need the *v* equations since we are not asked for any speeds).
Now set *y*_{1}=*y*_{2} and solve for *t*
and find *t*=1.25 s. Put this *t* into either *y*
equation and find *y*=42.2 m. You could go on and write the v
equations to find out the velocity of each when they collide. *v*_{1}(1.25)=20-10x1.25=7.5
m/s and *v*_{2}=40-10x1.25=27.5 m/s.

**QUESTION: **

Take a look at this website:
http://web.jjay.cuny.edu/~acarpi/NSC/3-atoms.htm
It's from CUNY so they
are not exactly cranks. Note in the 3d paragraph they say centrifugal
force keeps the electron from coming into contact with the nucleus. Is
the CUNY website wrong?

**ANSWER: **

This is atrociously poorly
written! Believe me, centrifugal force is not a real force. In even the
most elementary physics course we learn that a force perpendicular to
the velocity (as in an orbiting particle) causes the direction, not the
speed, to change. Hence there is no reason to ask the ridiculous
question of what "keeps the two particles from coming into contact with
each other" since the orbiting particle just orbits. Let me try to
clarify what centrifugal force is. As I have alluded to above, we
easily calculate a circular orbit for a particular force and velocity
using Newton's second law, *F*=*ma*, where *F* is the
electrostatic attraction to the nucleus, *m* is the electron
mass, and *a *is the acceleration where *a=v*^{2}*/r*
for circular motion and* r *is the orbit radius. Now, suppose
that you are standing on the electron; how do you describe the
situation? Well, Newton's laws are not true in an accelerating system
which is the case here. And it is really obvious that they are not
valid because there is only one force and yet, if you are in the
electron's frame of reference, no acceleration. But suppose that you
insist on using Newton's laws to describe your motion; the only way you
can do that is to invent fictious forces to make things work out. In
the case we are discussing the electron is not accelerating and there
is one real force pointing toward the nucleus of some magnitude *F*
(this is referred to as the *centripetal* force, __ center
seeking__ if you know your Latin); but the sum of all forces must be
zero and so you must postulate the existence of a force which has
magnitude *F* and points away from the nucleus (*centrifugal*
force, __center fleeing__ if you know your Latin). That is not
really there but it is often very much to our advantage to force
Newton's laws to be true in accelerating (so called noninertial frames
of reference) for computational reasons. Let me give you a couple of
other examples of fictious forces.

- Suppose you slam your foot on
the accelerator of your car. You feel a force pushing you back in your
seat, right? There is no such force; the only force on you is the seat
back pushing you forward and since you would like to use Newton's first
law your brain perceives there to be a force pushing you back.
- What force makes weather
patterns circulate? Because we are on a rotating earth there is a
fictious force called the coriolis force. Long-range artillery gunners
have to correct for this "force".

I can't imagine what course the
CUNY page was supposed to serve, but probably a physics for artists
kind of course where the students were assumed to be incapable of
understanding Newton's laws or what acceleration is. My own feeling is
that anybody can understand these if motivated.

**QUESTION: **

What is the correct equation
for momentum in Newtonian physics? I thought it was mass X
acceleration. (And I've never understood why it would be mass X
acceleration.) It seems to me it should be mass X velocity. When I
looked up momentum on Wikipedia, it gave the equation: mass X velocity.
(Which makes sense to me.) But I could swear when I was in college the
equation for momentum was mass X acceleration. On the other hand, I
didn't do so well in college physics, so maybe I'm remembering it wrong.

**ANSWER: **

You are right, it is*
p=mv. *The reason that *ma* sticks in your head is that
Newton's second law may be written *F=ma.*
There is another connection: since *a* is the time rate of change
of *v*, d*v*/d*t *(do you know calculus?), Newton's
second law may be written *F*=d*p*/d*t, *that is,
force is the time rate of change of momentum. This is how Newton
originally expressed it and is the way you must express it in special
relativity, that is *F=ma *is not true in special relativity. In
special relativity, though, momentum must be redefined to be *p=mv*/√(1-(*v*^{2}/*c*^{2}))
where *c* is the speed of light. Note that when *v<<c,
p≈mv.*

**QUESTION: **

I don't know very much about
how light works. And for some reason this idea just came to me. if
there was a video camera that took the video with an extremly high
frame-rate would some of the frames be blacked out, or would there be
some picture missing from it because there wasn't any light in it at
the time? So is it possible that light could travel in waves of
particles, much like this: ))))) So everything we see is actually like
a series of pictures with a rediculesly high frame-rate? ( . the dots
are pictures the video camera takes and, ) brackets waves of light
particles and the image that comes with it) could the camera take
pictures between the waves. like this: ).).).).)?

**ANSWER: **

Light may be thought of
either as a wave or as a stream of particles (called photons). However,
it would not be possible to take light which you would otherwise send
into a camera and make a shutter speed high enough to let through zero
photons; there are simply too high a density of photons in a visible
beam of light. However, if you had a very low intensity light ray, you
could arrange it so sometimes the shutter would let through only one
photon, sometimes none. So each frame would have zero or one little
dots on it. If you ran the movie you made at say two frames per second
you would see individual flashes as the photons hit the film; if you
ran it at real time the frames would be too close together for you to
perceive anything but the totality of all the photons, the image of the
original object.

**QUESTION: **

A friend of mine who is an
electrical engineer told me that a prof once told him electrons don't
actually orbit the nucleus of the atom. Is this true? My friend says
there is experimental evidence that sometimes the electron goes right
through the nucleus. We were drinking beer when he told me this, so is
this just BS or is there some truth to it? Lastly, assuming electrons
really do orbit the electron, I believe they move very fast. Do they
move fast enough to gain mass due to relativity? Also I assume the weak
nuclear force has to be pretty strong to keep the electrons from flying
away due to centrifugal force. On the other hand, even a weak battery
can make electrons flow in an electrical current. So how can the
electrons withstand centrifugal force as they orbit the nucleus and yet
move so easily in the flow of electricity?

**ANSWER: **

Part of your question has
been answered earlier.
It is a useful but inaccurate picture to imagine electrons in little
planetary orbits around the nucleus. When scales get as small as atomic
distances the identity of a particle becomes inaccurate and we should
think of particles as being represented by probablility distributions,
that is a mathematical distribution that allows you to predict the
probability of finding the "particle" in some particular small volume.
Therefore it is more accurate to visualize an electron as being a cloud
in the atom, the cloud being more dense where the particle is more
likely to be. This probability distribution extends right into the
nucleus and therefore there is a nonzero (but still very small)
probability of finding the electron inside the nucleus so, indeed, the
electrons do sometimes pass through the nucleus.

Electrons move very fast, but
relativity is only a minor correction. Anyway, I have argued that
you shouldn't think of mass increasing with speed.

The final question is completely
different from the others. A solid is bound together by the clouds of
adjacent atoms interacting and forming bonds. In some materials, which
we call conductors like copper, silver, *etc*., the outer
electrons become essentially free to move around in the material; in
fact these electrons behave pretty much like a gas inside the solid.
When a "weak" battery is connected across such a material, it is like a
fan in a gas and it causes the electrons to drift in the direction from
negative to positive.

**QUESTION: **

How do you go from the fully
relativistic form for Kinetic Energy, to the more well known ke=1/2mv^{2}?

**ANSWER: **

This is a standard
derivation which can be found in nearly any textbook which covers
special relativity. The trick is to do a binomial expansion of the
square root:

KE=*m*_{0}*c*^{2}[(1-b^{2})^{-1/2}-1]≈*m*_{0}*c*^{2}[1-(-½)b^{2}+…-1]≈½*m*_{0}*v*^{2
}where b=*v*/*c* and *c* is the speed
of light. I have used (1+*x*)^{n}≈1+*nx*+… for
small* x*.

I hope this was not a homework
problem since I don't like that and you would have cheated!

**QUESTION: **

Is there any relationship
between a sine wave and the bell shaped curve used in statistics? They
look similar. Is there a reason for this or is it just a coincidence? I
suppose a mathematician could come up with a formula to describe the
relationship. However, would such a formula have any significance? (It
just occurred to me I'm asking the same question twice. If such a
formula lacks significance that implies any relationship between the
two curves is just coincidence.)

**ANSWER: **

You have been looking over
too restricted range if you think that a bell-shaped curve and a
sinesoidal function have similar shapes. To the left is a comparison
between the two. Once you get away from the central maximum of the
bell-shaped curve there is no relationship between the two. There is no
mathematical relationship between the two functions however you could
make a bell-shaped curve by adding an infinite number of sinesoidal
curves with appropriate weights; this is called a fourier transform
representation of a gaussian function (another name for a bell-shaped
curve).

**QUESTION: **

There is a lot of "missing
mass" in the Universe. Galaxies furthest away from us are receeding at
close to light speed (~c) -- and we are receeding from them
(relatively) at ~c. When objects move at close to c their mass
increases. Could galaxies receeding from each other (relatively) at ~c
be gaining extra mass that accounts for the "missing mass" in the
Universe?

**ANSWER: **

First, I always have told
students to not take too seriously the often stated claim that mass
increases with velocity; see the answer to an earlier question to
see my viewpoint on mass. I had a long discussion with a friend who is
an astronomer quite well versed in the theory of general relativity. He
argues that this could not possibly explain dark matter for a number of
rather esoteric and complex reasons which are beyond the scope of this
site. However, there is one simple example which should put the matter
to rest: in our own galaxy where no objects have speeds anywhere near
approaching the speed of light relative to earth, there is a severe
dark matter problem. The orbital velocities of stars around the center
of our galaxy cannot be understood in terms of observable mass in the
galaxy; the similar motions of other galaxies as well as our own are
the best evidence that we do not understand something about celestial
mechanics and the postulation of a mysterious dark matter is one
hypothesis to explain these problems.

**QUESTION: **

is there pure concussive
effect of an explosion in a vacuum

**ANSWER: **

I am not sure what you are
asking. However, concussive means the ability to shake or agitate and
in the case of an explosion would mean the propogation of a pressure
pulse and, of course, that cannot happen in a vacuum. When you see a
space movie and there is the explosion of a Klingon starship, you would
not really be able to hear it even though all space movie directors
seem to think you could.

**QUESTION: **

Would it be possible, with
respect to efficiency, to build a minature electrical generator to
attach to an axle of a car, transfer the electrical energy generated by
the rotating of the axle to a rechargeable battery? This would be done
in order to transfer the stored energy to your home when your car is
parked in your garage. If you had a system set up where you had a plug
that you could connect from your rechargeable batteries in the car to
the input of electricty to your house? This question has been on my
mind since I read about using wind and or hydroelectic power to cut
down on your energy bills.

**ANSWER: **

This is essentially how the
electrical system of your car already works, that is your alternator
recharges your battery so you can always start up your car (or listen
to the radio when the car is not running). If you put a generator on
your car you can't turn it for free, that is you must supply the energy
which you are storing in batteries and so your gas mileage will
plummet. Furthermore, if you are going to carry enough batteries to
make a serious dent in your household needs, the large weight of these
will also cut down your mileage. Since electricity is relatively cheap
and gasoline is relatively expensive, this idea is not a viable one.
You may be interested in an alternative which is one of the ways hybrid
cars work: if you connect your generator to your wheel *only when
you want to brake*, then the kinetic energy of your car will be
converted into electrical energy instead of into heat which is what
conventional brakes do. This energy from braking is used to charge up
the batteries used to run the car in its electric mode.

**QUESTION: **

i really need help with
prooving/finding something. I have no idea how to do it and everyone i
ask has the same problem, but i think it can even be done without
calculus. The question goes as follows: If i have a box on a surface
with coefficient of friction= mu (not given) and i pull the box with a
force T at theta degrees above horizontal, find as a function, at which
angle will i MAXimise the acceleration for any value of mu? (as a
function?). So naturally my first step was to realized what they wanted
and i got:
T(cos[theta]) - ({mu}[mg - Tsin{theta}]) = ma (where m= mass, a =
acceleration etc..) Now i have tryed rearanging it, finding
inequalities and many more things but i just cant find it!! I really
dont know how to do it and i would be so happy if you could show me!

**ANSWER: **

I don't know how to solve
this without calculus, but it could probably be done if you were
clever. Your equation is correct, *T*cos*q* -*mmg*+*mT*sin*q*=*ma. *If
you solve for *a* and then differentiate *a* with respect
to *q* and set the result equal to zero you will find: tan*q=m.*

**QUESTION: **

I have learned that we all
will inhale (at least once in our lives) the very same atoms as our
ancestors from thousands of years ago. If this is true, does this mean
that our bodies atoms are bound to this Earth and remain here
permanently after we die. Does our atmosphere and (or) gravity restrict
our atoms (after death) to the Earth, or can our atoms find their way
off the Earth into space and possibly to other worlds? I ask these
questions for spiritual reasons and out of true scientific curiosity.

**ANSWER: **

Suppose that we assume that
the atmosphere gets completely mixed up by weather patterns after a
relatively short time, say a year; this essentially means that a
molecule here today is equally likely to be anywhere else in the world
in a year. Now, I calculated the volume of the atmosphere assuming it
to be 20 km thick; that would include most of the molecules. Now, I
assumed a typical human breath is about 1 liter; then I find that the
number of lungs full of air there are in the atmosphere is roughly
1.5x10^{21}. Next I roughly estimate the number molecules in
one lung full of air to be about 3x10^{22}. So, if I take one
breath and redistribute the air over the whole atmosphere, I will find
about 20 molecules of that air in any other breath. So, very roughly
speaking, each breath you take will have 20 molecules of the last
breath John Kennedy took before he died. But, we might more likely be
interested in the number of molecules over a lifetime; taking Leonardo
da Vinci, who lived to age 67 as an example, the number of breaths
breathed in his lifetime was about 7x10^{8 }(I assumed about
20 breaths/minute), so every breath you take will contain about 1.4x10^{10}
molecules (that is about 14 billion) that were breathed by da Vinci!
Keep in mind that my calculations are very rough but they should give a
good approximation of orders of magnitude.

Your second question is not
really related. Gravity does a good job of keeping most molecules in
the atmosphere confined to this world. However, there are virtually no
hydrogen molecules or helium atoms in the atmosphere because they have
escaped into space. Helium is recovered as a byproduct of natural gas,
having been confined underground where it cannot escape. The reason for
this is that temperature is a measure of the average kinetic energy of
the molecules and lighter molecules have much higher speeds than say
oxygen or nitrogen at the same temperature. The speeds are large enough
that the fastest have a velocity larger than the escape velocity and
fly off into space. For the same reason, the moon has no atmosphere
because the escape velocity is much lower and all the gas escapes.

**QUESTION: **

I've been wondering for a
while about the effects of fusion on
gravity. Fusion is a process by which lighter elements join to make
heavier elements, releasing large amounts of energy at the expense of
small amounts
of matter. However, concentration of large amounts of matter defines
gravity as a curvature of space.
If matter is lost due to fusion, does the gravity which that matter
represented go away too? Is it redistributed somehow?

**ANSWER: **

Let's imagine a universe
with no mass, just photons. Then I believe that spacetime would be
flat. So, when mass gets smaller spacetime gets less curved. Realize,
however, that the fractional change of mass in a star over its lifetime
never really approaches a large fraction. You should not think of
gravity as being something which is conserved (as implied by your
question "Is it redistributed somehow?"). If there is one mass there is
a gravitational field; if it is made to go away (conserving energy),
the gravity goes away too.

**QUESTION: **

I don't know if this is a
silly question or not, but I can't find it in your old answers (at
least, not in a form that I understand).
There is a lot of "dark matter" in the Universe; and mass increases as
matter moves nearer the speed of light; the galaxies are moving away
from each other at the speed of light.
Therefore, doesn't the mass of the galaxies increase enormously as they
are moving away from each other? Couldn't this account for the missing
mass of the "dark matter"?

**ANSWER: **

For starters, dark matter is
hypothetical and has never been directly observed. The universe is
expanding but the speed of the most distant objects is not the speed of
light, in fact not really close to the speed of light even though they
are moving rapidly, just not that rapidly.

**"CORRECTED"
ANSWER:**

I talked with an astronomer friend and found out that in fact
the most distant objects are moving with a speed quite close to the
speed of light (about 95%). Nevertheless, this cannot be the answer to
the dark matter puzzle for reasons explained in a
similar answer above.

**QUESTION: **

A metal spoon and a wood
spoon have been in boiling soup for a long while. If I take out both
spoons, the metal one will feel hotter. Does the metal spoon in fact
have a greater temperature or is it just a better conductor? I guess my
real question is how can this guy be holding a white hot space shuttle
tile in his bare hand that is 1260 degrees C? Can two objects have
equal temperature where one burns you yet the other does not? http://upload.wikimedia.org/wikipedia/en/thumb/5/5b/TPScube.jpg/300px-TPScube.jpg

**ANSWER: **

It is because the metal is a
better conductor. They both have the same temperature (assuming that
they were both submerged). This is why you never see fire walkers walk
on red-hot metal surfaces. The reason the man can hold the
hot shuttle tile is because it has been heated up locally so that
it is hot where it was heated up but not hot where he is touching it;
this is because the tile is a very poor conductor of heat. In the spoon
example maybe I misunderstood what you meant. If the two spoons are in
the soup with their handles sticking out, the metal handle is hotter
the metal is a better conductor.

**QUESTION: ;**

The reason for this email
it’s because I have a question about the ocean tides here on earth. I
understand that gravity bends time/space based on Albert Einstein’s
theory. My question is: Do the ocean tides follow the path of the space
bent due to the presence of the moon? I'm working on a presentation and
I wanted to talk about this subject and at the same time give a
graphical representation of this phenomenon. For some reason I keep
thinking that this phenomenon can be explain showing the fabric of
space being bent by the two bodies (Earth and Moon) resulting on the
ocean tides in other words, the earth will look oval due to the ocean
waters. The small deformation of space due to the moon's presence will
create an oval looking basket on earth's space forcing the waters to
fallow this shape depending on the moon's position. It’s this some what
correct?

**ANSWER: **

Suppose the oceans were full
of molasses; the tides would be much smaller, probably not perceptable
at all. And yet, the curvature of spacetime would be the same. It is
therefore fallacious to assume that the shape of the ocean reflects the
shape of spacetime. Curvature of spacetime is best visualized by
observing the bending of light by strong gravitational fields. Research
this and "gravitational lensing" for your presentation.

**QUESTION: **

Who was most responsible for
the Grand Unification Theory?

**ANSWER: **

There is no single GUT. Read
the Wikepedia
entry on GUTs.

**QUESTION: **

why does fire burn up? I
mean if you point a match down the falme still goes up, why doesn't
gravity draw the fire to the ground rather than the sky?

**ANSWER: **

I have previously answered
this question.

**QUESTION: **

My question relates to how
icebergs reflect the heat of the sun back out of the atmosphere. I know
that white reflects light, but does it also reflect heat? This is
mysterious to me.
What about a mirror? If the sun shines on a mirror, does the mirror
effectively redirect the light and the heat?
If, in a dark room, I blow hot air onto a white block of ice, will it
reflect away? Are the sun's light and heat one radiation or two?

**ANSWER: **

When we talk about heat we
are talking about energy transfer and that can be accomplished in
several ways thermodynamically. Heat energy from the sun is simply the
infrared portion of the electromagnetic spectrum which is comprised of
light with wavelengths somewhat larger than can be seen by the eye.
When this heat hits a reflective surface it is reflected much the same
a visible light. Blowing hot air, however, is a very different kind of
heat transfer; this is basically forced convection where you move a
volume of hot air to replace a nearby volume of cooler air. It is
essentially meaningless to talk about reflection of this kind of heat
transfer. There are other ways to transfer heat, the most important of
which is conduction; for example, sticking an iron rod into a fire and
waiting until your hand gets burnt.

**QUESTION: **

The situation is a ball
attached to a string like a swing. Apparently, no work is done on the
string, but surely the weight of the ball has a component that is in
the same direction of the motion of the ball, so some work is done on
the string.

**ANSWER: **

In the case of a simple
pendulum the ball is considered to be a point mass and the string to be
massless. If the string is massless you cannot do work on it because it
can acquire neither kinetic nor potential energy. If, however, the
string has mass, work will be done on it by the ball and by its own
weight. In fact, if the string has mass you don't even need a ball at
the end. This is called a physical pendulum, one consisting of things
other than point masses and massless pieces.

**QUESTION: **

The strong nuclear force is
said to have a very short range, owing to the short lifetime of its
carrier particle (at least as I was taught in high school many years
ago). This rang is said to determine the maximum size of an atomic
nucleus, hence this is why Uranium is the heaviest naturally occuring
element; any larger a nucleus and the electromagnetic force would start
to take over and the nucleus would fall apart.
My question is: the above make sense only if the strong force
originates from the centre of the nucleus, but it has always been
explained to me as though all nucleons (even the ones on the edge) can
experience the strong force (the classic demonstration involves magnets
coverred with velcro to show how the replusion is overcome if you get
close enough). So where does the strong force really come from and why
do the outer nucleons 'feel' it to a lesser degree?

**ANSWER: **

It is an oversimplification
to say that nucleus becomes unstable because of the Coulomb force
becoming dominant over the nuclear force. And, it is incorrect to
simply say that in a large nucleus the outer nucleons are "out of
range" of the nuclear force. The nuclear force is the force between
individual nucleons and so each nucleon interacts only with its nearest
neighbors due to the short range of the force. The nucleons on the
surface see only neighbors inside the nucleus and so they are bound to
the nucleus as a whole. Those on the inside see essentially no force
since each sees just as many neighbors in one direction as the opposite
direction and all forces approximately cancel out. In fact the simple
model that the nucleus is an impenetrable sphere (particles move freely
but cannot escape) does a remarkably good job describing nuclear
structure as long as you include the nuclear spin-orbit force which I
will not go into here.

**QUESTION: **

Does the acceleration due to
gravity change between day and night? During the day, the sun would
pull us toward it thus lowering the earth's pull. At night, it would
add to the the earth's pull, increasing gravity. Is this reasonable?

**ANSWER: **

The answer is yes, but the
effect is very small, probably not measurable. I calculate the
acceleration due to gravity at the earth's orbit due to the sun to be
about 6x10^{-3} m/s^{2}. Assuming that *g*=9.8 m/s^{2},
the two values would be 9.806 and 9.794 at the equator, less than 0.1%.
This is small compared to variations in *g* due to the
nonsphericity of the earth, local mass variations, the rotational
motion of the earth and other effects.

**QUESTION: **

I am reading Roger penrose's
The Emperor's New Mind, and on page 301 he says that when two slits are
open the intensity at the brightest part of the screen is 4 times what
it was before, rather than twice, as common sense would predict. I took
that to mean that photons which are subject to positive interference
carry more energy than before they passed thru the slits.

**ANSWER: **

I have previously answered a
similar question.

**QUESTION: **

Regarding radiolysis, I have
read about it in textbooks, but I still have the following questions:
If the body is 80% water, doesn't radiolysis happen alot in diagnositc
radilogy? If yes, why is this not a big concern-or is it?

**ANSWER: **

Radiation can be used to
dissociate water. However, the probabilities are very small. A number
that I could find to give an example is that only about 20 molecules
dissociate for every 100 electron volts of radiation energy deposited.
The energy of a typical xray is like 1000 electron volts so if
completely absorbed could result in 200 destroyed atoms. And, of
course, most xrays are not absorbed. Even if a million of them were,
200,000,000 is a tiny number compared to the number of water molecules
in a thimble full of water.

**QUESTION: **

I'm sorry to bother you but
this is something that has been bothering me for a while and I'd really
appreciate your help. In Feynman's book on QED he cites that the
probability that an electron will couple with a photon squared is 1/137
(or aprox.
.085). He goes on to say that the proton has a 'magnetic moment' of
2.79. Now I assume that these two things are the same, the probability
of and electron/photon coupling and the 'magnetic moment', since
electromagnetic force is carried by photons. Therefore I would expect
the 'at rest charge' of one proton would be greater than that of one
electron in proportion to their coupling amplitudes; because in Feynman
diagrams it is said that the reason particles of like charge repel each
other is because they exchange a photon and the photon momentum knocks
them away from each other; like billard balls. However, when I watched
an online lecture from MIT on electricity and magnetism, the professor
stated that the force between two repulsive electrons and two repulsive
protons was aproximately the same. This is my point of confusion. Why
are they the same?

**ANSWER: **

You have several very
different things jumbled up here.

- First the 1/137 number is
called the fine structure constant and is the number which is used to
characterize the strength of the electromagnetic interaction. It is a
particular combination of physical constants like electron charge,
speed of light, Planck's constant,
*etc*.; see the Wikepedia
entry for fine structure constant to get the exact definition.
- The magnetic moment of the
proton has nothing to do with the fine structure constant. Most
elementary particles look like tiny bar magnets and the magnetic moment
is simply an experimental measurement of the strength of that magnet.
It is dependent on the structure of that particle and reflects what the
density of electric currents is. A simple (overly simple) model would
be that a proton is a charged sphere which is rotating and the rotation
of the charge comprises a current which gives rise to a magnetic field.
- The third statement, I
believe, simply states that the electric charge on a proton is of
opposite sign but identical magnitude as the the charge on an electron
and has nothing to do with the magnetic moments or magnetic forces.

**QUESTION: **

I don't understand Newton's
Third Law. If it is true then surely, for example, it is impossible to
move your hand through a table since the reaction will always equal the
weight.

**ANSWER: **

Newton's third law (N3) says
that if one object exerts a force on another, the other exerts an equal
and opposite force on the one. Many students misunderstand this law as
you demonstrate in your example. Instead of talking about a hand, let
us assume there is a book on the table. Are there any forces on the
book? Yes, there is its own weight straight down (let's call that force
*W*) and maybe the table, which touches the book, also
exerts a force on the book (let's call that force * T*). Since
the book is not accelerating, the total force on it must be zero (that
is Newton's first law, N1) and so *T* must be a force straight up
which is of the same magnitude as *W*. These forces are equal and
opposite because of N3, right? **WRONG, WRONG, WRONG**! These
forces are equal and opposite because of N1 and they have absolutely
nothing to do with N3. They cannot be a N3 pair because both are on the
same body (book) and N3 addresses forces on different bodies. So, what
is the N3 (reaction) force which pairs with the force *T*? Since *T*
is the force *the table exerts on the book*, N3 tells us
that **the book exerts a force down on the table** which has
the same magnitude as *T*. And, what is the N3 (reaction) force
which pairs with the force *W*? Since *W* is the force *the
earth exerts on the book*, N3 tells us that **the book
exerts a force up on the earth** which has the same magnitude as *W*.
That's right, the book exerts a force on the whole earth. N3 can never
cause something not to move because the relevant forces are on
different objects.

**QUESTION: **

In a standard Newton's Rings
experiment, we place a convex lens of large radius over an optocally
plane glass plate. What will be the fringe pattern if the optically
plane glass plate is replaced is replaced by a concave lens, such that
its radius is larger than that of the convex lens?

**ANSWER: **

It will still be a bullseye
pattern but the fringes will be farther apart because the air gap
widens more slowly as you go out.

**QUESTION: **

Why does the refractive
index of a material change with wavelangth?

**ANSWER: **

Basically it is because the
permittivity (e)of a material depends on the frequency of the electric field
it experiences. And the speed of light is proportional to 1/√e. The reason the permittivity depends on
frequency is that the interaction of varying electric fields is mainly
the interaction with electrons bound to atoms. A simple model is to
imagine the electrons bound by tiny springs to atoms. This then becomes
the driven damped oscillator model and the response depends on how
close the frequency is to the natural frequency of the electron on the
spring (resonance).

**QUESTION: **

When a detector is placed at
one of the slits in the double slit experiment with light, is the wave
function collapsed by the observation of people or by the presence of
the detector? (i.e. if a detector was placed at one slit, but no one
actually looked at the results would you still get a interference
pattern?) Also I am not including the actual interference pattern in
the results, only the information given by the detector, the
information of course being which hole the particle went through,

**ANSWER: **

Any measuring device which
determines which slit the photon passes through will destroy the
pattern, it does not require a human to know.

**QUESTION: **

When the leaf has fallen a
certain distance its speed becomes constant, why?

**ANSWER: **

It has to do with air
friction. When an object passes through a fluid like air it experiences
a retarding force. This is how you can feel the wind, for example. This
force depends on the speed of the object; it is easy to convince
yourself of this by putting your hand out the window of a car at low
and high speeds—greater force at higher speeds. To a good
approximation, the force is proportional to the square of the speed so
something going 80 mi/hr will experience 16 times the force as
something going 20 mi/hr (which is why you should not drive too fast if
you want to conserve gasoline). A falling object is speeding up as it
falls from rest because of its weight which is a force down; but the
air resistance, which is a force up, gets bigger and bigger as it
speeds up until the force is equal to the weight of the object. Now the
object experiences zero net force so it stops accelerating. This speed
is called the terminal velocity. You can read much more detail in an earlier answer if you like.

**QUESTION: **

2 bicyclists on identical
bicycles roll down a hill (starting from a stop or identical starting
speeds). One bicyclist is heavier than the other; will this person
reach the bottom of the hill faster?

**ANSWER: **

It depends on the
assumptions you make. I will outline the essential considerations:

- If there is no friction then
they should both get to the bottom at the same time. This is because
the force down the hill on each is proportional to the weight which is
proportional to the mass so the accelerations are the same (I am
assuming you know Newton's second law).
- But there is friction in the
bearings of the bike, the rolling friction of the tires, friction of
the roadway,
*etc*., but these are also approximately
proportional to the weight, so again there should be a tie.
- Air friction is determined by
geometry and speed, so it is not determined by weight. The greater the
speed the greater the force of air friction (approximately proportional
to the square of the speed), so eventually an object will have a force
from air friction precisely equal to but opposite the force from
gravity and it will stop accelerating; it has reached its "terminal
velocity". An object moving under the influence of gravity and air
friction experiences a greater. The terminal velocity for the heavier
person is larger, so if air friction matters (and it does because
pedaling into wind is much like going up a hill) the heavier person
will win. You can see more detail about air friction in an earlier answer.

Friction can be a complicated
thing, so it would be interesting for you to try things out
experimentally.

**QUESTION: **

Coulombs constant 9 x10^9
can be found as 1 / (4 pi x permittivity of free space ). It is also
found as c^2 x 10 ^-7, or 1 / permittivity x permeabilty x 10 ^-7), why
is this?

**ANSWER: **

If you measure the force
between two point charges separated by a distance* r,* this force
is found to be proportional to product of the charges and inversely
proportional to *r*^{2}. If you measure the charge in
Coulombs and the distance in meters, then *k*=9x10^{9} Nm^{2}/C^{2}
as you state. This is simply an experimentally measured number, that is
the force between two charges each 1x10^{-3} C and separated by
1 m would be 9000 N, a number you could measure to get * k*.
Suppose that you have a number *N* and you want to define a new
number *M*=2*N*; that is all permittivity is, a redefinition
of * k*, e_{0}=1/(4*pk*).
Your last question is most interesting. The permeability of free space
is m_{0}=4px10^{-7 }Ns^{2}/C^{2}
and, like *k,* it is just a proportionality constant which tells
you the magnetic force between two current carrying wires. Now, it
turns out that when you do the mathematics you find that the equations
of electricity and magnetism (called Maxwell's equations) predict waves
which have a speed of *c*=[e_{0}m_{0}]^{-1/2} and this speed
just happens to be the speed of light in a vacuum. And so if you now do
the simple algebra, you find that* k*=10^{-7}/[e_{0}m_{0}]=*c*^{2}x10^{-7}.

**QUESTION: **

I have heard that if one
inhabited a two-dimensional macrocosm and a three-dimensional sphere
passed through this macrocosm, then one would see a point grow into a
circle, before collapsing into a point and disappearing again. Now I
apologise for asking you about such an unscientific conjecture, but
could it be that the appearance and subsequent disappearance of
particles and atoms and so forth which has been observed by physicists
to be occurring constantly; could it be that these transient particles
are, de facto, entities from a higher cosmos passing through this
three-dimensional cosmos?

**ANSWER: **

You are referring to virtual
particles as you indicated in a later message. How can a particle, with
energy* mc*^{2}, simply appear from nothing? The answer is
that you can violate energy conservation as long as you also obey the
Heisenberg uncertainty principle, *i.e*. as long as the time
during which you violate energy conservation is short enough.
Quantitatively, The product * ET* (energy time time) must be on
the order of about Planck's constant which is a very small number (on
the order of 10^{=34} in SI units). So, you may spontaneously
create 1 Joule of energy as long as it does not exist longer than 10^{-34}
seconds. This picture has done remarkably well in understanding virtual
particles. (Incidentally, you cannot have a virtual electron, for
example, because that would violate conservation of electric charge;
instead you must have a vitrual electron-positron pair.) Could they be
understood as evidence of higher dimensions? Scientists are loathe to
say anything is not possible, but more than simple conjecture would be
needed to convince anybody—predictions of nature are required for
acceptance of a hypothesis.

**QUESTION: **

If there was no wind present
what force would a raindrop hit a piece of wood, (siting on the gound)
at?
At what point would the force generated by a raindrop be enough to
cause damage to a piece of wood? What is the wood was covered in a
tar-like substance?

**ANSWER: **

A large raindrop has a
terminal velocity of about 20 mi/hr. Have you ever been hit by a large
raindrop? It does not really hurt so the force must be pretty
negligible. The force of a raindrop hitting wood will not damage it.

**QUESTION: **

I've been looking at various
videos on Youtube about homompolar motors. In some videos a battery is
used and in other there is not, but in both types of set-ups... What is
it that causes the spinning action. I can some what understand the
spinning when a battery is used. In a battery set-up there is a current
in the wire that makes a magnetic field around the wire, or wires, and
it is this magnetic field that conflicts with the current in the wire
causing it to be pushed away. But in the videos that don't use a
battery what is making the whole assembly spin? I is my understanding
that magnetic flux fields are stagnant. So when a charge is applied to
the "no battery" homopolar motor is there a current traveling along the
flux lines causing it to spin? I've attached some links to clarify my
question:

http://www.youtube.com/watch?v=2hHfkK4iGBQ

http://www.youtube.com/watch?v=hXbFfMBW97A&mode=related&search=

**ANSWER: **

In each of your examples
things get started with two wires. These are attached to a battery
which supplies the current and gets things spinnining. A good
explanation is given at
http://www.evilmadscientist.com/article.php/HomopolarMotor . After
the wires are taken away the motor continues spinning but because there
is very low friction; it is not being driven anymore. If you let it go
long enough it will eventually stop.

**QUESTION: ;**

I think no object can travel
any faster than whatever the force that pushes it travels. Like a
bullet from the muzzle of a gun. I assume its greatest speed in its
journey is at the muzzle of the gun.
If true, and baseball pitchers routinely pitch 100 mph baseballs, how
is it possible for the pitchers finger (s) to decelerate from 100mph in
a space of what can't be more than a fraction of an inch in a fraction
of a second. Seems like that would tough on any part of the body.

**ANSWER: **

Well, you should not think
of a force as being something which has a velocity; it is simply a push
or a pull. The velocity of something is maximized or minimized as
determined by the acceleration which is determined, via Newton's second
law, by the force. In your example of a bullet, the velocity is likely
greatest just as the bullet leaves the barrel because there has been a
large force acting on it and a small force acting against it (air
friction). As soon as it leaves the barrel, the only forces on it are
air friction (which slows it down in the direction it is moving) and
gravity (which accelerates it in a downward direction). The pitcher
example can be understood as follows:

- The instant that the ball
leaves the hand the hand must be moving with speed 100 mi/hr and, as
you note, must experience a force to stop it.
- But the hand does not stop in
a fraction of an inch, it probably travels a couple of feet or more.
- Understanding this you can
see one of the reasons for "follow through" in throwing balls, golf
swings,
*etc*.
- A rough calculation of the
force is: let the time to stop be 0.2 s, the initial velocity be 100
mi/hr=45 m/s, the mass of the hand be 1/2 lb=0.23 kg, and the distance
traveled be 1 m=3.3 ft. Then the average acceleration is 45/.2=225 m/s
^{2}=503
mi/hr/s. Then the average force is 225x0.23=52 N=12 lb. The source of
the force on the hand is the wrist. Note that the distance does not
factor into calculating the acceleration, just the change of speed and
the time. The distance and time are not independent and making the
distance larger makes the time larger which makes the acceleration and
force smaller.

**QUESTION: **

Is there any type of matter
which cannot be melted, even when heated?

**ANSWER: **

It depends on factors like
the temperature and pressure. So there is no simple answer to your
question. Many compounds will not melt for some pressure ranges but
they will sublime, that is turn into a gas directly from the solid. An
example is carbon dioxide (dry ice) which does not melt at atmospheric
pressure, but it does sublime.

**QUESTION: **

How far would a person need
to fall before they accelerate to their "terminal velocity." 100 feet?
500 feet? Higher? I'm told that terminal velocity is about 125 mph for
a person free falling.....and that the acceleration formula is 33
feet/second/second. But I don't know how to reverse that math.

**ANSWER: **

What the terminal velocity
is depends on a number of things including the skydiver's weight, the
density of the air, and how he orients himself relative to his fall. If
he orients in a belly flop position he will have a lower terminal
velocity than if he falls feet first. Also, he technically never
reaches the terminal velocity but just approaches it asymptotically.
But you can estimate when he is within, say 95% of the terminal
velocity. The details of the physics are given in a previous answer; I will just give
you the results for your situation here. Choosing the mass to be 100 kg
(about 220 lb), the air density to be 1.3 kg/m^{3}, cross
sectional area to be 1 m^{2} (more like the belly flop
position), and the drag coefficient 1.2, I find a terminal velocity of
about 35.4 m/s (about 79.4 mi/hr). The characteristic time is about 3.6
s; this is the time it takes the speed to go to about 76% of the
terminal velocity. If you wait twice the characteristic time, about 7.2
s, you will reach about 96% of the terminal velocity. The
characteristic distance is about 64 m; this is the distance it takes
the speed to go to about 63%. If you go three characteristic distances,
192 m (about 630 ft), you will reach about 95% of the terminal
velocity. If you are interested, the characteristic time is *v*/9.8
s and the characteristic length is 19.6/*v*^{2} m where *v*
is the terminal velocity in m/s. It is interesting to note that cats
that fall out of skyscrapers usually survive because their terminal
velocity is slow.

**QUESTION: ;**

How can motion be
generalized by simply looking at an objects velocity and acceleration.
More specifically, why do we only use the first two derivatives of
distance to explain the change of distance? Why don't we consider
higher order derivatives? Wouldn't an inclusion of these higher order
derivatives be necessary to fully account for motion? The question is
"Why can we generalize changes in distance by looking only at two
derivatives of distance?"

**ANSWER: **

Actually, you don't really
need anything but the position as a function of time to know everything
there is to know about the motion of a particle. Once you know that,
just differentiate it to get the velocity which is the rate of change
of position. If you care to know the rate of change of velocity
(acceleration), differentiate the position twice. If you wish to know
the rate of change of acceleration (which engineers often do and call
"jerk"), differentiate the position three times. If you want to know
how the jerk changes, differentiate four times. And so forth. But every
bit of this information is contained in the position as a function of
time. Physicists are normally only interested in velocity and
acceleration because, among other things, Newton's second law (N2) says
that a force causes an acceleration. It turns out that accleration is
not a useful quantity in the theory of special relativity since N2 in
the form *F=ma* is actually not correct in relativity.

**QUESTION: **

Do electrons maintain a
standard orbit about the nucleus?

**ANSWER: **

Actually, the idea of
electrons being in well-defined orbits in an atom is just a pictorial
way to qualitatively understand atomic structure. Originally Niels Bohr
solved the puzzle of how atoms are constructed but his ideas later
evolved into a much more complete theory of atomic structure. An atom
consists of "clouds" of electrons around the nucleus, that is the
electron does not maintain its identity as a point particle but becomes
"smeared" over the volume in a way which is determined by the
properties of the "orbital" it is in. This is quantum physics. However,
if you say that the shape of the cloud represents the orbit, then, yes,
electrons in one atom have the same distribution as in any other atom
of the same element.

**QUESTION: **

Hypothetical situation: I'm
walking in the park. Then, the earth explodes, casting the fragments of
earth to outer space. Not unlike the big bang. Now, I am smack dab in
the middle of one of those fragments. What is the cause of my death?
Will my tendency to remain unmoved turn me into a meat puddle? Or will
some other force counter act that so that I die from the loss of
atmosphere and loss of oxygen (I doubt this)? From freezing (I doubt
this too)? Your help is great appreciated as to what method in which I
would die, and about how long my existence will be from explosion to
death.

**ANSWER: **

The fragment you are on
suddenly experiences an enormous acceleration as a result of the
enormous force it experiences. It pushes outward on you to give you the
same acceleration, so it must push on you with an enormous force, far
more than your body is designed to survive. It is basically the same as
your hitting the ground with a very high speed (like after jumping from
a tall building)--the huge acceleration of your stopping requires a
force and that force kills you.

**QUESTION: **

If I heated my oven to
something like 500 deg F, and it was a perfect insulator, would the
temperature inside eventually decrease due to irreversible processes
such as friction between gas molecules and possible deformation from
molecular collisions?

**ANSWER: **

By definition a "perfect
insulator" will not let any energy out. We never talk about friction
between two atoms or molecules since it is a macroscopic phenomenon
resulting microscopically from interactions between molecules. In this
context if one molecule gains energy in a collision the other mus lose
exactly the same amount. I do not know what you mean by deformation,
but at normal temperatures the only excitation possible is rotational
excitation and this is already included in the microscopic description
of the hot gas. So, the temperature will not change.

**QUESTION: **

I recently read an article
about "nothing" in the center of the universe.
Since the "hole" is 5 to 10 Billion light years away, how long would it
take to get there using current technology (such as the fastest
man-made object: 250,000 km/h) and in a space craft traveling at 99% of
the speed of light? Also what would be the relativistic age difference
(earth vs spacecraft observer)?

**ANSWER: **

(I will take the 10 billion
light year distance; everything is half as large for 5 billion light
years.) The first velocity you quote, 250,000 km/hr is about
0.00023=0.023% the speed of light, so both observers would see the same
elapsed time which would be 10x10^{9}/2.3x10^{-4}=4.3x10^{13}
years, about 43,000 billion years. The case of a speed 99% the speed of
light, we would see it take about 10 billion years (just a hair longer)
but the observer in the space craft would see much less time elapse. He
would see the distance to the hole to be contracted to 10x(1-.99^{2})^{1/2}=1.4
billion light years; so the time it would take him, according to his
clocks, would be 1.4/.99=1.42 billion years.

**QUESTION: **

An acquaintance and I are
having a heated discussion relating to the 1960 jump from 103,000 ft
from a gondola by Joe Kittinger. According to several reports,
Kittinger reached speeds over 600 MPH after he jumped. Since I can't
prove that he did, I'm no physicist, he believes he must be correct.
How can I determine the speeds that were reached in this jump?

**ANSWER: **

In principle, this is a
simple free fall problem. In practice, we need to worry about air
resistance since that becomes important in real life at high speeds.
However, there is very little air above about 60,000 feet, so let's
assume that there is no air resistance and see how far he has to fall
to reach a speed of 600 mi/hr and if it is less than about 40,000 feet
he probably achieved that speed. The acceleration due to gravity is
about 21.8 mi/hr/s; that is a freely falling object will gain about
21.8 miles/hour as each second clicks by. One pertinent physics
equation is *v*=*at* where *v* is the speed (assuming
we start from rest), *a* is the acceleration, and *t* is
the time. So, putting 600 in for *v* and 21.8 in for *a* we
can solve for *t*: *t*=27.5 s; in other words, after about
a half a minute the object will be going 600 mi/hr. The second
pertinent equation is *s*=½*at*^{2} where *s*
is the distance traveled in time *t*. Solving for *s* I
find *s*=12,000 ft, that is he will have a speed of 600 mi/hr
when he is at about 90,000 ft, still far above where there is
signficant air. (Incidentally, in the second calculation I used *a*=32
ft/s/s so the units would come out right, * viz*. feet.) So, I
would say that yes, he must have gone at least 600 mi/hr. I did a
little research and saw 714 mi/hr quoted as the highest speed he
achieved. Once he starts encountering significant amounts of air he
will begin slowing down.

**FOLLOWUP
QUESTION: **

This is a follow-up, and didn't know if I should post it
online or not, since you've already answered it. But, the person with
whom I'm having this discussion still insists you're answer is wrong.
He fancies himself smarter than a nuclear-physicist, I guess, and, by
his calculations , the top speed that Kittinger could have reached is
350 mph. Here is his argument and his calculations, referring to your
response.

"That's
just a repeat of what the other professor said, and in both cases they
conveniently ignore drag. If you're going to ignore drag then ignore it
and the guy keeps falling at increasing speed. Why stop accelerating at
the point that corresponds to what the claims are? When you plug the
drag variables into NASA's algorithm Kittinger doesn't get to 614mph.
The professors don't bother to verify that the air is too thin to have
any effect.
Tell the college professor's to go to the Chemical Engineer's Handbook
and look up Fluid and Particle Dynamics. In there is a table that
describes the activity of bodies in free fall through a fluid. When
they're going slow, they are stable. As they increase in speed they
first start to tumble erratically, then they start spinning about their
axis of least inertia. The tumbling starts somewhere around Mach 0.4
and the spinning around Mach 0.6 That's the flat spin the story eludes
to, and the college professors ignore. If he fell at 614mph he's at
Mach 0.9 and is in a flat spin.
The big problem is all the contradictory statements that are attributed
to Kittinger. He the first supersonic skydiver. He gets to an estimated
614 mph or 714. He has no sense of speed, yet he knows he keeps
accelerating after the drag chute opens. That chute opens at 13 secs,
or 16 secs or at 96000 feet.
First of all drag doesn't work like a break. A body sitting still has
no drag. As it speeds up drag increases and keeps increasing until the
force propeling the object and the force of drag are equal. Then the
object stops accelerating and moves at constant speed as long as force
and drag stay the same. Drag is related to Velocity(speed) by the drag
equation. D = 0.5 x Cp x p x A x V^2 So as long as you keep the Cp,p,
& A the same, there is one value for drag for every value of speed
(V)
I'm not going into all the other crap, but the force pulling Kittinger
down and causing him to speed up is gravitiy working on his weight. At
roughly 300 lbs it takes 300 lbs of drag to stop him from accelerating.
He's the shape of a brick, roughly half as wide as long and 1/3 thick
as long. The Cp of a brick is 2.1. We use that to compute air flows
through our tunnel kilns at the brickyard. The density of the air is
about 0.00004 slugs/cuft. He is exposing about 15 sqft of area to the
"wind". So if we plug in all those numbers in the Drag equation and
solve for V(speed), he stops accelerating at 690 fps or 470mph. I'd say
the air is thick enough to make a difference.
But that doesn't take into account the drag on the small parachute he
deployed to keep himself from going into that flat spin. It's 6' in
diameter that's 28.26 sqft of area. The Cp for a round chute is 1.5. So
as long as the drag on the chute and the drag on Kittinger doesn't
total 300 lbs or more he is still accelerating. At 13 secs the total
drag is 254lbs and his speed is 283 mph. He'll accelerate for less than
a second more and get to about 290 mph. At 16 seconds the total drag is
384 lbs, so he'll decelerate from 347 mph with a pretty good jerk. I
have no idea where or why the 96000 ft comes from, so I'm going to
ignore it. He supposedly used a timer to deploy the chute.
The speed of sound is around 660mph and tumbling would start somewhere
around Mach 0.4 which is 0.4 x 660 = 264mph. That's damn close to the
13 sec mark.
We'll never know based on the info available, but I don't think he got
over 300-350mph."

Here are
the facts, as presented in an article at http://www.centennialofflight.gov/essay/Explorers_Record_Setters_and_Daredevils/Kittinger/EX31.htm

1. Kittinger jumped from 102,800 ft.

2. His weight is approximately 300 lbs.

3. He was falling in a backward orientation

4. After falling for 13 secs, a small chute, 6 ft. in diameter, opened.

5. He feel for 4 min. and 36 secs more bringing him to 17,500 ft.

**ANSWER: **

Your friend certainly makes
some quite good points, although he is maybe a bit overemotional and
maybe a little hostile to us college professors. It is true that we
often simplify problems to get to the core of a problem. So let me be a
little more careful and go over the calculation of your friend the way
I would do it since some of the numbers he quotes are undocumented and
some of them (in particular slugs/ft^{3}) are completely
incomprehensible to a modern physicist! Your friend must be an
engineer. His equation is quite correct, that is the terminal velocity
is given by *v*=[(2*mg*)/(*rAC*_{p})]^{1/2}
. Now it is easy to see how disputes can arise because the answer, of
course, depends the choice of constants some of which are not easy to
estimate (for example, I would say approximating the man as a brick is
what some nutty college professor might do). The density of the air at
100,000 ft is about 1/100 the density at sea level and, since the
density at sea level is about 1.3 kg/m^{3}, I will take *r*=1.3x10^{-2}
kg/m^{3}. I searched the web for tables of drag coefficients
and found that a
parachutist has *C*_{d}=1-1.4 (not 2.1 as your friend
assumed); I will use 1.2. The cross sectional area also requires a
rough estimate since it depends on whether he is falling, for example,
feet first or is falling "belly flop" orientation. I will assume the
latter so as to get as small a speed as possible and I will estimate
the area as about *A*=2 m x 0.5 m=1 m^{2} (your friend
uses 15 ft^{2}, about 1.4 m^{2}). Using *m*=136
kg (300 lb) and g =9.8 m/s^{2}, we are ready to estimate *v*;
I get *v*=413 m/s= 924 mi/hr.

But, there is important
information which you did not tell me the first time through--the
opening of the small chute. So now the cross sectional area is about
2.5 m^{2} and the drag coefficient is about 1.42 (I model it as
an open hemisphere
into the wind). So now I get a reduced terminal velocity of *v*=240
m/s= 537 mi/hr.

Now I have the terminal
velocities, what happens in our specific example? The space is too
limited here to put in all the details, but I have assumed a constant
density for the first 4000 m (about 12,000) of fall. I went back to an
intermediate mechanics book to find the dynamic analysis of the falling
body with quadratic velocity dependent drag force and I could apply
(knowing the terminal velocities from above) the analysis to this
specific problem. In the first 13 seconds I find that he falls about
1000 m and ends up with a speed of 130 m/s (291 mi/hr). Then, after he
has fallen 3000 m more he will have a speed of 208 m/s (465 mi/hr). But
he is still accelerating but now the air gets denser so his
acceleration decreases even more; nevertheless, as he falls, since he
is still fairly far below terminal velocity (240 m/s) he will end up
going faster than 465 mi/hr.

So who is right here? Well, your
friend is right in that we will never know based on information we
have. I can easily imagine that I have made a factor of two error in
the density, the area, or the drag coefficient (and so could your
friend); increasing all by a factor of two would reduce the terminal
velocity by almost 2/3 which is the difference between 600 mi/hr and
200 mi/hr. The results are too sensitive to modest changes in the
parameters.

**QUESTION: **

At our work we have gone
stupid over GREEN Issues, we have been instructed to turn off the hand
dryer at the wall plug when our hands are dried, thus saving some of
the blow cycle.
Now when you dry your hands you turn it on at the plug, get the
remaining part of the last cycle and then have to turn the blower on by
the big silver button on the dryer.
Are we saving enery at all or is "turning on/starting the dryer" the
big user of power? Thus it would be better for it to finish its cycle
each time

**ANSWER: **

It is not true that turning
an electric appliance on and off uses more energy. (It is also not true
that turning a car off and back on at a long traffic light consumes
more gasoline than running the whole time.) Electric heaters like your
hand dryer are among the worst energy hogs so running them only as long
as necessary to dry your hands does make sense. However, if your
employer is really serious about energy conservation, he would
uninstall the electric dryers and replace them with paper towels or,
even better, one of those machines which has a long cloth roll which is
simply washed and then reused when it is all used up.

**QUESTION: **

Compressing gaseous nitrogen
makes liquid nitrogen which is very cold. But compressing things makes
them hotter. Any help alleviating my confusion will be greatly
appreciated.

**ANSWER: **

The compressed gas does get
hot, but that is not the end of the process. Here is a link
with an explanation.

**QUESTION: **

This question has to do with
television signals emitted from this planet. If there is a star that is
say exactly 40 light years from us, how weak would our "electromagnetic
reflection" be from the star or a planet (I'm assuming a reflection is
possible?) by the time we get it back, some 80 years after it left?
I realize that probably not all stars would reflect equally, so my
question is geared toward whether there might be anything at all that
could be measured and analyzed someday.

**ANSWER: **

Almost anything will relfect
electromagnetic radiation. The real problem here is the intensity. The
intensity of radio waves emitted from the earth will fall off
approximately like 1/*r*^{2} where *r* is the
distance. So, if you have a certain intensity 1,000 miles from earth,
the intensity 1,000,000 miles away will be (10^{6}/10^{3})^{2}=1,000,000
times weaker; and 1,000,000 miles is a very small number compared to
the distance to a star. And the reflected signal will lose just about
the same fraction coming back. My guess is that the intensity would be
so low that no information could be obtained from it.

**QUESTION: **

If an object is completely
submerged in water (let say sitting on the bottom of a lake) why does
buoyant force help you to lift the object out of the water. What I'm
confused about is why the pressure of the water pushing down on the
object doesn't hurt you as much as help you?

**ANSWER: **

Let's think of it as a box.
The bottom of the box experiences a force due to the pressure in the
water which pushes up. The top of the box experiences a force due to
the pressure in the water which pushes down. But the force on the
bottom is bigger in magnitude than the force on the top because the
pressure gets bigger as you go deeper. Therefore there is a net upward
force on the box which we call the buoyant force.

**QUESTION: **

What is the speed of gravity?

**ANSWER: **

This quetion has been previously answered.

**QUESTION: **

How would i calculate the
number of grains of sand on Earth ???

**ANSWER: **

There is, of course, no way
to calculate it. You could estimate it, however. I am not a geologist,
so I really don't know how much sand there is in the world but it must
be a lot. I will take a wild guess that there is enough sand to cover
the entire earth to a depth of 10 cm =10^{-1} m (there is
probably more than that). The surface area of the earth is about 5 x 10^{14}
m^{2} (from *A=*4*pR*^{2})
so the total volume of sand is about 5 x 10^{13} m^{3}.
Now, I will guess that a typical grain of sand would have a diameter of
maybe 0.1 mm=10^{-4} m so the volume of a typical grain of sand
would be about 10^{-12} m^{3}. So the number of grains
of sand would be the ratio of the volumes (volume of sand/volume of one
unit of sand), about 5 x 10^{26}, quite a lot! This is
comparable to about how many atoms there are in your pencil.

**QUESTION: **

during the double slit
experiment, i understand the bright patches are caused by the peak of
one wave interfering with the peak of another to form a doubly high
peak. but when the bottom of two waves also interfere with each other
to produce a doubly low wave, does this also produce the bright patch?

**ANSWER: **

Every point on one wave
interferes destructively with the corresponding coincident point on the
other wave.

**QUESTION: **

One of my classmates claimed
during our study group that if you glue two permanent magnets together,
north to north that eventually they will reverse poles… is this true?

**ANSWER: **

What happens depends on many
things like the materials from which each magnet is made, temperature,
how strong each magnet was, *etc.* One thing is for certain,
though: they will not both reverse their polarities. Either neither
will or one will or both will become demagnetized.

**QUESTION: **

Let's say I have a metal rod
about a half an inch thick and 300,000 kilometers long. Then say I give
one end of said rod a mighty whack with a hammer, propelling it forward
by one inch in a mere fraction of a second. My questions is, wouldn't
the impact of my hammer cause the other end of the rod to move forward
one inch just as rapidly as the end where I whacked it? And would this
violate Einstein's law that states that nothing can move faster than
"C"? Or would the far end of the rod have to wait one second after my
whacking my end before moving forward by one inch?

**ANSWER: **

Have you thought about the
implications of your question? I figure the mass of the rod would be
about 10^{10} kg. Suppose that you exert a constant force such
that after 0.1 s it is moving with a speed of about 0.5 m/s; it would
have moved about an inch in this time. The force is the change in
momentum divided by the elapsed time so, roughly speaking, the required
force is about 10^{12} N. Where are you going to get such a
force? Anyhow, to the meat of your question: no, the other end would
not start moving instantaneously. It could not begin moving until at
least one second later than your end started moving for the reason you
state: no information can travel faster than *c*. In reality, it
would be much longer than one second because your "mighty whack" will
compress the rod and this compression will move with the speed of sound
in the metal and this compression is what travels to the other end to
move it.

**QUESTION: **

If I were to stand on the
moon with my head facing directly forward into the line of orbit, would
I weigh more than if I were standing on the exact opposite side of the
sphere, in the rear so to speak? In other words, does the movement of a
planetary object either add or subtract from one's mass depending on
where they might be situated?

**ANSWER: **

Your weight is the force
which you experience due to the gravitational field you are in.
Assuming the moon to be a homogenous sphere, your weight is independent
of where you are on the surface and of the motion of the moon. Your
mass is the inertia you have in your rest frame and it is independent
of everything. Rest mass is an inherent property of an objece, weight
is determined solely by mass and field.

**QUESTION: **

Given that gravitation and
acceleration are locally indistinguishable, and that "gravity" is
causing the light to bend in gravitational lensing, can acceleration
also cause gravitational lensing in some aspects?

**ANSWER: **

Suppose that you are in an
accelerating elevator with a hole drilled in the side; if a beam of
light enters parallel to the floor, you will see it follow a parabolic
trajectory as it crosses the elevator. So the answer is, yes, light
bends when observed from an accelerating frame of reference.

**QUESTION: **

Given initially that a
Powerful large magnet and a heavy soft iron are attached magnetically
to each other , we obviously have to expend a lot of ENERGY to separate
it away from each other. But by law of conserv. of energy and E=MC^2
,should the soft iron(or magnet) initially attached to magnet (or iron)
weigh more? If not where is the energy we expended? if so it is unclear
where we should bring relativity to solve it.
(Same can be asked with gravitationally strong object.But it would
bring Gen.Rel into question, which would be uncomfortable for this
simple question)

**ANSWER: **

Yes, the magnets will be
more massive after you have separated them. But, the amount will be
unmeasurably small. Suppose that you do 100 J of work to separate them.
Then the mass increase will be *Dm*=100/(3x10^{8})^{2}
kg, about 10^{-15} kg!

**QUESTION: **

If an object weighing 500lbs
(let's say an elevator) falls from a height of 1,000ft (without any
resistance other than air) and hits the ground (concrete), how much
energy would it be equal to. And if you would, please translate into
sticks of dynamite.

**ANSWER: **

The energy when it hits the
ground is about 680,000 J which is equivalent to about 0.16 kg of TNT.

**QUESTION: **

Whats the lowest Temperature
ever attained here on earth according to latest details ?? .Some
unconfirmed source told me that it was less than a millionth degree
above 0 kelvin

**ANSWER: **

The lowest temperature I
have found reference to is 100 pK. That is one ten billionth of a
degree Kelvin.

**QUESTION: **

often aluminum outboard
props bend and warp, the manufactures answer is that over trimming the
engine so that it sucks air down into the props vortex, the air becomes
traped, supper heats and then warps or melts the prop. wouldnt that
trapped air have to reach 660 degrees to melt the prop? is that even
possible?

**ANSWER: **

The prop is not being
melted, just warped. At high temperatures metals become softer, more
easily deformed (that's why the village blacksmith had a hot fire).

**QUESTION: **

To our eye + brain, a
material has color when it absorbs all wavelengths of the visible
spectrum and reflects 1 wavelength. For example, a red brick has color
because it absorbed visible light and reflected light with the
wavelength associated with the red color. Why did all the other
wavelengths of light get absorbed and the red light not get absorbed?
Are all wavelengths absorbed and the red color wavelength is radiated?
Does this have anything to do with the HOMO-LUMO Gap (chemistry)?

**ANSWER: **

Of course, your explanation
is a little oversimplified. Nothing absorbs everything except one
wavelength. A red brick absorbs more of the light in the shorter
wavelength (blue) end of the spectrum than in the longer wavelength
(red) part of the spectrum. But your general idea is right. What gets
absorbed is determined entirely by the properties of the molecules in
the material, it is an atomic-level effect. All molecules have
absorption and radiation spectra and they vary from material to
material. I have no idea what the HOMO-LUMO gap is.

**QUESTION: **

Light, radio signals, and
audio are all types of waves which can be measured in Hertz. I know
that what we hear (audibly) are compressions of air created by the wave
(let's assume for this question we have an audio wave of 900Hz). Light
is also a wave, lets choose yellow which would be 515THz ( terahertz ).
Considering this, light can travel accross empty space (obviously) as a
wave. Here is where I find a problem that I want answered: If a 900HZ
wave were created from a source in space (not as sound, just a 900hz
wave) and was directed toward earth could we (on the earths surface)
detect the 900hz signal? If so how, wouldn't this cause sound
compression when it reached our atmosphere, making it audible? If not
then why, 900hz is a wave just like 515THz, is it possible to have a
900hz wave that you can't hear on the surface of the Earth with air? Or
If 900hz can not travel through space then why can a lightwave (or
whatever wave) travel through space at 515THz but a 900Hz wave cannot,
radio and lightwaves do not require the presence of air to travel
through space? Unless there is another possibility I have not thought
of above, all the options seem contrdictory to what I Understand about
physics, sounds waves, etc... I am by no means a scientist or even a
physics student, just a pondering thinker.

**ANSWER: **

The whole key is "what is
doing the waving". For sound, as you note, it is the air. For
electromagnetic waves (radio, light, xray, gamma ray, microwave, *etc*.)
it is electric and magnetic fields. You can hear compression waves in
the air but you cannot hear electric or magnetic fields. Your eye can
detect electromagnetic waves in a narrow frequency range and we have
instruments to detect other frequencies. Hence, if the 900 Hz wave came
across space then it must have been electromagnetic so you could not
hear it but you could detect it with an appropriate antenna and
electronic receiver. By the way, the wavelength of such a wave would be
about 333 km.

**QUESTION: **

Hi I'm a 52 year old high
school teacher and this is a problem I could not solve in the new
curriculum. Here it is, word for word:

A red ball is stationary on a
billiard table OABC. It is then struck by a white ball of equal mass
and equal radius with velocity u( -2i + 11j ) where i and j are unit
vectors along OA and OC respectively. After impact the red and white
balls have velocities parallel to vectors -3i + 4j, 2i + 4j
respectively. Prove that the coefficient of restitution between the two
balls is 1/2.

**ANSWER: **

First, allow me a little
rant! It is utterly ridiculous that this problem is part of a high
school curriculum. Coefficient of restitution (COR) is one of the least
important concepts in classical mechanics. Furthermore, it is nearly
always defined in terms of a one-dimensional collision which the
collision in your problem is not, so it looks like the problem writer
is trying to confuse the reader (which I consider to be poor
educational method). Furthermore, I find that I do not get 1/2 for the
coefficient of restitution when I work the problem. I will outline the
solution to the problem and give my results. You can reconstruct the
solution and see if I have made any errors. First, the COR *e* is related
to the energy loss *Q* in the collision by *Q*=½*m**v*^{2}(1-*e*^{2})
where *m=m*_{1}*m*_{2}/(*m*_{1}+*m*_{2})
(reduced mass) and *v* is the incident velocity (if one of the
two particles is at rest as it is here). It makes no difference what
the actual masses are since they are equal, so I shall choose *m*_{1}=*m*_{2}=1
kg such that *Q*=31.25(1-*e*^{2}) J. (I have used *v*^{2}=125
m^{2}/s^{2} as given in the problem.) Now, just
calculate *Q *to get *e*. The information given about the recoiling
velocities is their directions, not their magnitudes; to get the speeds
you must do momentum conservation. The red ball moves at an angle of
53.1^{0} above the negative *x* axis and the white ball
moves at an angle of 63.4^{0 }above the positive *x*
axis. Conserving momentum in *x* and *y* directions I now
find the speeds of the red and white balls:* v*_{r}=7.5
m/s and *v*_{w}=5.59 m/s. Hence the energy after the
collision is 43.75 J and before the collision 62.5 J, so *Q*=18.75
J. Solving now for COR: 18.75=31.25(1-*e*^{2}), *e*=0.63, not ½.

There is actually another way
you can do it: if you work in the center of mass system it essentially
looks like a one-dimensional collision since the two particles after
the collision move colinearly apart with speeds of 3.54 m/s each so
that the speed of separation is 7.08 m/s and the speed of approach
before the collision is 11.18 m/s. The COR is defined as the ratio of
the speed of separation over the speed of approach which works out to,
you guessed it, *e*=0.63! Now I have more confidence in my
solution.

**QUESTION: **

what, if any, would be the
major 'noticeable' differences in the universe if the speed of light
were drastically higher, say 10x, 100x or 1000x?

**ANSWER: **

For starters, you would not
be here to ask this question. The existence of life as we know is very
sensitive to the values of the most important physical constants, the
speed of light, * c*, being one of them. The easiest way to see
dramatic effects is from good old *E=mc*^{2}. If *c*
were 10x bigger, the energy equivalent of mass would be 100 times
greater, so the energy being produced by the sun would be 100 times
what it is; talk about global warming! Assuming that protons and
electrons still existed you could still have hydrogen since atomic
physics is not very affected by relativity, but when you tried to make
a nucleus you would find that the masses of the nuclei were very much
less than the sum of its components due to the enormous binding
energies. In fact, I do not think you could have a neutron so you could
make no nuclei and therefore you would have no chemistry and the stars
would not be able to make energy using fusion.

**QUESTION: **

What is the basic physics
behind laser cooling.

**ANSWER: **

The basic physics is
essentially momentum conservation. If a ball is moving toward you and
you shoot it with a bb gun, the ball slows down (cools) a bit. Many
collisions with bbs will slow it down more. In laser cooling, the ball
is an atom and the bbs are photons from the laser. A nice simple
explanation can be seen here.

**QUESTION: **

Given COMPLETE information
about Hydrogen and Oxygen and Using physics laws "as it is now" to its
full extent (forgetting about the mathematical and Quantum mechanical
complexities) can we basically "predict" how a combination of type H2O
out of these gases behave? for example ,"Predict" that such a material
would be liquid under room temp. and has 1Kg/cc density, etc etc.?(we
can dispense with all other branches of science and make physics
"universal"

**ANSWER: **

When you say to forget about
"quantum mechanical complexities" you guarantee that the answer to your
question is no. However, "complete information" really means detailed
wave functions of hydrogen and oxygen atoms; given that information,
excellent predictions of the properties of H_{2}O may be
calculated.

**QUESTION: **

I was wondering why
increasing the distance between the plates of a parallel plate
capacitor (when it's charged and not connected to a circuit) increased
the Voltage. I realize that since this decreases the capacitance and
the charge remains the same then by then equation Q=CV the voltage must
increase. But logically this doesn't make sense to me. Since the
equation for voltage is V=kq/r, this would imply to me that as you
increased the distance between plates you'd also be increasing the
distance between charges. Thus I would think voltage would decrease.

**ANSWER: **

The voltage you quote is for
a point charge, not parallel plates. For parallel plates the electric
field *E* is uniform and so the potential difference is *V=Ed*
where *d* is the spacing between the plates. The field is
determined by the charge *Q *on the plates and the area *A*
of the plates, *E=Q*/(*e*_{0}*A*) so the field stays the
same when the plates are separated.

**QUESTION: **

Which weighs more. There are
two identical water bottles both are filled with the same amount of
liquid water. One is then frozen.
Both bottles arer taken on a hike. The dew point is such that the
frozen bottle starts to form condensation on the outside. Will the
frozen bottle endup weighing more due to the condensation that forms on
the frozen bottle ?

**ANSWER: **

Freezing the water will not
affect its weight so both bottles will weigh the same after one has
been frozen. So, the condensation will cause the cold water to be
heavier. [A technicality: because *E=mc*^{2}, the frozen
bottle, because energy has been taken from it to cool and freeze the
water, will actually be lighter. However, the amount by which it will
be lighter will be unmeasurably small, so it may be ignored. A rough
estimate: suppose that 1,000 J of energy are removed in doing the
freezing; the mass equivalent is 10^{3} J/(3 x 10^{8}
m/s)^{2} which is about 10^{-14} kg!]

**QUESTION: **

This is a question that's
bugged me for a long time. If you can shine a light into a hollow
perfectly smooth, reflective sphere with no means of the light escaping
that sphere - is any sort of energy built up within?

**ANSWER: **

There is no such thing as a
perfectly smooth, perfectly reflective surface. If there were, energy
would build up inside the sphere.

**QUESTION: **

I understand that the speed
of light is a constant, ie it is always the same in all circumstances.
I have also been taught that refraction is caused as light hits a
substance, through which it can pass, at an angle and is slowed. The
lower part of the wave hitting before the upper, relative to the
surface, and slowing causing an angle in the lights path..
So which is it, is light actually slowing when it travels through a
substance or not?

**ANSWER: **

The law is that the speed of
light * *__in vacuum__ is the same for all observers. Light,
when passing through matter, moves slower.

**QUESTION: **

Real life question: Tire pressure on
and off the car: I am getting a new tire for my car. While it's on the
rack, they check the pressure and it's a perfect 32 psi. They put the
tire on my car, then lower the 3000 pound car back down on it, and say
see ya' later. I say,"Shouldn't you check the pressure while the weight
of the 3000 pound car is down on it?" "Nah", they say, it doesn't
change. That doesn't make sense to me. I actually asked this question to
my brother who is a ultra-high vacuum physicist at Sandia Labs, and he
didn't know. I also asked this question at the famous Cartalk.com forum
and got laughed out of it.

**ANSWER: **

Here is the basic physics, the ideal
gas law: *PV=NRT* where *P* is pressure, *V*
is volume, *T* is absolute temperature,* N* is the amount of
gas, and *R* is a constant of nature. Let's assume that* T*
stays the same when the car is lowered off the rack. Now, presumably the
volume of the gas in the tire decreases a little bit; therefore, the
pressure must increase a little bit to keep the product *PV *equal
to the constant *NRT*. However, the volume changes by a very small
amount compared to the total volume of the tire, so for all intents and
purposes (but not exactly) "it doesn't change".

**QUESTION: **

If you consider a rock
hanging from a two vertical massless ropes with a symetrical wieght
distribution, and the system is staionary, is there anyway possible
that the tension in the ropes will be greater than or less than half
the weight of the rock?

**ANSWER: **

It depends on where the
strings are attached to the rock. If one is directly above the center
of mass, it will carry all the weight and the other will have zero
tension. If they are equal horizontal distances from the center of
mass, each will carry half the weight. The thing is that the sum of all
the torques about the center of mass must be zero. So *T*_{1}*d*_{1}*=T*_{2}*d*_{2}
and *T*_{1}*+T*_{2}*=W*. where *d *is
the distance of each string horizontally from the center of mass.

**QUESTION: **

How does High voltage
transmission of electricity through long distances helps in reducing
the energy loss during transmission?

**ANSWER: **

The power* P *dissipated
in a resistor *R* is *P=IV*; if you increase the voltage
and keep the power the same, the current becomes small. But, in the
transmission line, if you use Ohm's law *V=IR*, P=*I*^{2}R,
so low current means low power loss.

**QUESTION: **

By the phrase "High Tension
wires" what should we asssociate the meaning for "Tension"? Frequency
(Hz) ? Volts ? Current strength? (Amps)?

**ANSWER: **

The voltage is high. The
current is low. The frequency is 60 Hz.

**QUESTION: **

I have a question concerning
a dream I had when I was 12. Now I am 22 but I just thought of it
again. I'm not much for math, but this question has more to do with
physics and the rules of the universe. So, my dream was about Jimminy
Cricket of "Pinocchio" fame sitting on the Jolly Green Giant's shoulder
while floating in the middle of outer space. In the dream the Green
Giant was two light years tall while Jimminy was like an inch or two
high. The question I woke up with was how long did it take each
(Jimminy and the Giant)to see the Green Giants feet? Would it take both
the Giant and Jimminy two years to see the Giant's feet? Is mass in
anyway associated with the speed of time, with the greater the mass,
the faster the time? I think that the Giant would be able to see his
feet before Jimminy could. Sort of like how smaller moving objects,
like insects, blood and obviously atoms appear to be moving fast for
someone of human size, but does blood or an atom feel they are going
ridiculously fast? I know that this question must have been asked and
answered, but I don't know where to find the answer. And you guy's
appeared in a google seach titled 'ask a pysicist.'

**ANSWER: **

The way you "see" something
is to detect the light which came from it. Both the giant and the
cricket, at any given time, see light which left the giant's feet 2
years ago. It makes no difference what the masses of the detectors are.

**QUESTION: **

The question deals with the
center of gravity for a very specific object.
Given a cylinder 12 inches in diameter and 8 inches long which is made
of a homogeneous mass distribution; that has a 1.5 inch hole through
it's center in the radial plane and is subjected to a uniform field.
Viewed from the radial plane and aligned so as to see through the hole
where would the center of gravity be?
Viewed from the radial plane but orthogonal to the through hole where
would the center of gravity be?
I really don't need a specific numerical value but only to know if the
center of gravity moves or does it stay located at the same place and
is it the center of the volume?

**ANSWER: **

The center of gravity is
independent of any external field and independent of how you view it.
This object has the center of gravity on the axis of the cylinder and 4
inches from one end.

**QUESTION: **

Could antimatter ever be a
threat to space travellers especially for space travelers within a
solar system?

**ANSWER: **

Certainly not in the solar
system since if there were any significant amount of antimatter we
would certainly have observed its effects. There is also no evidence
that there is a significant amount of antimatter anywhere in the
universe. So, I would say, the answer to your question is no.

**QUESTION: **

I had a question about
gravity. I have read that Einstein said gravitation is caused by
geodesics and the tendency of mass to follow them. Is gravity a force?

**ANSWER: **

A force is something which
causes an object which feels it to accelerate; so gravity is certainly
a force in the classical sense. What is the origin of this force? That
is what general relativity answers by saying that space is warped by
mass, that is the gravitational force results from the geometry being
altered by the presence of mass.

**QUESTION: **

I am a librarian assisting a
library patron. The patron says at one time he had a book that gave him
a formula to compute the weight of an object. If you put an object,
such as a car, on a tire or ball or something that is pressurized, and
you know the PSI, you can measure the size of the point of contact with
the ground (the flat surface of the tire on the ground) and calculate
the weight of the object.

**ANSWER: **

Consider a piston of cross
sectional area *A*, vertical, which has a pressure *P*
under it and a weight *W* sitting on it and everything is in
equilbrium; for simplicity, neglect the weight of the piston itself or
imagine it to have been absorbed into *W*. We must not forget
that there is an atmospheric pressure *P*_{a} pushing
down on the cylinder. Then Newton's first law specifies that the sum of
all the forces must add to zero, and so *PA-W-P*_{a}*A*=0
(pressure time area equals force) so W=(*P-P*_{a})*A. *But
(*P-P*_{a}) is what is called the guage pressure, it is
the pressure which most pressure guages read, the amount over (or
under) atmospheric pressure. So 30 psi means, usually, 30+14.7 psi
since *P*_{a}*=*14.7 psi. This seems to me to be
equivalent to your question. Let's check it for reasonableness: suppose
a car has each of its four tires in contact with the ground by an area
of 6"x4" and the tire (guage) pressure is 30 psi. Then the weight of
that car would be 6x4x4x30=2880 lb which is about what cars weigh.

**QUESTION: **

Is it possible to accurately
measure the speed of a moving vehicle by just watching it?

**ANSWER: **

Well, I guess that depends
on what you mean by "accurately" and what you mean by "watching it". In
order to make an accurate measurement of speed you need to measure a
time accurately and a distance accurately. Hence, if you know the
distance between two landmarks and time the car from one to the other,
its average speed is the ratio of distance/time. If you use your
experience to judge the speed, I would call that estimating the speed
not measuring it.

**QUESTION: **

If the moon were to leave
earth orbit into space, what would be the effect(s) on earth .

**ANSWER: **

The most noticeable would
likely be that the tides would nearly stop. Obviously, there would be
no more solar (or lunar) eclipses. It is well established that many
biological systems depend on the timing of the phases of the moon to
time their functioning, but I am no expert on that. The moon also
affects the precession of the axis of the earth, but this is a pretty
small effect.

**QUESTION: **

what is the difference in
brightness of three lamps if they are connected in parallel/series

**ANSWER: **

I assume they are identical.
I will also assume that the light intensity is proportional to the
power dissipated by the bulb; this is not a very good approximation
because the resistance of tungsten wire is dependent on its temperature
which is in turn dependent on the current through it. Then brightness
depends on power which is proportional to *V*^{2} where *V*
is the voltage across the bulb. The bulbs in series will have only 1/3
the voltage across each as the bulbs in parallel, so they will be only
1/9 as bright.

**QUESTION: ;**

Is there a scientific proof
that the atom is neutral?

**ANSWER: **

Basically you are asking if
the magnitudes of the proton and electron charges are equal. Many very
sophisiticated experiments have been done and the best results to date
indicate that the charges are equal to an order of about 10^{-21}
where the magnitude of the electron charge is 1. In other words, you
would have to go to at least the 21^{st} decimal place to see
any difference.

**QUESTION: **

What keeps the protons and
electrons together to form an atom?Gravity?Let`s speak on a simple atom
of hydrogen.How can the proton+ which is 1840 the mass of the electron-
be electrically balanced?

**ANSWER: **

The Coulomb force holds the
atom together; this force is due to the electrical charges on the p and
the e and those are equal but opposite in sign (there are two kinds of
charge). Gravity is totally negligible in atoms and the relative masses
of the two has nothing to do with the problem. Actually, that is not
quite true: if a proton and an electron had equal masses they would
orbit around a point halfway between them but this has nothing to do
with gravity.

**QUESTION: **

The medieval model of the
solar system, which places the earth at the center and the other
planets (including the sun and moon, per the medieval definition of
"planet") in orbit about it, is incorrect; however, if one makes a
mathematical model of the solar system by, e.g., assigning a position
vector to each object, and then subtracting earth's position from each
object, one obtains what seems to be a consistent, working geocentric
model. In fact, it vaguely resembles the less popular medieval model
designed by Tycho Brahe.

Is there a reason that this
model is inaccurate? It seems that the heliocentric vs. geocentric
argument is really just a question of which reference frame should be
preferred, when in fact there is no preferred reference frame. Granted,
the geocentric model I have suggested is cumbersome and less useful for
practical purposes, but it seems that it is accurate. Most people
believe that the sun is at the center of the solar system and that
ignorant persons of the past believed that the earth was at the center.
It seems more appropriate to say that one can arbitrarily choose a
center, and that ignorant people of the present think that the choice
of center is important.

Am I wrong? I have been really
curious to discover whether or not I'm just missing some important
point.

**ANSWER: **

Suppose that you are in a
very large rotating drum (they have rides like this at an amusement
park sometimes). You perceive yourself as being pushed into the wall
and if the drum spins fast enough you will be crushed by this "force".
What is actually happening is that, because you move in a circle, you
are accelerating even though your speed stays the same because the
direction of your velocity is constantly changing. Because of Newton's
second law, a force is required to keep you moving in this circle and
the wall of the drum exerts a force on you to achieve this
acceleration. Now suppost there is a man at rest standing in the center
of the drum. He feels nothing at all. Now, you want to say, "Let's
choose me as being at rest and the other guy going in a circle around
me; that will be just as good a description of the situation." But,
alas, as you can see, there is a world of difference. If two objects
have constant velocity it makes no difference which you consider at
rest, but if one is accelerating and the other is not, they are not
equivalent. Finally, you know that the earth moves the way it does
because there is a force on it by the sun; the sun feels the same
force. But since the sun is so enormously more massive than the earth,
there is no way this force could cause the sun to move in an orbit
around the earth.

**QUESTION: **

Why gravitational constant
cannot be determined accurately just like c=299792458 m/s.As far as
possible this was the result-:
G=6.6732 X 10^-11 in units -m^3 kg^-1 s^-2.

**ANSWER: **

There are several answers.
First, since the meter is defined in terms of the distance light
travels in a given time interval, the speed in m/s is, essentially, a
definition and not a measurement. Still, in order to make this
definition, the speed of light had to be measured very accurately in
terms of the older definition of the meter. The speed of light (or
anything) is relatively easy to measure accurately: if you have very
accurate clocks and rulers you can measure a speed very easily. The
gravitational constant, on the other hand, requires that you measure
very accurately a mass (not too hard), a length (not too hard), and a
force. But the gravitational force between two laboratory-sized masses,
say a couple hundred kilograms, is very difficult because gravity is
nature's weakest force. A group at the
University of Washington has been performing innovative experiments
for many years trying to improve the accuracy of G.

**QUESTION: **

Has any 2 (atleast) of the 4
fundamental forces been successfully unified just like electricity was
joined to magnetism earlier?

**ANSWER: **

The weak interaction has
been unified with the electromagnetic interaction; one refers to the
electroweak force. The weak, electromagnetic, and strong forces have
been unified into what is referred to as the standard model of particle
physics. Gravity is the odd guy out.

**QUESTION: **

The law of physics are the
same on every point of the surface of the planet Earth or not?

**ANSWER: **

If it is truly a law of
physics, it is true everywhere in the universe.

**QUESTION: **

Please can you explain what
happens to the energy released by the shattering of a glass on a hard
surface? We are told that the energy on Earth has remained constant
since the formation of the planet so what is the fate of the energy
produced by this event?

**ANSWER: **

What makes you think energy
is released? Why does a piece of glass not just spontaneously break?
The fact is, you must put energy into the glass to make it break. If
you drop it, it has kinetic energy when it hits and then the surface
does work on it by exerting forces on it. So the question should be
what happened to the energy which got put into the glass to break it.
It takes work (energy) to break molecular bonds which were holding the
glass together before it broke; there goes some of the input energy. It
makes a big crash; there goes some more of the energy (sound). It will
heat up a little bit; there goes some more of the energy.

**QUESTION: **

What sort of interaction
between the atoms and photons makes them to be reflected (bouncing of
the mirror) and/or refracted (like through diamond) ?.If the answer
involves quantum mechanical implications does that pose any limitation
to the possible making of perfectly reflective mirrors?

**ANSWER: **

Photons interact with
electrons via the electromagnetic force. However, it is much more
fruitful to understand reflection and refraction by considering light
as waves. Then, whenever a wave encounters a medium of a different
index of refraction (that is the light travels at a different speed) it
has the possibilities of either reflecting or refracting. The amount of
each depends on numerous things, particularly angle of incidence, both
indiexes of refraction, and polarization. There already is a perfect
mirror which is total internal reflection which is used for fiber
optics for example. (Please note that I say "perfect" in a hypothetical
way since no surface is perfectly smooth and all media absorb light, so
no reflection is really 100%.

**QUESTION: **

Fusion of (ionized) hydrogen
molecules is done by increasing their temperature AND squeezing them
using powerful electromagnets.(right?). If so, is it possible to "FUSE"
them under normal room temperature just by indefinetly increasing the
electro-magnetic force?. If so possible, what about "FUSION" under
temperatures near 0 Kelvin ?

**ANSWER: **

The magnetic fields are not
to "squeeze" them but to confine them. The high temperatures are
required so that the positive ions have enough energy (that is enough
speed) to overcome the electric repulsion from other positive ions.
They need to get close enough to feel the nuclear force for fusion to
occur and slow ions cannot do this. Furthermore, magnetic forces are
perpendicular to the direction of motion so this force cannot squeeze;
also, the magnetic force is proportional to the speed of the particle,
so the slower the particle is moving (cold) the smaller any magnetic
force is.

**QUESTION: **

Are there any acceptable
alternatives to the current Big Bang model of the Universe?
What are they? What is the best evidence for the Big Bang model?

**ANSWER: **

I know of no reputable
astrophysicist who would not accept the big bang as the only viable
theory of the beginning of the universe. This is not to say that there
are not problems (like where did all the energy come from?). The best
evidence for the big bang are the
microwave background and the fact that the universe is observed to
be expanding out from a single point. A more interesting question to
most astrophysicists than the birth is the ultimate fate of the
universe; answering this question involves the currently fashionable
topics of dark matter and dark energy.

**QUESTION: **

SIr why does gravity so
different from other forces that it doesn't depend on the mass of the
object where the gravitational force acts?

**ANSWER: **

I guess you are asking why
all objects have the same gravitational acceleration; the reason is,
simply that the acceleration is inversely proportional to the mass but
the force is proportional to the mass and so mass cancels out. See an earlier answer for more
details.

**QUESTION: **

am a member of a group of
people with an interest in space & the universe. We have been
having a debate that is no closer to being solved than when it first
arose. This is topic being debated: If an alien race were to live on a
planet several light years away from Earth, we know that Earth would
look like a star in their night sky. We also know that the light they
saw would've left Earth many many years ago; perhaps even when the
dinosaurs lived. If they were to have a telescope SO powerful that it
could zoom in on the living animals on the surface of Earth, would they
be zooming in to see the animals of present-day Earth? Or, would they
be looking at the dinosaurs? I would VERY much appreciate if you could
help us in finally putting this debate to rest.

**ANSWER: **

To see something, your eye
(or telescope) must detect light which was emitted from that object (or
reflected from it). So, when you look at a friend who is 100 m away,
you are not seeing him as he is right now but how he was 100/3 x 10^{8}=3.3
x 10^{-7}s ago. 1/3 of a millisecond is a quite measurable
time. Now suppose you are on a planet which is 100 light years from
earth. When you see the earth you are seeing as it was 100 years ago
because a light year is the distance light travels in a year. The moon
is 1.3 light seconds from the earth and the sun is 8.3 light minutes
from the earth. So, when you see the moon you are seeing it as it was
1.3 seconds ago. If the sun were to blow up right now, you would not
know it for 8.3 minutes.

**QUESTION: **

Is there a thought
experiment that shows (we can deduce from it) how mass increases at
relativistic speeds just as there's plenty of such to show how
coordinates transform?

**ANSWER: **

I am not aware of a simple
explanation such as those used for length contraction and time
dialation. In fact, there is no particular need to even say that mass
increases; what you must do is redefine momentum such that momentum is
conserved for an isolated system and one possible interpretation of
this redefinition is that mass increases. See my earlier discussion of
this topic.

**QUESTION: **

In the phenomenon of
polarisation, when a ray of light is passed through a crystal, the ray
splits into two, on the basis of the direction of vibration. How is it
possible when the light is a combination of electric and magnetic
vectors vibrating in mutually perpendicular direction?

**ANSWER: **

An unpolarized beam of light
has electric fields pointing in random directions; for each ray there
is also a magnetic field normal to the electric field. Light which is
polarized has all electric fields pointing in the same direction and
all magnetic fields are perpendicular to the electric fields. It is
convention to choose the direction of the electric field as the
direction of polarization but the magnetic field is still perpendicular
to that direction. The phenomenon you cite is called birefringence and
the split beams have different polarizations.

**QUESTION: **

why do the astronomers say
that viewing an event like a supernova is like looking back in time?

**ANSWER: **

Because they are far away
and when we witness the event, the light has been traveling for
thousands or millions or billions of years to get to us.

**QUESTION: **

is the energy carried by an
infrared photon greater or smaller than the energy carried by a visible
photon light?

**ANSWER: **

The energy is proportional
to the frequency. Infrared has a lower frequency than visible light, so
the infrared photon has a lower energy.

**QUESTION: **

why do bats and owls have
good night vision compare to humans?

**ANSWER: **

You have probably heard the
phrase "blind as a bat"; well, bats are not really blind but their
eyesight is not very good. The way they "see" using sound waves like
radar: they emit ultrasound which then bounces off things in their
environment and they are able to navigate by hearing the echos. They
might as well be blind. Owls, however, have very good night eyesight.
There are several things about their eyes which give them good night
vision:

- Their eyes are quite large,
- the iris can open very far to
let in more light,
- the eye is cylincrical rather
than spherical which allows the retina to be larger,
- the retina is packed with a
great many "rods", cells most sensitive to low-level light (cones, the
other type of vision cell, allow color vision), and
- the back of the retina is
reflective which means that light which does not interact with the rods
on its way in gets another chance.

Most animals have better night
vision than we do because of the reflective layer called the *tapetum
lucidum * which we do not have. That is the reason that the eyes of
many animals at night tend to shine when light is shined at them--it is
reflected back.

**QUESTION: **

Why does the fundamental
wavelength of a string increase as the tension on the string increases?

**ANSWER: **

You are putting the question
wrong since "fundamental wavelength of a string" really has no meaning.
The fundamental frequency of vibration of a string clamped at both ends
depends on the length of the string and the speed of waves in the
string. For the fundamental, the wavelength on the string is 1/2 of a
wave and the velocity is proportional to the square root of the
tension. The wavelength l on the string stays the same as tension
increases but velocity *v* increases. The frequency with which
the string vibrates is given by *f=v*/l, so the frequency increases when the tension
increases (which is, of course, the way you tune a stringed
instrument). If you are asking about the wavelength of the resulting
sound (which has frequency f) then it is given by *l*_{s}*=v*_{s}/*f *where
*v*_{s} is the speed of sound in air and * l*_{s}
is the wavelength of sound in air, so that wavelength is shorter when
the tension is increased because the frequency is larger.

**QUESTION: ;**

I understand the theory
behind evaporation - some molecules have average kinetic energy that is
great enough to enable them to escape the intermolecular forces that
hold them together as a liquid. I'm given to understand that the
kinetic energy is a Maxwell distribution? A bell curve? Also, when
evaporation occurs, the liquid becomes cooler, because it, as a whole,
has less energy. If this is so, why does evaporation go to completion?
So the majority (or large portion of molecules) dont have enough KE to
escape, and when the ones that DO have enough KE to escape, actually do
so, the temperature (and hence average KE) decreases for the liquid -
shouldnt this mean that LESS molecules have enough energy to escape,
and then evaporation will eventually stop?

**ANSWER: **

The Maxwell distribution is
not a bell curve since it cannot exist below zero. And, this
distribution of kinetic energies is for ideal gases. But neither of
those points are really germaine in answering your question; the
important point is that the distribution is something which has one
maximum the position of which depends on the temperature, approaches
zero as kinetic energy approaches infinity, and is zero at kinetic
energy equals zero. So, as you state, a small but nonnegligible number
have kinetic energies large enough to escape; of course the direction
of the velocity matters too (velocities into the fluid will not come
out even with enough energy). Now, when the high-energy particles
escape they leave a gap in the distribution and so, in order to
maintain the same distribution of energies some lower-energy particles
speed up but, in order to conserve energy this means the whole
distribution must shift to a lower temperature (that is some other
paricles slow down); that is the cooling. Rate of evaporation does
depend on the temperature, but this is not a huge effect for modest
temperature changes. In the real world the fluid is usually in contact
with its environment and tends to come to thermal equilibrium with it;
hence, when you set a glass of water on the table in a room at a given
temperature, water will evaporate at a pretty constant rate as the room
continually warms up the water. The most important factor affecting
evaporation rate is the surface area and that does not change. Finally
we get to the situation where only the last single-molecule layer is
left. Now the overriding factor is how does it bond (or not) to the
substrate. But even if this last layer of water stayed there, you would
likely judge the container as bone dry because the number of molecules,
while still very large, would be tiny compared to a macroscopic amount
of fluid (say a teaspoon of water).

**QUESTION: **

When two objects “a” and “b”
make an elastic linear collision, the after ci=ollision velocity of
object “b” is given by Vb'=(2Ma/(Ma+Mb))Va+((Mb-Ma)/(Ma+Mb))Vb And a
similar equation holds for object “a”. As I understand it, these
equations are derived algebraically from conservation of kinetic energy
and conservation of linear momentum. Suppose the objects are billiard
balls and each is rotating about its center of mass with constant
angular velocity. If I assume no energy is lost due to friction when
the two surfaces are in contact (ok, maybe not realistic, but it
doesn’t seem too unreasonable for an approximation ??), would analogous
equations hold for angular velocities? ie, can I replace mass by moment
of inertia and replace velocity by angular velocity in the above
equation to get after collision angular velocity? I can’t see why not,
given that angular momentum and rotational kinetic are conserved, but I
have not seen such formulae anywhere.

**ANSWER: **

The equations you quote are
true only for one dimensional collisions, collisions where all the
velocities before and after are directed along a line. There is a much
more general solution if the balls scatter to different directions. You
are right, angular momentum must also be conserved if the balls come in
with spins as long as the table is frictionless; otherwise the table
would exert an external torque. Also, the angular momentum due to the
velocity of the balls could not be ignored; they have no such angular
momentum in a head on collision, but that would probably not be the
case usually. In addition, the pertinent inertial parameters would be
moment of inertia, not mass. If there were friction when the balls were
in contact, angular momentum would still be conserved but energy would
not, further complicating the problem. So the answer to your question
is a resounding no: there is no such simple equation for the real world
situation. The problem is sufficiently complicated that numerical
methods on a computer would likely be required to make accurate
prediction.

**QUESTION: **

The compressions and
rarefactions of sound waves generate adiabatic temperature fluctuations
in the medium (take air). Is there any limit to the temperature
fluctuation? or., is it possible to create sound waves with such an
intensity that TEMPERATURE inside COMPRESSION reaches SEVERAL THOUSANDS
(if not possibly millions) of degrees (and temperature of rarefaction
reaches NEAR ABSOLUTE ZERO)? (it is useful to completely sterilise the
air)..

**ANSWER: **

Let's look at the pressure
fluctuations in a sound wave. At the threshhold of pain, the loudest
sound you can hear without feeling pain, the pressure variations amount
to about 30 N/m^{2}; compare this to the pressure of the air,
about 100,000 N/m^{2}. I believe that the resulting local
temperature fluctuations would be negligible.

**QUESTION: **

How would I draw a diagram
that shows refraction of light that causes "water-like" mirages on the
pavement.

**ANSWER: **

I plagarized this from
Tipler's excellent book *Physics For Scientists and Engineers*,
Freeman/Worth Publishers.

**QUESTION: **

Why does a diamond glitter
so much?

**ANSWER: **

In a nutshell, it is because
diamond has a very high index of refraction, 2.42. For reference, the
indices of refraction of glass and water are about 1.5 and 1.3
respectively. What this means is that light travels much more slowly in
diamond than in air and the result of this is that it is very much bent
when it goes from air to diamond or *vice versa*. It also has the
effect that much of the light which enters the diamond does not go
through but is reflected back (due to something called total internal
reflection, also the way that fiber optics works). This effect can be
accentuated by cutting the diamond cleverly and that is the purpose of
the facets. Therefore, the "glittering" is because most of the light
which strikes it bounces back toward you.

**QUESTION: **

I am learning about magnetos
in school, and we were taught that they have a tendancy to arc at high
altitudes. Why is this? Does the Permittivity of air change with
temperature and pressure?

**ANSWER: **

The only thing I found about
this topic is very interesting. It says that the arcing is temperature
dependent, not altitude dependent. Thus, when a pilot takes off the
temperature of the coil is relatively low but, as time goes on, the
temperature of the magneto gets higher and, of course, this will be
happening at higher altitudes so the pilot reports that the magneto
problems occur at higher altitudes but the culprit is really
temperature. You can read a more complete explanation here.

**QUESTION: **

If the effects of general
relativity are taken into account then does mass of an object A near
another large massive object B depend on A's distance away from B?.

**QUESTION: **

Consider this situation
where a heavy ball of'rest mass' of value 'm0' be thrown upwards at
velocity 'v' such that it reaches the height 'h' before falling back;
according to the law of conservation of mass-energy, the sum of kinetic
energy,potential energy and the energy of 'rest mass' (m0c^2) are
conserved at ground as well as at height h. But the gamma factor isn't
same. Let m1 be the relativistic mass due to velocity at ground and m2
be the 'rest-mass' at height h. Apparently m2=m1 since the mass-energy
is conserved. but m1=m0*gamma(v) at ground,hence m2 = m0*gamma(v) at
'h'. clearly the gravity was little less at 'h' than it was at the
ground. Does that mean that the "rest-mass" will be more under less
gravity?

**ANSWER:**

These two questions both essentially ask the same thing--what
is rest mass in general relativity. Having done a little research, I
find that this is not an easy question to answer because several
different definitions are used. A discussion of this question would be
too lengthy for this site, but there is a good discussion at
Answers.com.

**QUESTION: **

A polythene rod can gain a
negative charge when rubbed with a cloth. a) Explain, with reference to
electrons, what has happened? b) Why is difficult to detect any charge
on the cloth?

**ANSWER:**

This is called the triboelectric effect. In fact, for charge to be
transferred from one to the other, only contact is required, not
rubbing. Different materials are placed in the "triboelectric series",
those near the top tend to give up electrons (become positively
charged) and those near the bottom tend to gain electrons (become
negatively charged). Polyethylene is near the bottom and wool or silk
near the top, so the polyethylene gains electrons on contact. The
magnitude of the effect depends on many different things and is
generally not very predictable. You can read a detailed explanation in Wikepedia.
I am not certain why the charge on the cloth is not so easy to detect,
likely that it is easier for something to gain electrons from the air
(lose positive charge) than to lose them (lose negative charge). Or
maybe it is because the cloth has so much more surface area over which
to spread the charge. Or maybe the sharp points (fibers, rough areas, *etc*.)
in the fabric encourage corona discharge.

**QUESTION: **

How can you tell if a point
is 180 degrees out of phase?

**ANSWER:**

I presume that you mean phase relative to some other wave. First,
define a periodic wave: it is one which, after some elapsed time *T *(period)
repeats exactly what the wave did since the time *t*=0 until time
*t=*2*T*, and so on. One could also define it in terms
of space: it is one which, at any particular time, repeats its shape
when you travel along a distance *l * (wavelength). Let us call the the time of the
beginning of the wave *t*=0 and the time of the end of that one
period *t=T*. Then 0 corresponds to 0 degrees and *T*
corresponds to 360 degrees. Thus, the exact middle of the wave
corresponds to 180 degrees. Now, if another wave of the exact same
shape is such that its beginning is at* t=T*/2, it is said to be
180 degrees out of phase with the other wave. An example of two waves
180 degrees out of phase (red and black) is shown at the right. Notice
that if you were to add these two waves up you would get zero; that is
another way you can tell if two waves are 180 degrees out of phase. You
really should think of waves, not points, as having relative phase.

**QUESTION: **

what would be the weight of
a astronaut standing on the moon whose earth weight is 180lb

**ANSWER:**

The acceleration due to gravity on the surface of the moon is about 1.6
m/s^{2} and on the earth it is about 9.8 m/s^{2}, so
the weight of something on the moon is (1.6/9.8)*W*_{e}
where W_{e} is the weight on the earth.

**QUESTION: **

When an airplane engine
spins, it creates an image of the propeller standing still or barely
rotating. You can also see this with car tires, fans, or any other
spinning things. What causes it to look as if the propeller is barely
rotating when it is at high rpm's?? Also, why does the image change
directions???

**ANSWER:**

I do not believe that you will see this effect in sunlight, just
artificial light which has an otherwise imperceptible flicker. Also,
you often see this effect in movies or on television (you know, the
wagon wheels on a western which look like they are going backwards).
The explanation is in an earlier
question I answered.

**QUESTION: **

How can photons exert
pressure (Nichols Radiometer) if they have zero mass?

**ANSWER:**

In special relativity we find that anything, like a photon, with zero
mass travels with the speed of light and that it posesses both kinetic
energy and linear momentum. Since a photon has momentum it can transfer
momentum to something and thereby exert a force.

**QUESTION: **

G is the graviational
constant, but I don't know what it's worth. I don't know what the mass
of an electron is either, or a proton for that matter. But what,
according to the best numbers we have, would be the strength of the
gravitational field of a electron, proton, or heck, even a neutrino be?

**ANSWER:**

You can easily look these constants up.* G*=6.7 x 10^{-11 }N
m^{2}/kg^{2}, *m*_{e}=9.1 x 10^{-31}
kg, *m*_{p}=1.7 x 10^{-27} kg, *F*_{g}*=Gm*_{p}*m*_{e}/*r*^{2}
where *r* is the distance between the two. I take r=0.5 x 10^{-10}
m, approximately the size of an atom. The force turns out to be about 4
x 10^{-47} N. To put this in perspective, the electrical force
between the two is about 9 x 10^{-8} N, so gravity is totally
negligible on the atomic scale. The neutrino mass is far less than that
of an electron, so gravity plays essentially no role in its
interactions either.

**QUESTION: **

As I was driving down the
street looking at houses on my right, I noticed my cars shadow on the
houses (approching the streetlamp on my left). My shadow caught up and
passed me. Like a lever and I was the fulcrum. Using this anology, if
light approched an object closer that its shadow was cast, wouldn't the
shadow be moving faster?

**ANSWER:**

Yes.

**FOLLOWUP
QUESTION: **

You answered "yes" to my
posted question about a light approching an object that cast a shadow
further than the distance of the lights approach. Faster than light
speed! I thought light was the theoretical limit?

**ANSWER:**

I guess I don't understand your question. There is no difference
between your moving or the source of light moving. For example, if you
move at 50 mi/hr, the source is at rest, and the shadow moves at 150
mi/hour then the shadow moves at a speed of 100 mi/hr relative to you.
If you are at rest and the source moves with a speed 50 mi/hr then the
shadow moves with a speed of 100 mi/hr relative to you. This assumes
that the geometry has not changed (distances between you and the source
and the shadow. The "speed limit" is that nothing can move faster than
the speed of light, not, as you seem to suggest, faster than the source
of the light. However, it is subtler than this. In fact, the shadow may
move faster than the speed of light because the shadow is not
"something". You more often see the example of taking, for example, a
laser beam and shining it on the moon; now rotate this laser very fast
so that the spot on the moon moves faster than the speed of light
(which is pretty easy to do). But, that spot, again, is not
"something". The acid test is that if you imagine the shadow moving
(more quickly than the speed of light) from point A to point B, you
must not be able to use this moving shadow to transmit information from
A to B.

**QUESTION: **

This question deals with
free-float. An object is falling toward earth. A tunnel has been
previously excavated completely through the earth at exactly the
location of the object's landing, through the core and out to the other
side of the planet. The object continues its fall through the tunnel
without touching the sides of the tunnel. I know the earth's rotation
is an issue, but imagine that the object makes it through untouched.
Where would the object stop its fall? Newtonian gravity was described
as an attraction to the center of the planet. But that is no longer our
understanding of gravity. Would the object, travelling at its terminal
velocity exit the earth on the opposite side, travel up into the air,
then fall back to earth? Or would the object travel just to the surface
on the opposite side, then fall back into the hole, thus continually
boomeranging through the earth? Or maybe something else?

**ANSWER:**

I recently answered
this question.

**QUESTION: **

Have you seen ' YouTube -
Walter Lewin Makes a Battery out of Cans and Water ' I have never seen
anything like it !! My friend asked me to give it my best shot.. we are
both in our 50's, and not students.. My response is below. Do you know
how this works?

**ANSWER:**

This is called Kelvin's thunderstorm or Kelvin's waterdrop
electrostatic generator. There is a pretty good explanation here.

**QUESTION: **

Which is the difference
between matter and waves? Which is property that says that matter is
matter and waves are waves?

**ANSWER:**

Everything is both particle and wave. If you look for a particle, you
will find one. If you look for a wave, you will find one. The classic
example is light. If you take light of a particular color (wavelength)
and do an interference experiment (for example the Young double slit
experiment) you will only be able to understand the experiment if you
say "light is a wave". If you take the very same light and shine it on
a metal and measure the properties of the ejected electrons
(photoelectric effect) you will only be able to understand the
experiment if you say "light is particles".

**QUESTION: **

If Resistance of super
conductors is ZERO then how would we calculate amperes if a current is
flowing through it formula:- Amps=Volts / Resistance.?

**ANSWER:**

Ohm's law is not universal, it only applies approximately to some
materials under some conditions. There is no reason to suppose a
superconductor is ohmic (obeys Ohm's law) but it does: *V=IR*, so
if R=0, then *V*=0 no matter what *I* is. So a current may
flow with no potential difference. Another way to say it is that a
superconductor is everywhere at the same potential regardless of any
current flowing through it.

**QUESTION: **

If two hydrogen atoms are
sitting alone next to each other, and they then combine to form a
hydrogen molecule, what happens to the energy produced by this
reaction? What form is it in?

**ANSWER:**

This is just a chemical reaction, and, as in most exothermic reactions,
the energy appears as heat. On a more microscopic scale, the energy is
in the kinetic energy of the H_{2 }molecules.

**FOLLOWUP
QUESTION: **

My question now is what kind
of motion does the hydrogen molecule acquire? When the (identical)
hydrogen atoms snap together to form the molecule they are moving
straight at each other; I can't picture in which direction the molecule
would move away, or is it the case perhaps that the molecule wouldn't
actually move away, rather the bond between the atoms would stretch and
contract in an endless oscillation (endless anyway until we introduce
something else into the system such as other molecules for this one to
bump into)?

**ANSWER:**

If the two were moving in opposite directions with equal
speeds, then they would have to be at rest afterwards (that is their
center of mass must be at rest). So the energy would have to be in
internal energy of the molecule, either rotating or vibrating. In this
case, the excited molecule would either break back apart or would decay
to the ground state via radiation. These "inelastic" mechanisims for
conserving the total energy could happen also in cases where the two
did not happen to have zero linear momentum before the collision. So,
if you want to understand it completely, it is more complicated than
just an increase in temperature.

**QUESTION: **

In a nuclear reactor, a
neutron hits a uranium atom, causing an explosion, then a chain
reaction. Where does the first neutron come from?

**ANSWER:**

A fissile material, like uranium or plutonium, will usually have a
small probability for spontaneous fission, that is fissions just happen
randomly in the material. Therefore you don't really need a source,
your fuel will provide needed neutrons to get the chain reaction
started. However, although I am not a nuclear engineer, I suspect most
reactions have a separate neutron source. The best known source
historically is to take an alpha particle emitter and coat it with a
light nucleus like berylium and there will be a reaction with neutrons
as one of the reaction products; one is the PuBe source, using
plutonium and berylium. you can learn form by looking for neutron
source in Wikepedia.

**QUESTION: **

What are the properties of
the cambdien rods that absorb neutrons in a reacto to control the rate
of reaction?

**ANSWER:**

I believe you mean cadmium. There are hundreds of stable nuclei and you
can shoot a slow neutron at any nucleus and there will be a probability
that the neutron will be absorbed. This probability is quantified by a
quantity called the neutron absorption cross section s, the larger the
probability the larger the cross section. Some cadmium isotopes have
unusually large values of s.

**QUESTION: **

what happened after Galilio
threw the two balls?

**ANSWER:**

It is my understanding that the experiment probably never took place,
that is it is an apocryphal story.
See this link. If it did take place as legend has it, the two balls
of different weights would have hit the ground approximately
simultaneously.

**QUESTION: **

How was the speed of light
calculated?

**ANSWER:**

I believe that the first part of an earlier
answer will answer your question. Essentially Maxwell's equations
predict waves which travel at the right speed.

**QUESTION: **

One thing that has always
been a question: When Rutherford fired "positive particles" at gold
foil, how was he able to separate atoms in order to "shoot" these
particles out? Similarly, when we talk about speeding protons around a
supercollider (like the Large Hadron Collider), again, how are these
protons isolated so they can be accelerated?

**ANSWER:**

Rutherford used alpha particles which came from radioactive decay from
heavy nuclei, that is these positive particles exist charged in nature.
However, one can rather easily make alpha particles from helium gas by
simply removing the electrons from the nuclei. Similarly the protons
for a proton accelerator can be made by ionizing hydrogen. There are
many types of ion sources but the simplest to think about is simply a
spark which is nothing more than a plasma of electrons and positive
ions in the gas allowing current to flow (mainly the electrons) across
a large voltage difference.

**QUESTION: **

Hi, if you change the mass
of a ball rolling down an inclined plane and the angle of the slope is
constant the final velocity of the ball will always be the same no
matter what its mass is! I know this is because acceleration due to
gravity on earth is constant but is there a better explenation. Is it
because you break the weight of the ball into two vector components:
Force parallel which accelerates the ball down the slope and also Force
perpendicular which supplies the normal force to the ball. When the
weight of the ball increases the two vector components also increase
and Force parallel increases to a magnitude which accelerates the ball
at the same rate if its weight were less. F=MA then if M increases F
parallel will also increase and A remains constant?

**ANSWER:**

You are making this harder than it need be. Essentially the reason
that the acceleration of gravity is constant is that weight is
proportional to mass and acceleration is proportional to mass and so
acceleration is independent of mass. See an earlier answer.

**QUESTION: **

When sleeping on an air
mattress does a person's body heat become lower than if they were
sleeping on a standard mattress? Is there any heat transfer?

**ANSWER:**

I think your question is answered by an earlier
answer. If you sleep on the cold ground, for example, heat will be
transferred more quickly from you to the ground by convection if you
are on an air mattress than if you were on a mattress which is a poor
conductor and consists of many "tiny air mattresses" as explained in
the earlier answer.

**QUESTION: **

How is it that gravitational
compression can dominate electrostatic repulsion between protons in our
sun to result in temperatures sufficient to support fusion? I am
anticipating ionisation of hydrogen and separation of electrons and
protons - the former to outer regions and the latter to core.

**ANSWER:**

I do not see why you would assume that the electrons and protons would
rise and sink respectively. In fact, when the temperature becomes large
enough to ionize the hydrogen, you have a plasma; if this plasma did
separate into positive and negative parts, then you would run into
problems with the Coulomb repulsion. In the unseparated plasma,
however, electrons around protons shield protons electrostatically from
other protons (and *vice versa*).

**FOLLOWUP
QUESTION: **

Why is it not reasonable to
expect separation of electrons and protons under the gravitational
force within the sun given the vast difference in masses of these two
entities?

**ANSWER:**

The dynamic effects of gravity are independent of mass; for example,
drop a bowling ball (proton) and a marble (electron) and both move
exactly the same.

**QUESTION: **

A 50-kg box is pulled by a
force at an angle of 30 to the horizontal. If the box accelerates at a
rate of 3 m/s2 , and coefficient of sliding friction is 0.4, what is
the magnitude of force pulling the box?
Problems I am having:
Imagining the box where is the rope attached? At the top right corner
or the bottom right corner?
I have not found a simple way to figure out which is cos and which is
sin. Please help!
I am studying for the MCAT.

**ANSWER:**

This is a problem where you are supposed to view the box as a point
mass, that is, you do not worry about torques, *etc*; it is a
simple Newton's second law, *F=ma*, problem. It makes no
difference where the rope is attached. The force has a component
horizontal which provides the acceleration, and a component vertical
which "helps the table hold up the box". So the equations to be solved
are:
50*3=-*f+F**cos30
0=-50*9.8+*N+F**sin30
where *f* is the frictional force which is *f*=0.4**N*
and *N* is the normal force. So you have three equations with
three unknowns, *F, N,* and *f.*

**QUESTION: **

Aside from the big bang and
black holes, are there other reasons to consider the unification of
gravity and the other forces (i.e. quantum mechanics) a fundamental
requisite for a complete theory of all that is?

**ANSWER:**

This is really a philosophy question rather than a physics question. It
is the philosophical bent of most scientists to seek to understand
nature using as few laws as possible. For example, if you found the
laws governing the flight of a baseball and the flight of a basketball,
you would be displeased to have separate laws for each; you would seek
an overriding law to describe the flight of anything.

**QUESTION: **

What is the medium through
which electromagnetic waves propagate? It's easy to see physical waves
go through water. And I can understand sound waves traveling through
air. But what is the stuff that carries electromagnetic waves?

**ANSWER:**

This is one of the classic questions in the history of physics and its
answer resulted in one of the great revolutions in physics, the theory
of special relativity. The simple fact is that, since it is electric
and magnetic fields which are "waving" and these fields may exist in
perfectly empty space, that electromagnetic waves may propogate through
perfectly empty space. They are the one wave which requires no medium
through which to travel.

**QUESTION: **

Is there a temperature at
which fire will not burn? Lets say that it is 10 degree F below 0. I
think you can create a burning fire at this temperature. But what if it
is 200 or even 2000 degrees below 0. Is fire still possible? Or is
there a point at which humans cannot create enough speed in the
molecules to create flames? Just a curious question. We were sitting
around and couldn't come up with a viable solution that we could all
agree on nor could we discover the answer online. We all agree that a
human probably couldn't survive at 2000 below 0 but you know.... Thanks
for any advice you might have..

**ANSWER:**

First of all, the lowest temperature is -459 F which is absolute zero.
It is tricky to just say the temperature at which you can have
something burn since it obviously depends on what you are burning. For
example, helium will not burn at any temperature and paper burns at 451
F (remember that book/movie *Fahrenheit 451*?). So a sheet of
paper below 451 F will not burn. But if you get it burning by elevating
the temperature at one corner, as it burns, since energy is being
released, the adjacent paper will heat up and burn until it is all
burned out; this is regardless of the temperature of the environment
around it as long as there is oxygen available to support the burning.
Oxygen liquifies at -130 F, so would not be available for burning
unless the paper were immersed in it.

**QUESTION: **

Chad Johnson,Wide receiver
of the Cincinnati Bengals football team recently raced a colt in a 100
meter race.Johnson covered the 100 meters in 11.720 seconds.How many
miles per hour was Johnson racing at?

**ANSWER:**

His average speed was 100/11.72=8.53 m/s. This can easily be converted
to mi/hr: 19.1 mi/hr. If you are interested in the details of the
conversion, write back.

**QUESTION: **

does light have weight?

**ANSWER:**

It depends on what you mean by weight. If you mean the classical
definition of the force which the earth exerts on something by virtue
of its mass, then light does not have weight because it has no mass.
However, if you mean is light affected by a gravitational field, then
you could say that it has weight because it bends in a gravitational
field as if it had gravitational mass; this phenomenon is explained by
the general theory of relativity where a gravitational field is viewed
as a warping of spacetime in the vicinity of a mass. An earlier answer may be of
interest to you.

**QUESTION: **

What is the definition of
dust and what is it's constituents?

**ANSWER:**

According to Wikepedia,
dust is defined to be anything with a diameter less than 500 x 10^{-6}
m. This is half a millimeter, so it seems rather large to me. At any
rate, dust can be composed of anything which exists as a solid at the
conditions of the environment.

**QUESTION: **

Our sky appears blue because
of the sun's light is scattrated by air molecules, and our sun appears
yellow/red at sunset for the same reason. My question is will the sun
appear white if you were viewing it from the surface of the moon?

**ANSWER:**

On the moon the sky is black and the sun is white.

**QUESTION: **

I'd like to ask how can I
convert Coulombs to Newtons, Newton to Kilograms and kilograms to
meters/second. For example how can I find the acceleration that can be
caused by the pressure of say, one ton?

**ANSWER:**

You might as well ask me how to convert elephants to tigers. All your
requested conversions are impossible to do because the units measure
different quantities. A Coulomb is a measure of electric charge, a
Newton is a measure of force, a kilogram is a measure of mass, and
meters/second is a measure of speed (and a ton is a measure of a force,
not pressure, in English units). The only possible answer I can give
you is that in common (not scientific) parlance in countries using the
metric system of units a kilogram is often used as a measure of weight;
this is technically incorrect because weights should be specified as
Newtons but in this context 1 kilogram is the weight of an object on
the earth's surface which is actually 9.8 Newtons. Hence, one could say
that 1 kilogram equals 9.8 Newtons when referring to the weight of an
object.

**FOLLOWUP
QUESTION: **

Yes converting was the wrong term.
What about deriving these units? For instance, by the coulombs law two
positive point charges of 1 coulomb gives an in-between repulsive force
of 8.988×10^9 Newtons. How they got to that number?

**ANSWER:**

One additional thing: it is the force between the two charges *
separated by 1 m*. Many laws of physics cannot be derived, they
must be determined experimentally. Th way you come up with what that
force is (after having appropriate operational definitions of what a
Coulomb and a meter are) is to actually measure the force. Of course,
you would not use 1 C charges because that is a huge amount of charge
(as is evident from the huge force). Rather you would take, for
example, two 1 mC charges separated by 1 cm in which case the
force would be 0.8988 N because *F=kq*_{1}*q*_{2}/*r*^{2}
where *k* is 8.988 x 10^{9 }N m^{2}/C^{2}.

**QUESTION: **

I have what I think are two
fairly simple and related questions about transfer of heat when a
person is sitting on cold metal bleachers. First, do people lose heat
faster through 1) the contact with the bleachers, or 2) the exposure to
the cold air (assuming no additional layers on either their lower or
upper half)? Second, when a person is in contact with a cold surface,
are pockets of air (like an air mattress) a better insulator than a
more solid insulation material (like a blanket or dense foam cushion)?
I am guessing that contact with cold metal draws more heat than cold
air, and that air is better than solid, but I don't have the science to
back it up.

**ANSWER:**

Heat is generally moved faster by conduction than by convection, so
your derrier will get cold faster sitting on the bleachers than
standing up; of course, since your body is a source of heat, it is
possible that you can actually warm the seat up which then reduces the
heat loss to the seat. The air is a better insulator than something
solid for the same reason. You are right on both counts.

**MORE:**

One thing I should have added is that an insulator made up of many
little "bags" of air is better than an equal volume of air (for example
something like styrofoam). A convection current in a big container of
air can be set up such that air flows quickly across the temperature
gradient whereas that cannot happen in the many little volumes. That is
why, of course, it is better to fill your walls with fiberglass
insulation rather than just let it be filled with air.

**QUESTION: **

I was thinking about
hydrogen and the fact that it is less dense than air, and water and the
fact that it is denser than air... Could the gpe gained by hydrogen,
and the gpe converted into kinetic energy by water be used?
By that i mean, water is allowed to fall, some sort of dynamo is turned
by the falling water (as in power stations) generating electricity.
This electricity is used to electrolyse water, producing hydrogen (and
oxygen). Hydrogen is allowed to rise, then when it reaches the top
again, it is burnt, producing water again. Surely there is an excess
energy here or am i missing something blindingly obvious? Surely the
larger the distance travelled down by the water and up by the hyrodgen,
the greater the excess energy.

**ANSWER:**

Here is the problem with your plan: If you drop 1 kg of water from a
height of 100 m it acquires about 1000 J of kinetic energy. This is the
most energy you could get out of the turbine generating electric power
if it were perfectly efficient (which is of course impossible). Now,
the energy required to do electrolysis on that water is about 1.3 x 10^{7}
J. So you would have only enough energy available to do electrolysis on
about 1/10,000 of the water which fell.

**QUESTION: **

My question is about the
momentum light is know to carry . I was wondering , if an object falls
into the sun , won't it get slowed down by light pressure so that it
will posses less kinetic energy as it would without light pressure.
Doesn't that mean the sun-object system is losing energy since the
photons carry energy and that energy was used to slow down (remove
energy) from the object and as they slow the object down the photon
cease to exist (removing energy again).

**ANSWER:**

If the photon transfers its momentum by being absorbed (perfectly
inelastic collision) then the photon disappears but its energy does
not. The object would get that energy in the form of heat or maybe
atomic excitations or ionizations. Energy of the system would not be
lost when the photon disappeared but just transformed to some other
kine of energy. You are right that the object will have a smaller
acceleration toward the sun than it would without light pressure, but I
suspect the difference would be trivial.

**QUESTION: **

Could you please answer this
question to me? it has had me wondering for about 3 months now:
What happens to energy carried by an electromagnetic wave when it
interferes with another?
If energy carried by a EM wave is like E^2, (E field intensity
squared), and in phased interference of two waves, they add linearly,
energy would be 4 times greater instead of two!
Another way to pose the same problem, but with resulting energy null:
Consider that I send a wave from point A, and in its way it sums with
another one in point B, which travels in the same direction and way, so
they share their path from that point forwards. Imagine that they add
with 180º phase difference: they will "destroy" (cancel) each
other, so from B onwards, there would be no EM field at all, right?
then... where did the energy of wave A, and the energy of B go??
Or maybe waves do not carry energy at all? Energy conservation must
hold.

**ANSWER:**

You should not think of there being energy at a particular point in
space due to the presence of electromagnetic waves. Rather, there is a
flow of energy through each point in space. Although there is always
zero energy * at* a point of destructive interference, energy is
flowing *through* that point. I do not believe there is any to do
your proposed experiment--they simply cannot be aligned to share their
paths exactly.

**QUESTION: **

I was told that with
artificial gravity (based on rotating an object), that you would have
to have something very large in diameter in order to provide the
uniform gravity required by our bodies to avoid interfering with blood
flow. Is there a set number for this and how was it determined?

**ANSWER:**

I am not aware of any rule. To set such a rule would require knowing
about physiology and how much of a variation we could tolerate. You can
make an estimate by making a reasonable guess. Suppose that we can
tolerate a 1% change over the height of a man, say 2 m. Then if *R*
is the radius of the floor, then the radius at his head is *R*-2
and so, *v*^{2}/*R=g* and *v*^{2}/(*R*-2)*=*1.01*g*.
If you solve these two equations you will find *R*=202 m, large
as you say. If our bodies could stand a larger variation, *R*
could be smaller.

**QUESTION: **

Imagine two billiard balls
coming at each other in a direct head-on collision. The billiard ball
coming from the left is going 10 m/s, while the one from the right is
going 5 m/s. They have the same mass and little deformation occurs in
the collision. I say that the ball going 10 m/s stops dead (for all
practical purposes) and gives its momentum to the other ball, causing
it to reverse its direction of motion and move away at a speed of 5
m/s. My friend says this is counterintuitive - that the ball with the
greater momentum should "win" (in his words). What's the correct
answer?

**ANSWER:**

Usually a billiard ball problem assumes a perfectly elastic collision,
so that is what I will do. The problem cannot be solved without
specifying energy loss in the collision, and elastic means no loss. So,
conserving both energy and momentum it is an easy problem. I find that
after the collision both balls have reversed their directions; the one
which came in with speed 10 m/s exits with speed 5 m/s and the one
which came in with speed 5 m/s exits with speed 10 m/s. A quick outline
of the solution:

- the mass does not matter, so
take it as 2 kg.
- The momentum before the
collision is
* p*_{b}=2x10 + 2x(-5)=10 kg m/s
- The energy before is
*E*_{b}=½x2x(10)^{2}+½x2x(-5)^{2}=125
J
- The energy after is the same
as the energy before,
*E*_{a}=½x2x(*v*_{10})^{2}+½x2x(*v*_{5})^{2}=(*v*_{10})^{2}+(*v*_{5})^{2}=125
- The momentum after is the
same as the momentum before,
*p*_{a}=2*v*_{10}+2*v*_{5}=10
- Here
*v*_{10}
and *v*_{5} are the velocities after the collision of the
balls with initial speeds of 10 and 5 m/s respectively. Now solve these
two equations for the two unknown velocities and you will get -5 and 10
m/s respectively. (You will also find a second solution, because the
energy equation is quadratic, of 10 and -5 m/s which corresponds
physically to a "miss".)

**QUESTION: **

Why does not the lightening
go in a straight line?

**ANSWER:**

Lightning propagates by a series of small steps called leaders. Each
leader shoots forward about 150 feet, then a new leader, often in a
different direction, is formed carrying the electric current, *etc*.
For the leader to be able to carry the current, the air must be ionized
and the field relatively far from the cloud does not have an intense
enough field to do this. However, the field at the tip of a leader is
strong enough to do this. There is a pretty good discussion of the
mechanisms of lightning at this
link.

**QUESTION: **

I know that Einstein's
account of gravitation involves the LOCAL interaction of masses. But
Newton's universal constant of gravitation, G, is global. Do we throw
out G as a consequence of the general theory of relativity?

**ANSWER:**

I am not sure I understand your question. Newton's universal law of
gravitation is an empirical law, simply a mathematical description of
experimental data. On the other hand, general relativity is a theory
which explains why Newton's law is correct, because of the warping of
spacetime in the vicinity of gravitational mass. Hence, you do not have
to throw anything out.

**QUESTION: **

Is CONDUCTION of temperature
--- none other than inter-molecular (or inter-atomic) transfer of heat
energy through RADIATION? Or is there any other factor involved which
makes CONDUCTION different from such radiation transfer.

**ANSWER:**

No, conduction is something different from radiation. If you heat up
one end of an object, the molecules will contain a higher vibrational
energy than their lower temperature neighbors and will transfer, *via*
the forces between molecules, energy to them. Think of two masses
connected by a spring and one of them is set vibrating; before long,
the other will be vibrating too. A simpler way to say the same thing is
that the energy is transferred by collisions.

**QUESTION: **

Would you answer a question
for me? Since a quark of a given flavor and its antiquark tend to
annihilate each other when they come together, how is it that
a phi meson (made up of a strange quark and its antiquark), a psi meson
(made up of a charm quark and its antiquark), and a upsilon meson (made
up of a bottom quark and its antiquark)
can exist in a metastable state and not immediately annihilate each
other?

**ANSWER:**

There is no reason why a particle and its antiparticle cannot exist in
a bound state. The best known example, perhaps, is positronium where an
electron and a positron appear in a ground state.

**QUESTION: **

Do gravitational waves
really take away the energy from system of rotating bodies?
how long will it take for earth to crash into the sun then?

**ANSWER:**

First let us establish that gravitational waves have never been
directly observed. However, there is indirect evidence where the energy
of a particular binary star system is decreasing at the rate which
would be expected if gravitational waves were being generated as
predicted by general relativity. The rate of energy loss depends on the
masses of the objects and, I am quite sure, the sun will run out of
fuel and die long before there is any noticable change in our orbit due
to gravitational radiation.

**QUESTION: **

I have a question about the
twins paradox that's been bugging me for a while. In it, the twin in
the spaceship is said to be under acceleration and therefore he ages
more slowly than his twin on Earth. But if no frame of reference is
privileged, couldn't one just as reasonably say that the spaceship
remains motionless while the Earth undergoes acceleration away from and
then back towards it? In that case, shouldn't the earthbound twin be
younger when they reunite? The same question would also apply to mass
change due to acceleration: why isn't it just as reasonable that the
Earth (and every other object in the universe) should gain in mass
instead of the spaceship?

**ANSWER:**

There is never any question as to who is actually doing the
acceleration. When the traveling twin slows down he feels being smashed
against the front of his ship. The earth-bound twin feels no such
force. Also, the ship needs to burn its engines to accelerate, the
earth does no such thing. However, I very much dislike the explanation
that all the aging takes place during acceleration periods. See an
earlier discussion of this. Regarding mass, there is
no mass change associated with acceleration. However, a moving particle
has increased mass and both twins would agree, as long as they are
moving, that the other has larger mass.

**QUESTION: **

If gravity is understood in
Relativity Theory as a distortions of spacetime, how is the use of
gravitons as the particle of gravitational exchange reconciled with the
relativistic model? Also, can we profitably model the electroweak and
strong forces as distortions of spacetime?

**ANSWER:**

For your second question see the following question. For your first
question, see my earlier
answer.

**QUESTION: **

I'm a senior in high school.
Over the past few years I have obtained a growing interest in
theoretical physics. Anyway, recently I have been thinking over general
relativity, Einstein's law of gravitation, and the Grand Unified
Theory. One question has been bothering me. If the force of gravity can
be defined as the curvature of spacetime, why can't electricity and
magnetism, or any other force for that matter be considered a curvature
in spacetime. I'm sure the answer is alot to explain in an email, so if
you would rather direct me to paper's or books, or simply telling me
that this approach has been tried before, I would be grateful.

**ANSWER:**

The answer is fairly simple, I believe. In the theory of general
relativity, mass "warps" the spacetime around it so that it is curved.
However, electric charge does not warp spacetime. Electric charge is
the source of electromagnetic fields and mass is the source of
gravitational fields. Also perhaps of interest to you is that there is
a good quantum theory of electromagnetism but there is no satisfactory
theory of quantum gravity.

**QUESTION: **

I have a question about
supercooling. Last year, a fisherman I know was changing his lobster
traps, and he checked the sandbags used to weigh down the traps. When
he took it out, the bag was well below freezing, and immediatly began
crystallizing the water in the air. I wonder if salt water can be
supercooled, and would the ocean floor be candidate for the
supercooling phenomenon?

**ANSWER:**

Two sequential questions, one about supercooling and one about
superheating; that's supercool! When the water is very deep, the
pressure is very high. If the pressure is high, that will keep the
water from becoming ice because it is necessary that ice have a lower
density than water, that is it must expand. So, if the pressure is high
enough, water will be below the freezing point but not freeze. Now,
bringing this water up to the surface where the pressure is lower will
allow it to solidify.

**QUESTION: **

I have been researching
zero kinetic energy and microwave fields so that I may find the answer
to a question between my brother and I. From all the research I have
gathered, I have not come up with proof that microwaves (from an actual
microwave oven, of any variety) can cause energy pulses to increase and
heat liquid well after the microwaves have ceased. Case in point - If
liquid is heated for a specified amount of time using microwaves, and
is then removed from the microwaves, can the kinetic energy cause the
liquid to continue to rise in temp for any duration of time? Even after
the microwaves are no longer affecting the liquid?

**ANSWER:**

Gee, I have no idea what you are talking about! I do not know what you
mean by zero kinetic energy. However, what you may be asking about is a
fairly well known phenomenon where a liquid will become superheated in
a microwave oven. Superheated is when a liquid has a temperature above
the boiling point but does not boil. This can be dangerous since it is
easy to cause the superheated liquid to boil violently (just disturb it
mechanically by putting a spoon in it, for example). Maybe this is what
you are referring to when you refer to a continued rise in temperature;
the temperature does not go up, it is just that the liquid boils. I
suspect the temperature would actually go down to the boiling point
when the boiling begins. For more information, go here.

**QUESTION: **

There are two observers
standing on a stationary platform. A spark of light is emitted from a
light source that is equal distance between them. From the frame of
reference of the two observers, they will see the spark at the same
time.
If the platform on which the two observers is moving and the light
source remains in the same spot as it was before. From the frame of
reference of the two observers, which would receive the light first?
Why is this the same/different from the first scenario?

**ANSWER:**

If there are two observers *at rest with
respect to each other* and their is a flash of light halfway between
them, they see it at the same time (regardless of how the source itself
is moving, as long as it is halfway between when it flashes). So the
answer to your question is that they will see the light simultaneously.
However, and here is the catch, if you are standing on the ground and
they are moving by you will not see them observe the light
simultaneously but the guy at the back will see the flash first and
then the second. Hence, you and the guys moving by do not agree on
whether or not these events are simultaneous. This kind of thought
experiment is one of the first hints leading to the theory of special
relativity which finds that time is not a universal thing but depends
on the motion of the frame you are in.

**QUESTION: **

Say there was a 1.0g bee and
it started out traveling north at 5.0m/s ( with respect to the ground)
and then as it was going along it collided head on with the windscreen
of a 10000kg truck that was traveling south at 20m/s ( with respect to
the ground) . The bee bounces off the window at 40.0m/s - north (with
respect to the ground) after an imapact lasting 0.08s.
Obviously the bee started out moving north and ended up moving south.
this means it must have come to rest with respect to the ground, during
the collision. Doesn't that mean the truck which it came into contact
also stopped for an instant? Is that possible, a bee stopping a truck?

**ANSWER:**

Let us calculate the average
force which the truck exerted on the bee during the collision time: *F==ma=m**Dv/Dt *where* v *is the velocity; this is just
Newton's second law. So,* F*=(10^{-3} kg)(40 m/s-(-5
m/s))/(0.08 s)=0.56 N north. Therefore the truck experiences (by
Newton's third law) the same force south. So the average acceleration
the truck experiences during the collision is *a=F/M*=(0.56 N)/(10^{5}
kg)=5.6 x 10^{-4} m/s^{2}; that means that after 0.08 s
the truck's speed will be decreased by 4.5 x 10^{-5} m/s. So, I
think we would agree that the truck's speed will never be zero. I think
your confusion comes from the reasonable but untrue assumption that the
bee and truck are at rest with respect to each other during the whole
time the collision is happening; they will only be at rest relative to
each other at one instant and that will not be the instant when the bee
is at rest but rather when the bee is moving with the same (northward)
velocity as the truck has.

**QUESTION: **

If I were to take an
extended trip at close to the speed of light, and my friend were
watching me, he'd observe me staying young as he grew old, due to time
dilation. I would see him staying young as I grew old. So here we have
two conflicting realities. How can both of these things be true?

**ANSWER:**

This is the well-lnown twin paradox although
it is not a paradox at all since it is fairly easy to show that the
earth-bound twin grows older. I have answered this question before; click here.

**QUESTION: **

Fill a large pot with water.
Mark the water level. Remove a fourth of the water and freeze it. Place
the ice chunk back into the pot. Because of the lower density of ice, a
portion of the ice chunk is above the water level. Even so, is not the
water level back to the original marked water level? In addition, does
not the water level remain the same as the ice melts?
The Arctic is a floating iceberg, while Antarctica is a landmass.
Presently, areas of the Arctic are losing mass, while Antactica is
gaining. Global warming enthusiasts warn that the melting of ice in the
Arctic will cause the oceans to rise by various amounts. If the above
is true, the cubic miles of ice at the Arctic are already reflected in
present ocean levels.

**ANSWER:**

You are correct that if all floating ice
melts it will have no effect on the ocean level. However, it is my
understanding that there is plenty of ice on land to cause a problem
should it melt (glaciers in Greenland, Canada, Antarctica, Siberia,
etc.). I was unaware that mass of Antarctica was increasing; what is
your source for this?

**QUESTION: **

Suppose a beam of light is
travelign perfectly back and forth between two mirrors, hitting the
same point on each mirror each time. Suppose these mirrors were to come
closer to each still maintaining the perfect back and forth beam.
Finally suppose these mirrors were to phase together. What would happen
tot he beam of light? during thsi process and after the process?

**ANSWER:**

There are real world
problems with your question. First, there is no mirror sufficiently
reflective so that your experiment can be done (see an earlier answer). If there
was a photon between two idealized mirrors, bouncing back and forth,
when the spacing started being comparable to the wavelength of the
light you would find that only at some spacings could you put in a
photon at all. These are integral multiples of half the wavelength of
the light.

**QUESTION: **

Two protons are moving side
by side (parallel). Is there a magnetic interaction or just an
electrical interaction?

**ANSWER:**

Sorry to be so long getting back to you, but
I had to go back and review some relativity. There is a magnetic
interaction. Imagine you are in the rest frame of one of the protons.
Then it sees only an electric field from the other (which is also at
rest); choose a coordinate system such that the field it sees is **E**=**z**E
where *z* is the unit vector in the *z*
direction. So the force it feels is in the +*z* direction and of
magnitude *eE. * Now, view this from a frame moving with speed *v
*in the +*x * direction. Because of the way that the
electric and magnetic fields transform (I don't think you want me to go
into details) there is now both an electric and magnetic field at the
proton we are watching: **E'**=g*E*__z__
and *B'*=(g*v*/*c*^{2})*E*__y__ where
g=(1-*v*^{2}/*c*^{2})^{-1/2},
*c* is the speed of light, and **y** is
the unit vector in the* y* direction. Now, in this frame the
proton we are watching has a velocity *v*=-**x**v
where __ __**x** is the unit vector in the *x*
direction. The force now is* ***F'**=e**E'**+e(**v **x**
B'**)*=e***E**. (I will leave it to you to verify that
last step!) So, the force is exactly the same, but it is composed of
both magnetic and electric parts if the protons are moving in our frame.

**QUESTION: **

When light is "slowed down"
because it enters a different medium what exactly is happening? How is
lights velocity rduced throught water or glass? Why does this
refraction happen?

**ANSWER:**

The answer is a little lengthy, so bear with
me. There are two important constants in electromagnetism (EM) which
essentially specify how strong the electric and magnetic forces are in
a vacuum; these are e_{0} (electric constant, called the
permitivity of free space) and m_{0} (magnetic constant, called the
permeability of free space). It turns out that when you do the
mathematics you find that the EM equations (called Maxwell's equations)
predict waves which have a speed of [e_{0}m_{0}]^{-1/2} and this speed
just happens to be the speed of light in a vacuum. However, things are
different in a material: because the material is composed of many
charges and the charges are moving, the whole medium is affected if
exposed to electric or magnetic fields. For example, an electric field
will polarize the molecules and this polarization will result in a
weaker electric field than if the material were not there. Hence the
strength of the forces are different so we need to measure new values
of permitivity (e) and permeability (m) both of which are
larger than the free space values. So now Maxwell's equations predict a
new (smaller) velocity [em]^{-1/2}. In a nutshell, the speed
changes because of the interactions of the electric and magnetic fields
of the light with the electric charges and currents inside the material.

**QUESTION: **

I am revising some
poorly-written curriculum materials for my Integrated Technology class,
and have stumbled upon this paragraph:
"Energy can not be seen since, unlike matter, it has no mass. However,
it can be measured, sensed, or otherwise detected. For example, we
cannot actually see the energy of a light bulb traveling through air,
but we can see its illumination reflected from this laboratory manual
or the walls of this room."
While there is some correct information here, the statement that energy
can't be seen strikes me as wrong. It seems to me the issues are: 1) We
can only see energy in the visible portion of the spectrum and 2) it
must be directed toward our eye for us to see it. The fact that light
is not matter doesn't, in fact, matter. In fact, I would say that we
can't see matter without (visible light) energy.
Is my assessment correct (the explanation, as written, is wrong or at
least misleading), or can you illuminate me on this subject?

**ANSWER:**

It is most unsettling to a
physicist to read garbage like this! Energy is, simply stated, the
ability to do work. It comes in all forms, not just electromagnetic
(light). A moving car has energy due to its motion (kinetic). A falling
skydiver has energy by virtue of his altitude (potential). A cup of hot
soup has energy by virtue of its temperature (heat). A bottle of
gasoline has chemical energy stored which can, as you know, be
exploited. To speak about "seeing" energy is ludicrous; can you see a
moving car, a falling skydiver, a cup of soup, a beam of light? It is
also inaccurate to say that energy does not have mass; as we know from
the theory of relativity, mass is energy--you know,* E=mc*^{2}!

**QUESTION: **

Is quantum physics and
quantum mechanics the same? If so, what is their similarities? If not,
what's the difference? What are they classified under?

**ANSWER:**

Quantum physics usually means the early
insights and advances in the study of the quantum theory. It would
include Planck's explanation of black body radiation, Einstein's
explanation of the photoelectric effect, the Bohr model of the atom,
Rutherford scattering, DeBroglie's hypothesis, etc. Quantum mechanics
is much more complete and less phenomenological and involves
considerably more mathematics. There is, however, no formal definition
of what each term covers and they may be interchanged more or less as
you like.

**QUESTION: **

A sky-diver is falling
toward earth. A tunnel has been previously excavated completly through
the earth at exactly the location of the skydiver's landing. He
continues his dive through the tunnel without touching the sides of the
tunnel. I believe that Newton would have had him stop at the earth's
core. Where would Einstein have him stop?

**ANSWER:**

First, since this is clearly an idealized
problem, let us neglect air friction (which is, of course, not
negligible because the skydiver has a terminal speed before he hits the
ground). Until he enters the tunnel he is accelerating with a constant
acceleration down. When he enters the tunnel, he experiences less and
less force as he goes deeper because there is less and less of the
earth pulling on him (all of the earth outside him exerts no force)
until finally at the center he has zero force on him but he has his
highest velocity of the whole trip since he has been speeding up the
whole time. Now as he moves away from the center he slows down. When he
reemerges at the other end of the tunnel he has exactly the same speed
as he had when he entered it. He continues until he reaches the
altitude from which he originally jumped at which point he turns around
and begins the process all over again. Newton an Einstein would both
agree on this. If air friction were included, he would not go as far
and if he happened to stop at the center of the earth, he would stay
there forever. If the air friction were included the general solution
to the problem would be that he would oscillate back and forth going
less far each time until he finally stopped in the center. There is an
interesting aspect of this problem: when the skydiver is inside the
tunnel, he moves exactly like he were a mass on an ideal spring.

**QUESTION: **

I was driving in my car
today and thought of my physics class I took a few years ago, and tried
to test my mental capability of remembering some simple concepts.
I was wondering if the acceleration of my car is constant relative to a
second car, is the acceleration also constant when comparing to a third
car ? Then I was wondering if the velocity of my car can reverse
direction when its acceleration is constant. And finally, is it true
that my car with a constant speed can not accelerate?

**ANSWER:**

If you mean that the second
and third cars are moving with constant velocities, then, yes your
acceleration as measured by any other car is the same. This is the
keystone of Galilean relativity and Newtonian physics since it means
that Newton's second law, * F=ma*, is "invariant", that is all
observers will agree on what the force is on an object. Yes, velocity
can reverse when acceleration is constant. The classic example, of
course is a projectile; if you throw a ball straight up its
acceleration, when it leaves your hand, is a constant 9.8 m/s^{2}
down at all times and it clearly reverses its direction at the top of
the trajectory. Acceleration is defined at the rate of change of __velocity__.
Velocity is a vector whereas speed is a scalar, the magnitude of the
velocity. Hence it is quite possible for you to accelerate if you move
with constant __speed__; for example, if you are moving on a
circular racetrack with a speed of 60 mi/hr you are constantly
accelerating because the __direction__ of your velocity is changing.

**QUESTION: **

Is it possible to use
hollowed out asteroid, and spin it to produce artificial gravity? While
I read from one of the answers that a spacecraft can only be a certain
size/mass, now I am wondering whether the same size, mass limit also
has effects for hollowed out asteroid, or since it has an extremely
thick shell, the size/mass limit is a lot greater?

**ANSWER:**

Anything which has the right angular
velocity can simulate gravity if you are inside it. For it to be a good
approximation, the size must be large compared to you so that your head
does not have a significantly different acceleration from your feet.

**QUESTION: **

How fast would somthing have
to travel to creat a sonic boom, so strong it could break glass? ( I
seen it in a movie and it seems like it should have been moving alot
faster)

**ANSWER:**

For there to be a sonic boom the source must
move faster than the speed of sound. Once there, a further increase in
speed has little effect on the strength of the boom. This is more
determined by the size and geometry of the source (a bigger airplane
has a stronger boom than a smaller one) and by its distance from the
observer.

**QUESTION: **

I have a calculator that
converts "lb to kg" and vice-versa. If F=ma and in the SI system my
force in newtons would be my mass in kilograms times my accleration
(m/s/s). In english units my force would in lbs would be my mass in
slugs??? times my accleration in ft/s/s. How can the calcualtor use kg
(a mass) to convert it to a (force) lbs? I also use a scale that has a
button that that allows you to switch between kg and lbs when "weighing
or massing" things.
I "weigh" about 220 lbs therefore should my mass be (220/32) 6.9 slugs
which would be the same as (in SI units) 99.7 kg's-but my weight in SI
units is 2156 newtons. How is they are using force and mass
interchangeably? (I have been out of school a while and used slugs but
was also taught there are lbs-mass and lbs-force.)

**ANSWER:**

Pounds and kilograms are conventionally used
both as a force or a mass which is really too bad. Physicists do not do
that. However, one often talks about 5 kg of onions, for example and
converts that to pounds. To be really precise, some people refer to the
pound-mass and pound-force; a pound mass is the mass of an object which
weighs one pound-force. When a kilogram is converted into pounds it
means pound-mass. It is
all very confusing and should not be worried about too much. The
problem arises mostly because the SI system has mass, length, and time
as the fundamental quantities and the English system has force, length,
and time. A slug is that mass which experiences an acceleration of 1
ft/s^{2} if a force of 1 pound-force is applied; almost nobody
uses the slug except maybe some engineers.

**QUESTION: **

What is it about the oblong
holes in a wiffle ball that makes it curve so easily? There's a lot of
information about curveballs in baseball but not so much about the
physics of a wiffleball. I was just wondering if wiffeballs, which are
hollow and have holes, curve for a different reason than baseballs,
which are solid and have seams.

**ANSWER:**

Anything which moves through the air has its
path determined by two things, gravity and air friction. To make an
airplane lift off, you must have a higher pressure under the wing than
you do on top of the wing. An airplane does this by the shape of the
wing. A curveball operates by the same principle except its asymetry of
pressure is the result of spin which causes the pressure on one side to
be different from the other. With a whiffle ball the holes cause the
effects of spin to be much larger (both because the holes disturb the
air more than the seams do and because the weight is smaller so gravity
has a smaller influence on the motion). I suspect the reasons for
oblong holes is that you can get different effects by spinning it about
different axes.

**QUESTION: **

Assume a batter who is 5'8"
tall and weighs 120 pounds is coming
up to the plate with a wooden bat, 26-28 ounces.
Against an 80mph fastball thrown from the major league distance of
60'6",
and assuming the ball makes contact with an acceptable point of the bat
(somewhere near the sweet spot), how fast does the batter have to swing
the
bat in order to hit the ball:
100 feet, 200 feet, 300 feet, and 400 feet.

**ANSWER:**

This is a typical example of expecting
elementary physics to be able to give a simple formula for everything.
The fact is that elementary physics gives us the tools to start
attacking real-world problems like this, but we cannot simply apply
simple physics to real world situations like this. The batter does far
more than just give the bat speed and these details count. The distance
is also determined by the direction with which the ball leaves. The
important thing you want to focus on is the speed with which the ball
leaves the bat and that is greatly influenced by how elastic the
collision is (wooden *vs*. aluminum bats, for example). If you
had some measure of elasticity, you could easily calculate the speed of
the ball after the collision using the masses of the ball and bat
before the collision by simply applying momentum conservation. However,
this is a very poor model for what actually happens because the bat is
not simply flying along by itself. This whole question would be better
addressed experimentally than mathematically.

**QUESTION: **

how much energy is needed to
enter the earths atmosphere rather than being caught in an orbit? for
example if a person with a hyperthetical suit that could withstand
entry through the atmosphere jumped towards earth off a space station
would they ever return to earth or forever be in orbit around the
earth?

**ANSWER:**

Your question is not
correctly framed. It is not energy to enter the orbit (whatever that
means) which you should think of. Rather, it is just a matter of
knowing how the person "jumped toward the earth". What determines what
the orbit of anything will be is simply its velocity (magnitude and
direction) at some particular point. So, if you just edged off the
space station you would orbit along with it since both satellites (you
and the space station) had identical velocities. If you push off really
hard straight toward the earth, however, you would exit with a
different orbit and if this orbit at some point intersects appreciable
atmosphere, you would reenter. What determines whether or not this
happens is basically how hard you push off.

**QUESTION: **

If you have a light source
going from piont A to piont B, and the didtance is 50 million light
years, (or whatever) and the source completely die's, you now have a
light beam traveling to point B, (earth) and at the same time an
asteroid breaks the beam by traveling by it, you now have a light beam
that has been broken, does the beam still go, but now in two parts?
Once the beam leaves point A, do you now have a light beam all on its
own?

**ANSWER:**

Let us suppose that the source has been on
for 1000 years when it goes out. You now have a beam of light 1000
light years traveling through space with the speed of light. If
something crosses exactly in the center of the beam and absorbs the
light from the beam for one year, then you have first a beam 500 light
years long, then a gap of one light year, then a beam 499 light years
long.

**QUESTION: **

Hi, i recently thought of
an invention regarding the producition of electricity. I know that
electricity is produced by various methods but ultimately all it takes
to produce electricity is to spin a turbine. I was wondering if a
turbine had north magnets on it and another turbine was facing the
first and it south magnets wouldnt the magents attract and if one
turbine was spinning wouldn't the other? This would yield twice the
electricity even though it only requires on of the turbines to be
powered. Would this work or is it unfeasible?

**ANSWER:**

Ah, the never ending quest
for something for nothing! Why not just weld the two turbines together
and attach each to a generator? It would be the same thing as your
using magnets to "attach them together". The fact is that you cannot
get more energy (electrical) than you put in (from hydro, or burning
coal, nuclear fission, or whatever). And imperfect efficiency dictates
that you get far less out than you put in. Now, suppose that you get
one megawatt from the generator attached to one turbine; if you attach
a second generator and demand one magawatt from that also you will have
to put in twice as much energy.

**QUESTION: **

If a black hole is a
singularity, how can black holes be different sizes?

**ANSWER:**

They cannot be of different geometrical
sizes (because a singularity is a point), but black
holes have mass and they can have different masses.

**QUESTION: **

You build a long train on a
very big circular track and set it running at 100mph. On the roof of
that train you build another track, and set a second train running at
100mph, so the second train is doing 200mph relative to the ground.
Assuming infinitely strong building material, and no atmospheric drag,
infinite friction between wheels and track, and that centripetal force
doesn't throw the trains of the track etc etc. Keep on building up and
up infinitely. What happens to the speed of trains at the very top of
the infinite stack when they are all doing 100mph faster than the train
underneath them? and how many trains in the stack to get to the maximum
possible speed?

**ANSWER:**

Let's not think about this
circular train since accelerations cause problems in special relativity
and I think we can answer what your question is without circular tracks
and, in fact, without having them on top of each other. Imagine trains
on parallel trecks: train A is at rest, train B moves with speed 100
mi/hr relative to A, C moves with speed 100 mi/hr relative to B and so
forth. There is no limit how many trains you can add in this way but no
train may move with a speed greater (or equal to) the speed of light
relative to any other. Thus, if you had 10^{50} trains, the
last train would not have a speed of 100x10^{50} mi/hr relative
to the first but would have a speed of just under the speed of light.

**QUESTION: **

ok this may be the holy
grail of science and is mostly unkown but.. The Large Hadron Collider
in CERN is as u probably know due to be turned on in november. Now i
just have 2 questions one being a concern of mine. Firstly if they do
find the higgs mechanism to be true or if they do find an equation for
everything then what will its uses be other than tick a box of
accomplishments. Like could this mean we could potentialy build new
life, exploit matter and time...? and secondly I assume that wen they
turn this on they will gradually add energy rather than full blast and
potentially rip apart the universe? because I would hope if they see
its too much energy as they turn it up they would stop and not get
carried away by ultimate glory. But im sure 2000 scientists together
have figured that out.

**ANSWER:**

The goal is purely intellectual, that is
knowledge for its own sake which, in my opinion, is one of the defining
characterstics of humankind. But, most knowledge eventually will lead
to applications someday; who would have guessed 200 years ago that
electricity would have ever been more than a curiosity? that someday
horses would be purely for recreation? Regarding your second question,
it is likely that the energy will be gradually ramped up as they start
using the collider because that is the best way to troubleshoot a new
accelerator. It is absolutely not because anybody thinks this could "rip apart the universe" the energy is called
high energy because the particles go very fast (just less than the
speed of light) so, given their size, they have very high energy. But
in an absolute sense, the amount of energy any particle has is really
tiny, not nearly enough, for example, to warm your cup of coffee.

**QUESTION: **

I THINK I understand that,
in the "twins paradox" experiment, that the space traveler ages more
slowly only during the period of acceleration; once she reaches the
experimental speed (whether its 60%c or 80%c), then - as long as she's
travelling in a straight line at a constant speed, she ages the same as
her twin on earth. Is this correct?

**ANSWER:**

Most elementary modern physics textbooks
explain the twin paradox as all the aging taking place during the
noninertial (accelerating) phase of the trip. I consider this to be
totally incorrect and a complete copout! One need introduce no general
relativity to understand the twin paradox, the period of acceleration
can be made infinetesmally short. I have previously outlined how to
think about the twin paradox and you should
read that; note that there is a
big difference between how fast clocks run and how fast they *appear*
to run to other observers.

**QUESTION: **

I recently read that all
matter within a black hole gets compressed to a singularity where
matter no longer exists. How can you have mass without matter?

**ANSWER:**

I think that what is meant here is that the
mass is not in the form which we normally associate with matter, *e.g.*
solid, liquid, gas... But mass has a much more specific definition.
There are two kinds of mass but they turn out to be the same (which is
explained in the theory of general relativity). One is gravitational
mass: it creates and feels gravitational fields and a black hole
certainly fulfils this criterion. The other is inertial mass: it causes
an objece to resist acceleration if a force is applied to it, also
certainly a property of black holes.

**QUESTION: **

Hello, I just wanted to know
if there are any gases that exist that are very good electrical
conductors, but do not respond to magnetism. Plasmas conduct
electricity, are there any types of plasma that do not respond to even
strong magnetic fields?

**ANSWER:**

Any moving electric charge
experiences a magnetic force when in a magnetic field and any unionized
gas is, in itself, a poor conductor. Therefore, the answer to your
question is no.

**QUESTION: **

the air contains
approximately 0.03% of carbon dioxide and this amount is almost
constant.why is this so?

**ANSWER:**

Why is it almost constant or why is it
0.03%? Much of the reason that CO_{2} is fairly low is that
plants absorb it from the atmosphere and give off oxygen. Therefore,
the northern hemisphere has a slightly higher amount than the southern
hemisphere because the amount of landmass is greater in the north.
Also, the level fluctuates seasonally because of the winter dormancy of
many green plants. Recently, as you probably know, the levels have been
steadily increasing because of people and their cars, factories, power
plants, *etc*.

**QUESTION: **

I read about Cerenkov
radiation and the "blue glow" that it causes. Is this glow always blue?
If not, does it depend on what the medium is (water, oil, etc.) or what
the particle traveling faster than light is?

**ANSWER:**

The intensity of the radiation is
proportional to the frequency. Therefore, the higher the frequency
(shorter the wavelength) the more intense the radiation (the spectrum
is continuous, not of a single wavelength). Therefore, it turns out
that most of the "light" is in the ultraviolet spectrum. You would
therefore think that Cerenkov radiation should look purple, but the eye
is more sensitive to blue so that is what we perceive. For the same
reason (sensitivity of the eye) the sky is blue and not purple.

**QUESTION: **

How can i plot the function
Sin[n pi/2]/(n pi/2)

**ANSWER:**

This is just basically the
function sin(*x*)/*x. *All you need to do is take your
calculator and, for several values of *x*, calculate sin(*x*),
divide it by *x*, and plot. You can make your correspondence to *n*
by *n*=2*x*/p. The only problem point is at x=0; here you
have to find the limit as *x *approaches zero. It may be shown
that sin(*x*)/*x=*1 for *x*=0. The curve looks like the
figure to the right.

**QUESTION: **

Could microwaves, 95GHz 3mm
wavelength, be focussed on a tiny point using lens or mirrors ?

**ANSWER:**

Yes, any electromagnetic wave is susceptible
to focusing using reflection or refraction provided that you design
your mirrors and lenses to work with the wavelength you are working
with. You cannot use the same lenses and mirrors that you would use for
visible light.

**QUESTION: **

Let m0 be the rest mass of a
photon. Since it moves with the velocity of light, its energy is, E= m0
c2----------(1) This means that m0 = E/ c2 ---------(2)
By Einstein’s Theory of relativity, m0 = 0
Hence, from (2) E/ c2 =0, Or, c=1/0 How is this possible?

**ANSWER:**

Your basic premise, the expression for
energy, is wrong. The energy is given by *E*=(*p*^{2}*c*^{2}*+m*_{0}^{2}*c*^{4})^{1/2}
where *p* is the momentum. Since the rest mass of a photon is
zero, * E=pc* which tells you the relationship between energy and
momentum for a massless particle. The energy of the photon is also
given by *E=hf* where *h* is Planck's constant and *f*
is the frequency of the corresponding electromagnetic wave.

**QUESTION: **

I'm an editor for Scuba
Diving magazine, and I wanted
to check something that one of our writers included in an article about
how
to save air when scuba diving. One of his tips is "Swim Slowly," and
here is
his explanation of why you should do so ...

"Water is dense and, unlike air, not compressible. To swim through it,
you
have to force aside your body¹s volume and (assuming you¹re
neutrally
buoyant) your weight in water every time you move forward the length of
your
body. (Imagine if you had to shove aside a 200-pound sack of sand to
walk
six feet.) Obviously, the faster you swim, the more body-weights of
water
you have to move aside in a minute, and the more energy and air you
consume
to do it.
The energy cost of speed is even more than you might think because
it¹s an
exponential function proportional to the square of the speed. So
swimming
twice as fast requires four times as much energy and air. But the
reverse is
true, too: Swim half as fast as you do now, and you¹ll use only
one-fourth
as much air."

**ANSWER:**

As we all know, it certainly
requires more effort to swim through water than to "swim" through air.
However, this has little to do with the compressibility of the fluids
and it is also not accurate to say that you are pushing the water out
of the way. The reason is almost entirely due to frictional type forces
and these turn out to be determined by the viscosity of the fluid (it
would be harder yet to swim through honey, but its density is close to
that of water). It also depends on velocity and geometry. The author is
correct that the force which the water exerts on you depends on the
velocity; for some velocities, fluids, and geometrical situations, this
dependence is approximately proportional to the speed squared as the
author states. Now, to swim through water with a constant speed
requires energy; the amount of energy is the force you must exert
(equal and opposite to the force the fluid exerts on you) times the
distance you swim. Assuming that the amount of air you consume is
proportional to the work you do, then yes it does require less air to
swim some distance slowly.

**QUESTION: **

which is hotter and which is
colder in water- black or white construction paper, and why?

**ANSWER:**

You have not given enough information for
your question to be answered. If you have a completely isolated system
in thermal equilibrium, everything will be the same temperature. If you
have two objects, one black and one white, in a very large amount of
water (so that its temperature is constant) being illuminated by light,
the black will absorb more of the light and the energy of this light
shows up as an increased temperature. The white will also absorb light
but not as much so it will not get as much hotter (like something black
in the sun gets hotter than something white). The water will be more
efficient at carrying off this heat and so the temperature difference
will not be as large as in air.

**QUESTION: **

I'm curious about the
wavelength and frequency of light and if either relates to its speed,
and if so, how? If I were to setup a laser motion detector (such as
ones often used in small mini-marts to ring an electronic bell when a
customer enters or leaves) and it were to operate using infared (800nm
to 1m wavelength) versus if I used ultraviolet (<248nm?) and I was
able to find something that moved incredibly fast in an attempt to move
through the beam of light without triggering the bell which would I
have a better chance with?

**ANSWER:**

There is a very simple relationship among
speed (*v*), frequency (*f*), and wavelength (*l*)
of a wave: *v=f**l. *
Furthermore, the speed of
electromagnetic radiation, be it visible light, infrared, ultraviolet,
is a universal constant (actually, it is speed of waves in a vacuum
which is constant for all waves but air is virtually indistinguishable
from a vacuum as far as light goes). So all light should perform the
same as far as timing is concerned. However, there will be some
dependence on the wavelength depending on what you are detecting; a
person would absorb or reflect visible light far better than radio
waves, for example.

**QUESTION: **

if their is a truck full of
birds and the birds are sitting at the bottom of a trailer ,does it
weigh the same as if all the birds are flying?

**ANSWER:**

There is more than one answer to this
question. Let us assume that the birds are hovering or moving with
constant velocities. In that case, each bird stays in flight because
the air exerts a force up on him equal to the bird's weight; but
Newton's third law requires that the bird therefore exerts an equal
downward force on the air. Therefore the net weight of the whole truck
is unchanged. All forces internal to a system cancel out in the
calculation of the net force on that system because of Newton's third
law. Another possibility would be if the birds have an acceleration
with a vertical component; the simplest example is that all the birds
are in freefall inside (probably not what you had in mind by "flying")
in which case the birds would not contribute to the weight (neglecting
any air friction or buoyancy). A similar question was
answered earlier which might interest you.

**QUESTION: **

my 10 yr old son aked me the
following question over the weekend and I have no idea if the answer
can ever be known - but here goes:-
If the universe started with a big bang and has been expanding ever
since - then in the second before the big bang - where did all the
matter come from?

**ANSWER:**

I believe that it is not understood where
the energy of the universe came from.

**QUESTION: **

I'm a martial artist
debating an old concept in martial arts that I find to be dubious in
terms of the physics. Suppose I punch a heavy bag that is initially at
rest. Prior to hitting the bag I have generated some momentum. At
impact, my arm and body will be decelerated by the reaction force from
the bag. The theory is that if I keep my rear foot flat on the ground
and have a solid body connection from that foot to the punching hand,
the ground now "supports" my punch and it will therefore have more
effect on the target. This is often called "hitting with the ground".
My suspicion is that this explanation is not quite correct. Among the
confusion is that I'm not a passive object, I can continue to apply
some force during impact by continuing to drive off the back foot, but
I suspect this results in more of an added "push" due to the extended
time interval of contact, and what I really want is the biggest
impulse. I need the help of a real physicist. Does "grounding" the
reaction force of a punch through my body to the ground give the punch
more power, or does it just matter how much momentum I can generate
prior to impact?

**ANSWER:**

In introductory physics courses we usually
talk about momentum in terms of collisions of point masses. Here, since
the various parts of your body move with different speeds, this is not
quite true. But, let's think in terms of a perfect point mass *M*
being your whole body moving toward the target with some effective
speed *V* so that you have a momentum *MV*. Now, for
simplicity, assume a perfectly inelastic collision and assume the
target has the same mass as you do (which seems reasonable since
martial arts are for fighting other folks). Then momentum conservation
has *MV*=2*MV' *where V' is the speed of the two of you
immediately after the collision. Hence, *V'=V*/2. The force which
your opponent (and you) feels is the time rate of change of his
momentum, that is approximately *MV*/(2*T*) where T is the
time the collision lasted, so one way to increase the force is to
minimize the duration of the punch. So, now let's get to your question.
If you keep a foot in contact with the floor what you are doing is
increasing your effective mass (the whole earth now becomes part of the
system). This increases the momentum which will, in turn, increase the
force applied (if *T* stays the same). This is a very simplistic
overview but gives you the flavor of what is going on.

**QUESTION: **

Taking the light as a
guiding agent (its invariant speed) in several thought experiments,the
lorentz transformation of coordinates can possibly be completely
derived,and time dilation,
lenght contraction,non synchronisation of simultaneous events,and such
things can be understood therefrom.But mass increase seems to be
detached from this continuity of explanations.
The explanation of "Mass" gets carried away by referring to Sir J.J
thompsons electron experiments.
Hence the question arises-
Is it possible to deduce the effect of mass increase
("Mass increases by gamma factor as velocity increases"{where
gamma=(1-(v/c)^{2})^{-0.5}}
by purely referring to lorentz transformations?without referring to
explanations and definitions from electromagnetism.
The relativistic addition of velocities seems to provide some clue.
Also an explanation as to how the time part of four momentum can be
treated as energy is needed.

**ANSWER:**

All the quantities which you can derive from
the Lorentz transformation are what we call kinematic quantities. Mass,
force, and more importantly linear momentum and energy are what we call
dynamic properties. So, just like in an introductory physics course
where, after we learn how to describe motion (kinematics), we next want
to understand how motion can be changed; in classical physics this
leads us to Newton's laws. What happens in relativistic physics is that
we quickly find that Newton's second law, in the form **F**=m**a**
is no longer a true law of physics; that is, if two observers both
measure the acceleration of a mass *m* they will get different
answers for **a**, so that would mean that force is no
longer a useful concept in that context. So what we do is look for the
relativistic equivalent of Newton's laws. To do this, write Newton's
second law as **F**=d**p**/dt where **p**=m**u**
is the linear momentum and *u* is the velocity of the
particle, so for an isolated system we expect to find *d***p**/dt=0,
that is the momentum is conserved. If *m***u **is the
definition of momentum, where *m* is what classical physicists
call the inertial mass, we find that momentum conservation is no longer
a true thing for isolated systems. So, what we do is to redefine what
we mean by momentum such that momentum is conserved and the new
definition becomes the old definition for small speeds. If we define
momentum as **p**=g*m***u **we find that momentum is
conserved in an isolated system and **p**≈*m***u**
for small **u**. So, you see, the gamma factor comes from
redefinition of momentum, not redefinition of mass. Almost all
introductory physics texts say that it is mass which increases, and
this is certainly a possible interperatation of the new definition of
momentum. I prefer to say that *m* is the inertial mass of an
object at rest and that **p**=g*m***u**. Your
question about energy being the fourth component of four momentum is
too involved for this site.

**QUESTION: **

Is ball lightning real or
hype ?
If real, how is it formed ?

**ANSWER:**

It is real. How it is formed
is, I had thought, not very well understood. However, I did find a news
story from 2002 which says the mystery is solved.

**QUESTION: **

I'm a fifth grade teacher. A
text for my students about butterflies says that the morpho butterfly,
which has a blue appearance, actually isn't blue. Rather, when light is
reflected off the edges of its scales, the wings appear blue. I have
heard this line of reasoning with children before, from a park ranger,
explaining to my students that a bluejay isn't blue either; rather,
it's the light reflecting off the wings that makes it appear blue. My
understanding of color is that this very reflection of light IS color,
and that you may as well say that nothing really has any color, but
rather, objects have properties that allow us to perceive color once
light hits them. Who's naive here, me, or the book and the park ranger?

**ANSWER:**

Anything has color by virtue of the
wavelength of light which comes from it. Our eyes can detect the color
of the light and it is that which defines something's color. Perhaps we
should be careful in our definition of the color of something: it is
the color which we see when the object is illuminated with white light
(which, as I am sure you know, is a mixture of all visible colors). I
do this so we do not have to confuse the discussion with, for example,
a white object which is illuminated by green light and therefore is
green; let's just say it's white. So, what determines what wavelength
(color) of light comes from something which is illuminated with white
light? The most common mechanism is that the object absorbs light of
some wavelengths but not so much others. So, if my wall has a paint
which absorbs much of the light which is not red but doesn't absorb red
very well, then my wall is red. But there is another very important way
which nature has found (many butterflies, birds like peacocks and
hummingbirds with iridescent appearances, *etc*.), and it is
called interference. Have you ever noticed the pretty colors on a thin
film of oil floating on water (like a parking lot after a rainfall), or
on a soap bubble? What is happening here is that light reflects from
both the front and back of the film and goes back to you. If those two
waves happen to emerge in phase (that is the peaks and valleys of the
light occur at the same time and same place) they add up to be very
bright in that color but other colors will not add constructively and
can even completely vanish if the peaks of one coincide with the
valleys of the other. Although biologically it is more complicated than
this (the interference comes from something called a diffraction
grating formed by the "scales"), the general reason is still similar to
thin film interference. If you want more detail, google __
interference butterflies__ or check out this
link.

**QUESTION: **

If an asymmetrical object,
say a spaceship shaped like a "7" in its dorsal perspective had an
engine assembly like a booster of some type attached to that left-hand
arm at its furthest point or very close to it, how much force in
relation to the forward force would be needed to compensate for the
drifting that would occur due to that forward momentum being produced
by the engine being so far out?
I ask because I am an Artist who enjoys (you guessed it, SciFi and
Space travel)...I have designed an ship that is very asymmetrical, with
the main drive being positioned practically on the farside of the rest
of the ship being held away at a distance. So I was thinking of using a
thruster assembly for a compensator, but I feel it would be better if
there was some actual thought on this one.

**ANSWER:**

When a force is exerted on an object two
things can happen: (1) there will be an acceleration of the center of
mass of the object in the direction of the force. And (2) there will be
an angular acceleration about the center of mass of the object and in
the direction of the torque (that is the object will begin spinning
about its center of mass). What you would want in a spaceship is to get
the first but not the second. Yes, you could put another little
"thruster" a large distance from the center of mass to have an equal
and opposite torque, but that would be impractical since I presume you
want the main engine to be very powerful so, unless you could put a
small engine very far out, it would not have adequate torque. What you
should do if you insist on this configuration is to point the main
engine so that the direction of the force it exerts passes through the
center of mass and would therefore exert no torque; this would
probably be not terribly off what you might call "straight ahead" since
the main engine is likely to have a very large mass and the center of
mass would therefore be relatively close to it.

**QUESTION: **

I'm a med student working in
the neonatal ICU. The attending and I were debating over this physics
problem....
So when the babies can't eat on their own (not strong enough to suck)
we put a tube in their stomachs and put the nutrition in for them.
Usually the 30mL of food per feed is put into an open syringe (ie. no
plug) which is connected to the thin tube going into the stomach. HE
says that the speed at which the food goes in is dependand on the
height of the syringe more than anything else. I said that this isnt'
true (though I just discovered on Wikipedia that it would be if it were
a syphon type system) and I think its more dependant on the length of
the tube, the diameter and the viscosity of the fluid. However, I cant
prove this mathematically. Could you help answer this question?

**ANSWER:**

Your friend is partly right if you are
dealing with an ideal fluid like most introductory physics texts deal
with. But you are the winner for real fluids. Imagine sending water
through your apparatus; then, with everything about the experiment
being identical, repeat it with honey. Surely your colleague would not
argue that the times would be the same. Indeed, you would still have a
good arguing point even with an ideal fluid: surely the fluid will leak
out a large hole faster than the small hole.

**QUESTION: **

What seems like a very
simple concept to me is something a friend of mine can't understand.
Could you explain this in a way he might be able to comprehend?
Car A is travelling along a road at 20m/s. Car B is 20m behind car A
and doing 22m/s.
Car C is travelling at 1000m/s. Car D is 20m behind car C doing
1002m/s.
Will the time taken for A to catch B equal the time taken for C to
catch D?
I believe the answer to this question is yes.

**ANSWER:**

The important concept to understand here is
called relative velocity. If you drive down the street at a speed of 40
mi/hr and another car comes toward you with a speed of 40 mi/hr, then
you see it approach you with a speed of 80 mi/hr. Thus, if two cars
start out at opposite ends of a football field each going 40 mi/hr,
they will crash at the same time as if one had stayed put and the other
approached going 80 mi/hr. They will not crash at the same place, and
maybe this is what is confusing your friend. If the cars are traveling
in the same direction, as in your examples, you subtract the speeds to
get the relative speed. The directions of all the speeds can be taken
care of by using vectors, but it is probably better to just use your
common sense if you are trying to get a feeling for it. For example, if
you are going 40 and the car in front of you is going 42, he is moving
away from you with speed 2; if he is going 38, he is moving toward you
with speed 2 and you will collide if you don't slow down. So what
matters is the relative velocity. In the specific examples you state,
if the two pairs of cars start simultaneously an equal distance apart,
say 10 miles, the two chasers catch up at the same time. They will not,
however, have gone the same distances before catching up as in my
example above.

**QUESTION: **

I am a biologist who
regularly uses chemiluminescence to expose x-ray film. During my
distant days as a chemistry student, I was oriented to the theories
that energy and light are transmitted as waves or packets. From one
perspective, sound is merely a lower energy/lower frequency than light.
Can you help me answer the two following questions:
1.Can one consider radioative emmisions (i.e. from 32-P) as merely
waves with very very high frequency?
2. X-ray film depends on a chemical reaction for it to be exposed. This
reaction requires energy from a source. Visable light, UV light, IR
light, and radioisotopes all produce enough energy to expose the film.
Can I cause the film to be exposed with high frequency audible sound of
long duration?

**ANSWER:**

First, sound is not just lower frequency
wave light waves because light is electromagnetic radiation which
travels in a vacuum; sound is a disturbance in the air or other
material media and cannot travel in a vacuum. There normally are three
kinds of radiaocative emissions and one of them, gamma-radiation, is
merely very energetic electromagnetic radiation. I am not very expert
at x-ray film but I believe that it occurs via the photoelectric
effect, that is one quantum of the x-ray is completely absorbed and
causes the chemistry to occur. So presumably x-ray film is sensitive to
a narrow band of frequencies of electromagnetic radiation and less
energetic photons would not expose the film. Sound waves are not
quantized and so cannot cause the chemistry to happen no matter how
loud it is or how long you "shout at it". (Actually, sound is sometimes
quantized inside crystal and the quanta are called phonons.) So if some
important chemical interaction requires a threshhold amount of energy
to cause it to happen, no radiation with less energy per photon will be
detected and sound will not be detected either.

**QUESTION: **

Well this may seem dumb, but
no one can answer it, no one can say why this is so? X^{2}+Y^{2}=
the square root of Z^{2}
Why is this so?
I had the hypotheses that it was related to the base number system, but
the conclusion was false.
X^{3}+Y^{3}= the three square roots of Z^{3} or
rather Z*Z*Z
But it did not work.
Proposition One, the hypotenuse cannot be greater than the opposite and
adjacent sides added together, neither can it be shorter than the
longest line, this logical, needing no proof,
Yet the space between is in question in Proposition One, X^{3}+Y^{3}=
Z^{3} this does not transgress Proposition One,
Nor does this
X^N+Y^N= Z^N
Z = the hypotheses, N equals the power of the base system number.
Proposition Two, Therefore we can infer Proposition One with the
equation above, which is X^N+Y^N= Z^N, to conclude this equation does
not transgress Proposition One. Therefore why is space defined with the
2=N?
To simplify, two products of themselves what is the root of them?
Why Is this so? Proposition three, space could have been defined in
another universe, as N=1.25, or N = 3.1, why in this universe N=2?
Given the equation X^N+Y^N= Z^N.
Are my Proposition correct, I think so, but why is it the power of 2 in
a base system, and not for say the power of 3 in a base system. Why is
this universal equation X^{2}+Y^{2}= Z^{2} to
space?
any help would be nice?

**ANSWER:**

Well, this is not really a well-focused
single question, but I will try to answer it. This is really a
mathematics, not physics, question. The Pythagorean theorem is true for
Euclidean geometry, that geometry in which we seem to live, the
geometry which we learn in high school. There are hundreds of
proofs which you can use to refresh yourself. It has nothing to do
with the number system we use to count with. An example of someplace
where the theorem is not true is on the surface of a sphere. Imagine
two lines starting at the north pole which are 90^{0} apart and
they run down to the equator and the equator then completes the
triangle; Then all three sides are equal. Although you seem to think
that it is not true that X^{3}+Y^{3}=Z^{3},
that equation can be true; given X and Y you may find Z to satisfy the
equation. For example, if X=1 and Y=2 then Z=(9)^{1/3}. What is
particularly interesting about the Pythagorean theorem is that there
are special cases where X, Y, and Z are all integers greater than zero,
*e.g.* (3,4,5) and infinitely many others.
One of the most famous of mathematics' unproved conjectures was known
as Fermat's
last theorem (1637) which states that there are no solutions where
X, Y, and Z are positive integers greater than zero to the equation X^{N}+Y^{N}=Z^{N}
with N>2. It was only recently (1995) that the proof was achieved by
Andrew Wiles.

**QUESTION: **

i dont know how reliable a
source this is, but i recently watched the movie "what the bleep do we
know" and it talked about electrons and how they jump in and out,
between places. it then mentioned that the nucleus of an atom does a
similar thing, popping in and out. i'm not sure if i misunderstood. is
the nucleus constant?

**ANSWER:**

I really don't know what you are asking. It
probably refers to vacuum polarization where the presence of an
electromagnetic field causes virtual electron-positron pairs to appear
and disappear spontaneously. There is nothing wrong with this as long
as it happens quickly enough that the uncertainty principle is not
violated; that is, it is ok to violate energy conservation as long as
you only do so for a very short time. Similarly, any
particle/antiparticle pair could appear and disappear. Since both
nuclei and electrons are electrically charged, this can happen near
either of them. It does not mean that the electron or nucleus are
popping in and out of existence, just the "clothing" in the vacuum
around it.

**QUESTION: **

How likely is it that the
laws of nature will change, making life in the universe impossible, say
within 1000 years, 1 million years, and 1 billion years?

**ANSWER:**

Since there is no evidence
that the laws of physics change at all, there is no chance based
on what we know. It is of interest to astrophysicists to look for
evidence that the fundamental constants of nature might change, but
there is no firm evidence of its happening. In any case, it certainly
will not happen within less than a million years.

**QUESTION: **

at what pressure and
temperature will carbon melt instead of sublimate?

**ANSWER:**

See the attached phase diagram.

**QUESTION: **

I was wondering, is it
possible for electrons and protons to annialate each other? Even though
an electron is an elementary particle and a proton a baryon?

**ANSWER:**

No, it is not possible. If it were the
universe would become empty of mass.

**QUESTION: **

Do Newton's Three laws
relate to each other?

**ANSWER:**

I don't really understand
what you are asking. The three of them together form the basis of the
dynamics and statics of classical mechanics, and they are therefore
related in that they all address the same types of problems. On the
other hand if you are asking if one can be expressed in terms of
another, that is if they are in some way redundant, the answer is no.
Although many people write off the first law as simply a special case
of the second law, that is not correct and each of the three conveys
unique ideas.

**QUESTION: **

I'm currently in an argument
with a few friends, some of which are in engineering whether gravity
and the idea's surrounding it are covered as the Theory of Gravity or
the Law of Gravity.
I've been lead to believe that it is the Theory of Gravity and as such
it is concidered a law merely because it has been around for so long.
However, it is still JUST A THEORY.
Now if I'm wrong I'll recant and apologise to them.
So, is it the Theory of Gravity or the Law of Gravity. And do you have
any links or references that I could use to either prove or disprove it
either way?

**ANSWER:**

I would say that it depends
on how you define a law and a theory. Here are my definitions: a law is
a mathematical statement describing *how* something is
whereas a theory is an explanation of *why* something is.
Now, I assume that you are referring to Newton's universal law of
gravitation, namely *F*=-*Gm*_{1}*m*_{2}/*r*^{2}.
This is an empirical law that tells you the force which two objects
exert on each other because of the gravitationsl attraction; it says
nothing about what the origin of this force is, that is why do two
objects which have mass attract each other. I would therefore say that
this is not a theory of gravity, it is a law of physics. On the other
hand, the theory of general relativity explains why two masses attract
each other (because the presence of mass "warps" the space around it}
and therefore is the operative theory of gravity. I should point out
that either a law or a theory might be applicable only in special
circumstances; for example, Newton's three laws of motion are
applicable in everyday life but when you try to extend them to very
large speeds or very small distances, they become inapplicable.

**QUESTION: ;**

while seeing from the ground
the towards the sky, the long distant flight emits smoke and the trail
of smoke behind looks like a cloud, like a rocket is going. Why is it
so.

**ANSWER:**

The condensation trail left behind jet
aircrafts are called contrails. Contrails form when hot humid air from
jet exhaust mixes with environmental air of low vapor pressure and low
temperature. Because of the high altitudes, contrails are composed of
ice crystals and become cirrus clouds.The mixing is a result of
turbulence generated by the engine exhaust. Cloud formation by a mixing
process is similar to the cloud you see when you exhale and "see your
breath".

**QUESTION: **

If I shoot a modern arrow
straight up into the air with a bow that exerts 75 lbs of thrust does
the arrow travel to the top of it's flight in the same amount of time
that it takes to fall back to earth?

**ANSWER:**

A freshman physics class would say yes but
that is if you neglect air friction. On the way up the arrow has two
forces on it: its weight down and the air friction also down. On the
way down it also has two forces on it: its weight down and the air
friction up. The problem is complicated somewhat by the fact that the
air friction force depends on velocity, so it is not possible, without
stipulations on the initial speed and the details of the air friction
to determine which will be quicker, up or down, but since the forces on
them are definitely different if there is any air friction at all, the
times will definitely differ.

.

**QUESTION: **

What is the efect of the
shape and the thickness of the slit in a single slit diffraction?

**ANSWER:**

By "thickness" I presume that you mean the
width of the slit. This is part of the standard single slit analysis
and it is found, as the slitt gets narrower the pattern expands. The
shape also determines the nature of the pattern. The simplest (extreme)
example would be the pattern from a hole. An example is shown at the
right.

**QUESTION: **

My question relates to the
double slit experiment. It is my understanding that when photons are
"shot" one at a time through a double slit, the screen records
individual dots - the pattern of which (over time) will be "striped"
(i.e. consistent with a diffraction/interference pattern). Hopefully
what I just said is correct? Anyway, my question is: what happens if
only one single photon is shot (i.e. there is no stream of
photons)...is there an inteference pattern on the screen with this one
photon, or does the photon appear as a dot in the spot on the screen
where one would expect it to be based solely on the particle theory? In
a general sense, my question is whether the interference patterns
arises from previous photons interfering with later ones rather than
one particular photon intefering with itself? A related question is
what happens if a stream of photons is shot but there is a
"significant" time delay (not sure what time frame) between shooting
each photo n...i.e. does the interference pattern disappear in this
case (assuming this expt is technically feasible)?

**ANSWER:**

You will see a dot from a single photon.
However, it will retain some of the properties of the diffraction
pattern.* E.g*. it will not fall where the dark stripes would be
for this double slit and it will not (necessarily) pass straight
through like a simple particle would. It is far better to think of the
photon interfering with itself rather than other photons. Indeed, the
kind of experiment you refer to ("one at a time") is the same as that
you allude to at the end, that is you can shoot photons through at a
rate of one per hour and the diffraction pattern will still be there.

**QUESTION: **

if atoms can "last" for
about 10^{35} years, what happens to them? do they just cease
to exist?

**ANSWER:**

This is not a fact but speculation. It has
been proposed that protons, along with electrons the stable components
of matter in the universe, will ultimately decay. Nuclei are composed
of neutrons and protons and a free neutron decays to a proton, an
electron, and a neutrino. The most likely proton decays ultimately end
up as two photons and a positron. The positron then finds an electron
and they annihilate to two more photons. Other decay modes include
neutrinos also. So what happens is that when all the atoms disintegrate
the universe will be filled with photons and neutrinos. I must
emphasize that this has never been observed even though large,
elaborate experiments have been done to try to see proton decay. The
"standard model" of elementary particle physics does not predict proton
decay, that is the proton is stable in that model.

**QUESTION: **

if a penny is placed on a
rotating turntable, where on the turn table does the penny require the
largest centripital force to stay in place?

**ANSWER:**

The centripetal force is given by *mv*^{2}/*R*
where *v* is the speed, *m* is the mass, and *R* is
the radius of the circle in which it is moving. The speed of an object
which is on a rotating rigid body (your turntable in this case) is *v=R**w* where *
w *is
the angular speed (in radians/s). Since * w* is a constant (every point on the turntable
has the same rotational speed), the centripetal force is *mR*^{2}*w*^{2}/*R*=*mR**w*^{2}.
So the force increases linearly with the radius, so the answer to your
question is the force is greatest on the extreme edge of the turntable.

**QUESTION: **

if I have the amount of
momentum an object has how can I convert that to the amount of
potential/kinetic energy the object has

**ANSWER:**

The kinetic energy is* p*^{2}/(2*m*)
where *p* is linear momentum and m is the mass of the object.
There is no general relationship between the momentum and potential
energy; however, in cases where total energy is conserved, as the
kinetic energy decreases the momentum will decrease and the potential
energy will increase. So, for systems where energy is conserved, you
may write *E*=*p*^{2}/(2*m*)+*V* where *E
*is total energy and *V *is potential energy. You can
now solve this equation for *p*.

**QUESTION: **

How do I make a guitar out
of scratch? My Physics class needs to construct an instrument out of
scratch and I don't know where to start. Can you help me?

**ANSWER:**

A guitar which demonstrates the principles
should be fairly straightforward to make. Probably not too good for
making music though. I would start by getting one guitar string and
stretch it between two nails on a board; it would also be good if you
made there be a way you could vary the tension, as the peg does in a
guitar. This is a rudimentary stringed instrument. You can demonstrate
that a plucked string makes sound and that the frequency (pitch) of
that sound gets higher as the tension in the string gets higher (how a
guitar is tuned). But the sound will be very small. That is what the
box of the guitar does--it resonates and thus greatly amplifies the
sound of the vibrating string. So get a box, wooden and closed on all
six sides. cut a circular hole in one side and stretch your string
across the hole; it would be best if the nails you strung the string
between were actually in the box. It would also be good if the wood was
not too heavy so that the wood itself can vibrate to contribute to the
sound. I have seen this kind of thing done with a wooden cigar box.

**QUESTION: **

What light source will
bounce/refract/reflect off of broken glass?
Will regular light, a laser, or some other source. Let's assume it is
clear glass

**ANSWER:**

Any electromagnetic radiation, and so any
light, when it strikes an interface between two media (for example air
and glass) will do two things: it will refracted into the material and
it will be reflected from the interface. The only exception is called
complete internal reflection where light inside glass, for example,
strikes an interface with a material with smaller index of refraction
with a grazing enough angle; it will reflect only, not leave the glass.
This is how fiber optics works. But that does not seem to be your
question and there will always be some light of any wavelength
reflected from glass in air.l

**QUESTION: **

How is it possible to
explain the movement of light with respect to its particle nature? that
particle will reach infinite mass due to the theory of relativity.

**ANSWER:**

Actually, the theory of relativity predicts
that any particle of zero mass must travel at the speed of light.
Photons are such particle. Until recently it was thought that neutrinos
were massless but we now know that they have a tiny mass. Although a
graviton has never been observed, it is believed that it travels with
the speed of light. A particle with a nonzero mass takes infinite
energy to accelerate to the speed of light, but photons have no mass
and so take no energy to accelerate to the speed of light since they
are already there.

**QUESTION: **

what math equaion can i use
to find PSI of water at diffrent hights.

**ANSWER:**

You want to calculate the
pressure at a depth *d* in a large body of water. The appropriate
equation is *P*=*P*_{A}+r*gd *where
*P*_{A}=10^{5} N/m^{2} is
atmospheric pressure, *g*=9.8 m/s^{2} is the
acceleration due to gavity, and r=1000 kg/m^{2} is the density of
water. A N/m^{2} is called a Pascal (Pa). On the other hand,
you might want to compute the guage pressure which is the amount above
atmospheric pressure in which case *P*_{G}=r*gd*; your tire pressures are measured in guage
pressure. Let's calculate an example. Suppose you are 10 m down. *P*_{G}=1000x9.8x10=9.8x10^{4}
N/m^{2}=9.8x10^{4}/6895=14.2 PSI. Note that I have used
the conversion 1 PSI=6895 Pa.

**QUESTION: **

Is there any heat associated
with visible light? I know heat is usually in the IR range, but is
there any heat in the visible range? If so, how much and or is it
measurable? For example, when using a 100 watt halogen light bulb that
when turned on produces enough heat to melt wax. How much heat is IR vs
Visible Light?

**ANSWER:**

Radiant "heat" energy usually means energy
which arrives via infrared electromagnetic waves. However, there is not
really a precise definition. All electromagnetic energy delivers energy
to whatever it is absorbed by, determined by the intensity. The reason
that IR is usually called radiant heat is of biological origin: we are
mostly water and water absorbs IR radiation very efficiently. So, if IR
and visible light, each with the same intensity, strike you, more of
the IR is absorbed.

**QUESTION: **

A piece of ferromagnetic
material having mass m is rolled under a permanent magnet suspended
above. When it gets close enough, it's pulled up against the magnet,
rising by a height h. The total work done is therefore mgh (g =
acceleration due to gravity). Where did the amount of energy mgh come
from?

**ANSWER:**

This seeming simple question
is a quite difficult and subtle one. Since the explanation is too
lengthy to give here, I am giving you a link here
where you can study the details. Essentially, this is Faraday's law in
action: when the ferromagnetic material gets magnetized it is
equivalent to a current loop; when a current loop moves in an
nonuniform magnetic field an electric field is induced; this electric
field does the work.

**QUESTION: **

Assuming the speed of light
is constant--light emitted from the front of a motorcycle at rest will
travel at the same speed as light from a moving motorcycle. This means
that if the motorcycle travels down a road with a light mounted
perpendicular to the motorcycle that the light being emitted will not
gain the motion of hte motorcycle, that is motion perpendicular to the
motion of the direction the light is emitted will not by in anyway
added to form a resultant direction and motion of the light emitted.
Are the above statements correct? If not why? If yes, does this mean
that the absolute motion of the earth can be found by emitting lasers
tangent to its surface and measuring the difference from the expected
path?

**ANSWER:**

As soon as you start having
velocities which are not along the line of motion, it gets more
complicated. If you have a component of the velocity perpendicular to
the direction of motion, the velocity seen by a "stationary" will be
affected by time dilation but not by length contraction. Hence, the
transformation for the transverse (perpendicular) and longitudinal
(parallel) components of velocity are different. If you are really
interested, you can get a discussion
here. The amazing thing is that the speed of light still comes out
to be the same, but the direction is altered; that is, if the light is
emitted perpendicular to the direction of travel, the velocity seen by
a stationary observer is in a direction different from perpendicular
but still of the same speed. It does "gain the motion of the
motorcycle" but loses just the right transverse velocity so that the
speed stays the same.

**QUESTION: **

What work is being done
while you walk?
I say the floor is doing work on you since the the floor is exerting a
forward force and your direction of travel is in the same direction. Is
this correct?

**ANSWER:**

Walking is a pretty complicated thing
because it is a periodic series of accelerations and decelerations. If
we look at the time averaged situation there is a constant velocity and
therefore, since the kinetic energy is not changing, no work is being
done. You are correct that the external force which does work in the
short term, either speeding you up or slowing your down, is the
frictional force between the floor and your feet.

**QUESTION: **

Do carbon nanotubes burn in
vaccum? like in space?

**ANSWER:**

Nothing burns in a vacuum. Oxygen is
required for burning.

**QUESTION: **

Do electrons move slower in
a colder environment, like air molecules move slower in a colder
environment, if not why?

**ANSWER:**

Yes. An important concept in physics is that
of an electron gas; this provides a good model for valence electrons in
a conductor since the valence electrons are essentially free to move.
And the average speed of the electrons deterrmines the temperature of a
gas just like in any other gas.

**QUESTION: **

You have a muon, which is a
fundamental particle(a fermion) like an electron, whose mass lies
between an electron and proton. It's lifetime is approximately 2.2
micro seconds. It then decays into a neutrino and antineutrino. My
question is this. Since neutrinos have at best an extremely tiny mass,
surely an antineutrino and a neutrino's combined mass does not equal
the mass of the muon. So where does this extra mass go when a muon
decays?

**ANSWER:**

For starters, you have it wrong regarding
the decay. A muon is either postively or negatively charged and the
neutrino or antineutrino is uncharged; therefore the decay mode you
assume would violate charge conservation. The most common decay of a
negative (positive) muon is m^{-}®e^{-}n_{e}^{*}n_{m} (m^{+}®e^{+}n_{e}n_{m}^{*}_{
}) where an asterisk
indicates an antineutrino. So you get one electron (positron), one
neutrino, and one antineutrion. But your question is still pertinent:
where did the missing mass go? There is no law that mass must be
conserved (in spite of what was postulated by 18^{th} century
chemists!) What must be conserved is total energy. Although in recent
years it has been discovered that neutrinos have a small mass, it is so
incredibly small that I may neglect it in this discussion. What must be
conserved is energy and mass is a form of energy. Thus, assuming that
the muon which decays is at rest (not necessary), the energy before the
decay is *Mc*^{2} where *M* is the mass of the
muon; after the decay the energy is *mc*^{2}+*T *
where *m* is the electron (or positron) and *T* is the
summed kinetic energies of the three decay products. We then equate
energies before and after to conserve energy. So the missing mass shows
up as kinetic energy. Since *Mc*^{2}>*mc*^{2},
it is not possible for all the decay products to be at rest after the
decay.

**QUESTION: ;**

If a radio signal is bounced
off an object that is directly above the sending or receiving station,
the signal strength is stronger at the receiver than if it bounces off
an object that is midway between the two stations. I have been able to
confirm this phenomenon in several books, but they all fail to explain
WHY. I tried to figure it out with optics, but was unsuccessful.

**ANSWER:**

Since radio signals fall off
roughly like 1/*r*^{2} (*r* is how far it travels) I
thought that this would be a relatively simple problem of calculating
the distance of the path of each and finding that the over the
transmitter path was shorter. However, choosing the height as 10 and
the ground distance as 500 (units are unimportant for qualitative
understanding), I found that the stronger at the receiver situation had
a longer path (about 510) than the weaker at the receiver
situation (about 500). So that ain't it! Next, the plane is not a
perfect reflector, so maybe that has something to do with it. I now
calculated, assuming a loss of half the signal upon reflection (and
still 10 and 500 distances), the following two scenarios: (I will call
the intensity at the transmitter *I*.)

- For the plane directly over
the receiver, the intensity it sees
*I*/100 and the reflected
intensity is* I*/200. Now, that signal must travel a distance of
(10^{2}+500^{2})^{1/2}, very close to 500. So
the final intensity is (*I*/200)(1/500^{2})=2x10^{-8}*I.*
- For the other situation, the
intensity at the plane is
*I*/(10^{2}+250^{2})=1.6x10^{-5}*I*
and the reflected intensity is 0.8x10^{-5}*I* . Now, the
distance to the receiver is (10^{2}+250^{2})^{1/2},
very close to 250. So the final intensity is (0.8x10^{-5})(1/250^{2})*I*=1.28x10^{-10}*I,*
substantially smaller.

So, I surmise, the reason is the
fact that a much larger signal eminates from the plane when it is close
to the transmitter.

**CORRECTED
ANSWER:**

It has been pointed out to me that my calculations above
would have arrived at exactly the same conclusion without the loss of
half the signal upon reflection. In fact, that is completely right:
just multiply both answers by 2 for 100% reflection and the conclusion
is still the same! So, it has nothing to do with the reflectivity of
the plane but rather with the strength of the signal at the time of
reflection. I stand corrected!

**QUESTION: **

Why is there no sonic boom
from light or radio transmissions?

**ANSWER:**

A shock wave (sonic boom in the case of
sound) happens if the __source__ of the waves is moving faster than
the waves themselves. Another example of a shock wave is the wake of a
boat if the boat moves faster than the water waves. Light and radio are
electromagnetic waves, not their sources. If you had a light source
moving faster than the speed of light, there would be a "lumen boom".
However, as you probably, nothing can go faster than the speed of light
in a vacuum. However, light travels more slowly in a material, for
example glass or water; then if a particle travels faster than that
light speed, shock waves occur. This is often seen in the water
surrounding a nuclear reactor since energetic subatomic particles
passing through the water are moving faster than the speed of light in
water; it is seen as a blue glow.

**QUESTION: **

If I have two cylinders, one
with an inside cross sectional area 2 square inches, and the other with
an inside cross sectional area of 1 square inch; each cylinder has an
airtight piston with an attached handle; each cylinder is the same
length; and each cylinder has a nozzle with an inside diameter of .5
inches; which cylinder will suck up more water with the nozzle if an
equal amount of force is exerted on the handle? And what are the laws
of physics that would govern this situation?

**ANSWER:**

You need the continuity equation and
Bernoulli's equation to do this. I find it easier to think about the
fluid moving the other way which is equivalent, so that is how I will
do it. I will use the following notations: at the the nozzle the speed
of the fluid is *v*_{2}, the cross sectional area is *A*_{2},
and the pressure is *P*_{2}; at the piston the speed of
the fluid is *v*_{1}, the cross sectional area is *A*_{1},
and the pressure is *P*_{1}.
The pressures are *P*_{1}=*P*_{A}+*F*/*A*_{1}
and *P*_{2}=*P*_{A} where *P*_{A }is
atmospheric pressure and *F* is the force applied. The continuity
equation states *A*_{1}*v*_{1}=*A*_{2}*v*_{2};
this simply says that the rate of fluid in is the same as the rate out.
So, you may solve for v_{2} which is not of interest to us: *v*_{2}=*A*_{1}*v*_{1}/*A*_{2}.
Now, Bernoulli's equation says that *P*_{1}+r*v*_{1}^{2}/2=*P*_{2}+r*v*_{2}^{2}/2
where r
is the density of the fluid. (This is not the most general form; if the
nozzle and were at significantly different altitudes *y* then
there would be a r*gy* term added to each side of the
equation.) Now, if you do all the algebra you will find that *v*_{2}^{2}=2*FA*_{1}^{2}/[(*A*_{1}^{2}-*A*_{2}^{2})r]. One important
thing to note is that if *A*_{1} is much greater than *
A*_{2} the speed out is independent of *A*_{2}:
*v*_{2}@2F/r.* *For your cases, *A*_{2}=.5,
*A*_{1}=1, and * A*'_{1}=2 (units are
not important since the areas enter as ratios), then *v*_{2}^{2}=2*.67
F*/r
and v'_{2}^{2}=2*.*13* F*/r so the thinner
piston moves fluid through the nozzle faster.

**QUESTION: **

If I drive slowly on my dirt
road it rattles my teeth. If I drive fast it feels better. What's best
for the suspension of my truck (and my teeth)? Driving fast or slow?

**ANSWER:**

If you have a bump and go over it you
experience an acceleration and Newton's second law says there must be a
force causing the acceleration. The faster you hit the leading edge of
the bump the greater the acceleration, so the greater is the force you
feel. This is basically how speed bumps work, However, if there is a
series of small bumps relatively close together the inertial of your
car might carry you from one to the other so that you do not have to go
up the leading edge. Also, since your springs are relatively stiff, a
high bumping frequency has the wheels bouncing but the car (and you)
not moving as much whereas at a slower speed the car and wheels and you
move more as one. I guess my rambling says you should go faster (as
long as you can maintain control).

**QUESTION: **

Is it possible the reason
why Electrons do not fall into the nucleus is; the closer an Electron
gets to the nucleus it's charge is diminished, or it begins to become
more positive and repelled? 2nd, the reason why it does not fly away
from the nucleus is; the farther away it gets from the nucleus, it
becomes more Negatively charged?

**ANSWER:**

Your suggestions are not
possible. One of the most sacrosanct of all physical laws is
conservation of electric charge. The charge of an electron never
changes under any circumstances.

**QUESTION: **

I have a question that no
one seems to be able to answer. If mass can be converted to energy at
the speed of light, under what condition(s) can energy be converted to
mass? I am trying to imagine what the inverse of the speed of light
might be.

**ANSWER:**

I do not know what you mean by "converted to energy at the speed of light"'
or "the inverse of the speed of light"; let's just say that mass may be
converted into energy. I take it your question is then "under what
condition(s) can energy be converted to mass?" Well, any condition you
like provided that rules like charge conservation, energy (including
mass energy) conservation, and momentum conservation are obeyed. Here
is one example: the nucleus of an atom has a mass smaller than the sum
of its parts (neutrons and protons). If you now disassemble the nucleus
you will, of course, have to add energy (that is, do work) which shows
up as increased mass of the system. Note that the inverse is also true,
that is if you take a bunch of neutrons and protons and push them
together you will get a net gain of energy by creating the final
nuceus; this is how stars work.

**QUESTION: **

Is it possible to create
elements like gold or titanium in the nuclear fission/fussion reactor?
Is it likely that we would be able to create at least a few atoms of it
sometime in the future?

**ANSWER:**

Not only is it possible, it happens all the
time. By definition, a fusion or fission nuclear reaction starts with
fuel and turns it into something else. In the case of fission, take
uranium, for example. When it fissions, it splits into two nuclei.
Those that you give as examples, gold or titanium, are unlikely (not
impossible) because the distribution of fission products tends to fall
mostly between rubidium and gadolinium (see
Wikepedia for more detail). For fusion, we get the sum of the
fusing nuclei, for example hydrogen plus hydrogen fuses to helium,
helium plus carbon fuses to oxygen, *etc*. Inasmuch as the early
universe was all hydrogen, the very existence of other elements today
proves that they were created (in stars) *via* fusion.

**QUESTION: **

I am interested in
determining the amount of friction (and subsequently heat) generated in
primitive friction fires. I have read about calculating coefficients
for static and dynamic friction, and am wondering if there is another
formula that is more applicable. The fire-making method I have in mind
involves the rotation of a wooden dowel (with a rounded tip, like a
half-sphere) in a wooden socket with a corresponding half-spherical
shape. I would like to be able to compare the amounts of friction for
various wood species, and use that information to determine how much
heat can be generated with a given diameter dowel. Any help would be
greatly appreciated.

**ANSWER:**

Friction is a very tricky thing. In its
simplest form, the frictional force, which will determine the heating
rate, is proportional to the normal force (how hard the two are pressed
together. In your case, however, the temperature varies and so the
proportionality constant (coefficient of friction) will not be a
constant at all but vary with the temperature. Physics is not just a
theoretical science but equally an experimental science. In a situation
like yours, the best way to study this problem is to do experiments.

**QUESTION: **

Are there places in an atom,
where the electrons are located, that make it more likely that
electrons will form bonds?

**ANSWER:**

I am not sure what you are asking. The
electrons most involved in chemical properties of atoms are the valence
electrons which are generally the outermost electrons.

**QUESTION: **

Why does light get dimmer as
it gets farther away?

**ANSWER:**

If you have a source which is radiating in
all directions, like a light bulb, then if you get a distance from it
which is large compared to the size of the filament, then, as you say,
the light gets dimmer as you get farther away. That is because light
carries energy and that energy gets spread out over a larger and larger
area as you get farther away. The intensity of light is defined as the
energy crossing a square meter in a second and that gets smaller, of
course, as the available energy spreads out. Not all light gets dimmer
as you go away: a laser is light which does not spread out but stays in
its narrow beam, so the spreading is very small so the intensity is
very nearly constant as you go farther away. Laser beams have been shot
to the moon, reflected back, and lose very little intensity.

**QUESTION: **

do have more than one point
free of electrical filed in a square with 4 charges at its edges

**ANSWER:**

I assume you mean equal
charges. Field will also be zero infinitely far away.

**QUESTION: **

Of what matter is moon made
of ?

**ANSWER:**

See
http://www.nasm.si.edu/exhibitions/cchoice/moonrocks/moonrocks1.htm

**QUESTION: **

I have heard that cold can
eventually "seep" through anything, no matter what it is made of. I was
wondering if this is correct.

**ANSWER:**

"Cold" is a qualitative concept and it is
meaningless to ask if "it" can "seep". If you have two objects with
different temperatures, then energy will be transferred from the higher
temperature to the lower temperature until equilibrium is reached
(equal temperatures); this will happen regardless of what is between
them (provided that it is an isolated system) since there is no perfect
insulator. The energy transfer, if there is a vacuum between them, will
be accomplished via radiation.

**QUESTION: **

Please tell me if you know
how to separate water into gasses with electricity or any other way for
that matter. - I would like the most to know how to do it at home and
possible safe one too, but anything is better tan none so please give
me any info that you can on this topic.

**ANSWER:**

Check out
http://www.reachoutmichigan.org/funexperiments/agesubject/lessons/energy/split_h2o.html

**QUESTION: **

I was watching the science
channel today and was learning about the theory of dark matter. I had a
fundamental issue with this idea because it simply places a unknown
into an equation that satisfies the answer which we expect/is projected
based upon our own understanding of physics. This idea simply seems too
easy a solution. I began thinking about quantum physics of which I know
little to nothing about. What I do know is that quantum physics is
necessary because the laws of physics which apply to our daily life at
human scale do not apply to that of subatomic particles. The show was
trying to explain the reasoning behind galactic rotation. The show
stated in order for galaxies to rotate at a uniform speed from their
inside to their outside without the galaxy destroying itself there must
be necessary unseen mass(Dark Matter). My question is why if on a small
anatomic scale physics is altered making mass behave differently
wouldn't it also, on a much larger scale relative to daily human life,
make particles also act in a completely unique form of physics? I was
wondering this because although it is a generally baseless theory the
idea would make dark matter totally unnecessary.

**ANSWER:**

Most astronomers and astrophysicists
seemingly have no problem postulating the existence of dark matter to
explain many observations which seem to indicate its presence. However
others, like myself, find this to be sort of akin to the postulation of
the "luminiferous aether" postulated to provide a medium through which
light waves could propogate. What you are suggesting is, in fact, quite
reasonable: until we can test with precision that our laws of nature
are the same at very large distances, it is somewhat presumptive to
assume that they must be. I should warn you, however, that most
mainstream astrophysicists would not be in agreement with this point of
view.

**QUESTION: **

If the earth suddenly
shrinks to half of its present radius, the acceleration due to gravity
will be what?and why?

**ANSWER:**

Assuming that the mass remains the same, the
gravitational force, and thus the acceleration due to that force, would
increase by a factor of 4 because the gravitational force is inversely
proportional to the square of the distance from the center.

**QUESTION: **

What is the temperature of
fire?

**ANSWER:**

It depends on many things, like what is
burning, what the environment is like, *etc*. Typical
temperatures are around 1500^{o} C. A little more detail on
different kinds of fires may be found on
Wikepedia.

**QUESTION: **

Is it possible for a
helicopter to hover above the Earth and have the Earth move under as it
rotates so that the helicopter would "travel" around the Earth in 24
hours?

**ANSWER:**

Inasmuch as the earth drags its atmosphere
with it, the helicopter would have to travel at a speed much larger
than helicopters go relative to the air to remain in the same position
in space as you stipulate. So, no it is not possible.

**QUESTION: **

What happens to the atomic
number and mass number of a nucleus when it emit (a) a positron? (b) a
gamma ray?

**ANSWER:**

- charge decreases by one unit, so atomic number decreases by
one; mass number stays the same.
- mass number and atomic number are both unchanged

**QUESTION: **

I am a 9th grade student
currently attending Nelson County High School in Kentucky. The other
day i learned in physics class that light travels slower through glass
than it does through air. Does this mean that light travels slower
through matter of lower energy?

**ANSWER:**

Light in a vacuum is the fastest thing in
the universe. Light traveling through any medium is therefore slower.
The fact that light travels more slowly through a medium like glass is
why lenses work. I do not understand what you mean by "matter of lower
energy".

**QUESTION: **

Will carbon molecules hold
an electric charge, i.e. could carbon be magnetised?

**ANSWER:**

Don't know just what you
mean. Yes, you can make a C negative ion, that is add an electron to
it. However, this has nothing to do with its being "magnetised". I
think what you must mean is can you make carbon ferromagnetic. The
answer is no since ferromagnetism depends on the crystaline structure
of the material and the interaction of the outermost electrons with
their neighbors, and it is most unlikely that you could make carbon do
this. All materials are "magnetised" in some sense, either paramagnetic
(attracted to a bar magnet) or diamagnetic (repelled); the effects are
much weaker than ferromagnetism.

**QUESTION: **

If there are four
fundamental forces--gravity, EM, weak and strong--how does the Casimir
force fit in this scheme?

**ANSWER:**

The Casimir force has its
origins in the electromagnetic force (vacuum fluctuations of the
electromagnetic field). You can read a nice discussion at Physicsweb.org.

**QUESTION: **

If one were to release a
standard, 20 lb., 8.5 x 11 inch sheet of white copy paper from, say,
the space station, with adequate velocity to exit orbit and fall toward
earth. Could it survive the trip? I seem to be the only one to believe
that it could. The strongest claims against this theory so far have
been meteorological- perhaps it becomes soaked with water, etc. what do
you rhink?

**ANSWER:**

The possibility of water
causing shoul not even be considered since, obviously, passing through
a good thunderstorm could certainly cause the paper to go to pieces.
The situation would depend on the speed at which the paper was moving
when it hit the top of the atmosphere. For example if you just
"dropped" it, that is caused it to fall straight down (which would
actually mean giving it a velocity of about 18,000 mi/hr opposite the
shuttle, I would guess it would make it since it would hit the
atmosphere with a relatively small velocity. On the other hand, if you
released it with just slightly less speed than the shuttle has but
enough less to leave orbit, my guess is that when it hit the top of the
atmosphere that it would "burn up" and be destroyed.

**QUESTION: **

i've noticed many
similarities between gravitational fields and electric fields. Is there
an analog in electricity to a black hole?, an infinite electric field
with infinite charge at a point? If not, why not? If so, what sort of
physical reproductions does (or would) this have on surrounding matter?

**ANSWER:**

The answer is no because a black hole forms
because the gravitational force is attractive and so as you add more
and more mass to an object it eventually collapses under the huge
gravitational force (this is a bit of an oversimplification, but
essentially how a black hole forms). The electrical force, however, is
repulsive, so you the more charge you add the more the object wants to
fly apart.

**QUESTION: **

is it possible to trap light
in a box if it were filled with mirrors? and since things have color
because of light ( ex.blue things reflect blue light and absorb all the
others) when there is no light is everything actually invisible?

**ANSWER:**

Light would be trapped only for a very short
time after which it would be absorbed by the mirrors (heating them up
slightly); there is no such thing as a perfect mirror. For some numbers
showing how quickly the light would disappear, see one of my previous answers. Regarding
your second question, if you define "visible" as being able to be seen
by the human eye, then, yes, things are invisible if there is no light.

**QUESTION: **

If the sun were to disappear
in an instant, would the Earth spin off into space IN DARKNESS?? or
would the "final light" from the sun, taking some 7-plus minutes to
reach Earth, arrive prior to the "release" of magnetic pull/gravity
occurrence as experienced on/by Earth? Perhaps my question has to do
with the nature of gravitational pull--is it a "chain/rope"-sort of
essence or some sort of wave, which would, I think, have to be at or
less than the speed of light and means the light would go out first. I
find my uninformed bias is toward the "rope" form, in which case we
would by leaving orbit while the sun was still shining on Earth.

**ANSWER:**

The speed at which a gravitational field
propogates has not, to my knowledge, been measured. It is generally
believed that it propogates at the speed of light. Thus, the earth
would leave orbit and go dark simultaneously. In any case, no physicist
would believe that the appearance of any force would be instantaneous.

**QUESTION: **

Heres a physics question...
I have a rubber band and three toothpicks. I loop the rubber band
around two of the toothpicks, and hold them apart, stretching the
rubber band. I have someone hold the two end toothpicks. I then slip
the 3rd toothpick in the dead center of the rubber band, and start
twisting it, winding the rubber band from the center. Then, I let go of
the center toothpick, at the same time as my buddy lets go of ONE of
the end toothpicks. The third toothpick is still held firm. The
question is: Which toothpick spins faster, the center one or the end
one. And more importantly, WHY? What physical theory causes this?

**ANSWER:**

First, since the the speeds
will depend on when you look at them, let us revise your question so
that we ask which will have the biggest acceleration at the start, that
is which will acquire the greatest speed in the first short time. Your
question is equivalent, at the beginning, to masses on springs. The
middle toothpick is analogous to a mass attached to two identical
springs, each stretched by some amount. The end toothpick is analogous
to the same mass but attached to one spring stretched by the same
amount. So when you first release them, the one with two springs has
the greater acceleration. This will only be true immediately after
release because the half of the rubber band between the two movable
toothpicks will untwist faster.

**QUESTION: **

If you built a machine that
would swing a weight and "kick" a ball along the ground, controlling
all the variables, excepting that you double the weight, why would the
distance the ball travel only be 30% more?

**ANSWER:**

You have not given me enough information
about the machine, but a little consideration of the answer leads me to
think that the machine must simply be the head-on elastic collision
between two balls of different masses, one initially at rest. If the
"kicker" has a mass *M* and incoming speed *V*, and the
ball has a mass *m* and is at rest, then if you
conserve both momentum and kinetic energy you will find the ball,
after the collision, has a speed *v*'=2*mV*/(*M*+*m*). So, let us do two
numerical examples:

- If
* M=m,* then *v'*=*V*.
- If
*M=*2*m,* then *v*'=(4/3)*V*.

Guess that answers your question
since the distance the ball travels (while experiencing a constant
retarding frictional force) is proportional to the initial speed.

**QUESTION: **

In the acoustic doppler
effect, i have found that the higher the original frequency, the
greater the shift in frequency.

**ANSWER:**

Quite simply it is because
the frequency difference is proportional to the original frequency. In
terms of a percentage change, there is no dependence on frequency.

**QUESTION: **

Does a hockey puck reach
it's maximum velocity at the last instant of contact with the hockey
stick, or is there such a thing as (for lack of the proper terminology)
'residual acceleration' I have considered this at great length..
>From what I know in physics if there is no longer force being
applied to the puck there should not be any accelertion after the
contact....
Almost a logical deduction.. however seeing replays and it's almost an
instinct telling me that I might be wrong.. It doesn't feel like the
stick is travelling at a the same velocity as the puck is.. 100mph
shots and all.. Perception maybe different than reality.. anyway, if I
am wrong and there the puck continues to accelerate for a short
distance after leaving the stick,. it's because of the flex in the
stick, the energy transfered into the puck has not fully caused it to
accelerate.. possibly like the flex in a golf ball..

**ANSWER:**

A short answer to your long
question: The puck cannot continue to accelerate (gain speed) after it
leaves the stick. In the physics sense, it does accelerate but with a
negative acceleration, that is it slows down.

**QUESTION: **

my question is how is the
current flowing through the different resistors connected in series
same f it is an axiom, then its ok. but if it has reason behind it,pls
tell me

**ANSWER:**

No, it is not simply axiomatic. The reason
is the conservation of electric charge. Consider just two resistors
connected in series. A certain amount of electric charge enters one
resistor in a certain time (electric current). Similarly, a certain
amount of charge exits the other resistor. If the charge out is less
(greater) than the charge in, where is the charge going to (coming
from)? Electric charge cannot be created or destroyed, and since it is
not piling up or being drawn from either resistor, the charge in must
equal the charge out so the current in each is the same.

**QUESTION: **

I've always wondered if
"time" is a man-made concept or if it really exists. I've heard that
the fourth dimension is time, is this true?

**ANSWER:**

This is more a philosophy than physics
question. As a physicist, I would say that time exists independent of
my perceiving it. Our intuitive notions of time, such as that time is a
universal thing throughout the universe for all observers is now known
to be incorrect. Two identical clocks given to two different observers
will definitely not run at the same rates if the observers are moving
with respect to each other. This is the unavoidable consequence of the
theory of special relativity. Time is the fourth dimension in the sense
that when it is realized that time and space are entangled with each
other, the result again of special relativity, the mathematics of the
physics involving both space and time is very similar to the
mathematics of a four dimensional space. For example, motion in three
space may be described as a rotation in four space.

**QUESTION: **

A 50cm silver bar becomes
shorter by 1mm when cooled.How much was it cooled? coeff. of linear
expn=.000018/c.
Which should be my original length ? 50cm or (50-0.1)cm?

**ANSWER:**

The equation you use, presumably, is
D*L*=aD*T*=a(*T*_{f}-*T*_{i})=(*L*_{f}-*L*_{i}).
Since *T*_{f}<*T*_{i}
you must have *L*_{f}<*L*_{i }so *L*i=50 cm.

**QUESTION:**

My cousin and I have a
dispute about the flushing power of a standard 1.6 gallon flush toilet,
versus an old-fashioned 5-gallon flush model. I use a lot of toilet
paper, and therefore must flush 2 or 3 times with the newer 1.6 gallon
models, or risk a clog, which has happened to me far too often. I
maintain that the 5-gallon flush model will be much more likely to
prevent clogs. Is there a formula for computing the pressure of a 1.6
gallon flush versus a 5.0 gallon flush? How would that be
mathematically computed with precision?

**ANSWER:**

There is no reasonable way
to compare them mathematically since they have different designs. The
low usage one is supposed to be designed to have comparable disposal
capabilities. Even if you are right that you, as an individual, must
flush more than once, from a conservation point of view it would still
be better to have an efficient toilet because you are likely not the
only user. My son uses way too much paper also and every once and a
while it clogs; I just pull out the old plumber's helper and in no time
all is well.

**QUESTION: **

Hello, I have solved this
question part of the way, but cannot figure out the end result! The
question is: In an x-ray imaging system operating at 70 kVp, each
electron arrives at the target with a maximum kinetic energy of 70 keV.
Because there are 1.6 x 10^-16J per 1keV, this energy is equivalent to
the following: (70keV)(1.6 x 10^-16J/keV)=1.12 x 10-14 J
Inserting this energy into the expression for kinetic energy and
solving for the velocity of the electrons, the result is: KE=1/2mv2
v2=2KE/m
v2=(2)(1.12 x 10-14 J)/(9.1 x 10-31 kg) =0.25 x 1017 m2/s2
I can get that far....the end result is: v = 1.6 x 108 m/s
If i use the equation v= mv2, I get:
v = (0.25 x 1017) (0.25 x 1017)2
which gives me - v=(0.25 x 1017)(0.063 x 1034)
and my answer comes out to v = 1.6 X 1051 m/s
How do they get the answer v = 1.6 x 108 m/s ?

**ANSWER:**

This looks like a
homework problem which the groundrules of my site prohibit! However, I
will give you the hint you need: your expression KE=*mv*2/2 is
wrong; this expression is true only for very slow (compared to the
speed of light) particles. The correct expression is KE=*E*-*moc*^{2}
where E is the total energy, *m*_{o} is the rest mass,
and *c* is the speed of light. *E *is given by E=(*mo*^{2}*c*^{4}+*p*^{2}*c*^{2})^{1/2}
where *p *is the linear momentum given by *mov*/(1-*v*^{2}/c^{2})^{1/2}.
Also, your equation *v*=*mv*^{2} is obviously
incorrect because it could be simplified to *mv*=1 which is
nonsense!

**QUESTION: **

My 11 year old has asked me,
"Does gravity bend light?" I did highschool physics about 20 years ago,
so am very rusty and not up to date with current thought. I have looked
at this discussion topic on the archives of many forums, but have ended
up very confused by the differing opinions/explanations. I would really
like an answer which is easy to explain to a child, but yet not so
simplistic that it is inaccurate. Am I asking the impossible? She has
read about the nature of light and also about gravity, and can't
understand how light can be affected by gravity, when it has no mass.
Is it because photons are energy and so can be used instead of mass? Or
is it that the gravitational pull around massive stars affects the
"space" around it and light just follows the stretched paths? If this
is true, how can some authors say that the light is still moving in a
straight line even when it is following a curved path?

**ANSWER:**

Here
is one explanation, probably the easiest for your daughter to
understand: Light being affected by gravity is a result of the
principle of equivalence in general relativity. This states that there
is no experiment which you can perform to distinguish between your
being in a gravitational field or in an accelerated frame of reference.
Thus, for example, imagine that you are in an elevator which
accelerates upward; if light enters through a hole in the side of the
elevator it will clearly appear to fall like a projectile because of
the acceleration of the elevator. So, the same thing will appear to
happen in a gravitational field the acceleration due to which is
exactly the same as the acceleration of the elevator. Hence, light
will "fall" in the earth's gravitational field with an acceleration of
9.8 m/s^{2}. You might be interested in the answer to an earlier question.

Here is
another: If we look at the world as having a Euclidean "flat" geometry
and watch a ray of light pass a very massive object, we see the light
bend. But, the way that general relativity describes the world
says that, if we are in the vicinity of a massive object the space
itself is not Euclidean but is curved; in this space the light follows
a "straight line" in that non-Euclidean geometry.

**QUESTION: **

what is error on T when T =
1.04 * sin (2.8 ± 0.2)/ sin (58.2 ± 0.2)

**ANSWER:**

The largest contributor to the error will be
the sine in the numerator since sine is small and changing rapidly at
small angles so a relatively small uncertainty in the angle will lead
to a large uncertainty in the sine of the angle. You can get a rough
feeling for the percentage of the uncertainty by estimating the percent
error of that term: (sin2.8-sin2.6)/sin2.8=0.071=7.1%. What you need to
know is that the uncertainty of the sin(A±a)
is approximately cos(A)*a (because d[sin(x)]={d[sin(x)]/dx}dx) and that
the percent uncertainty of a ratio (A±a)/(B±b) is approximately a/A-b/B. Putting your
numbers in I get about 6.7% (in accord with our rough estimate)
uncertainty for T, or about ±0.004. {When you are doing your calculations
it is important that angles (and their uncertainties) are expressed in
radians, not degrees.}

**QUESTION: **

Does the flow of linear time
as we percieve it (disregarding its pyschological variations) vary as
you get down to the level of quantum mechanics? Secondly, if so, I've
read at that level, all time is simultanteous, that it doesn't exist at
all at that level. Is this true, and why?

**ANSWER:**

The answer to your question is that we do
not know. Read my earlier
comments related to this question. Regarding your second question,
I never have heard it said that "all time is simultanteous" whatever that means. I have read
that it is the opinion of some very deep thinkers that the reason that
not much progress has been made in unifying gravity and quantum physics
is that we really do not understand time very well.

**QUESTION: **

how is it possible that
light can be both a particle and a wave! i need to know it's ruining my
whole life.

**ANSWER:**

Ruining your whole life? How is it possible
that my tie can be both red and green? That is just the way it is. I
know that this is an unsatisfying answer, but science is based an
measurements (experiments) and if you study light and look for a wave,
you will find one but if you look for a particle you will find that
also. This is called the wave/particle duality and it is, essentially,
a statement of experimental fact. And you can do experiments which
unambiguously see both possibilities in the same experiment. The best
known example is to do a double
slit experiment with very low intensity. If the intensity is so
low that there is, say only 1 photon per minute passing through, then
it has to pass through one slit or the other, right? Wrong--you still
get an interference pattern. So, you say, light is therefore a wave,
not a particle. But, imagine that the screen detects the light using
the photoelectric
effect which cannot be understood unless you treat the light as a
collection of photons. This detector will work perfectly well in
displaying the interference pattern. This duality is not unique to
light: any particle will exhibit wave properties; *e.g.* that is
how an electron microscope works, by exploiting the wave properties of
electrons. Maybe I shouldn't have told you this since it may compound
your life-ruining distress! Wave/particle duality is a reality of
nature, that is all.

**QUESTION: **

A sample of a particular
radioisotope is placed near a Geiger couinter, which is observed to
register 160 counts per minute. Eight hours later, the detector counts
at a rate of 10 counts per minute. What is the half-life of the
material?

**ANSWER:**

This sounds suspiciously like a homework
problem to me! However, I will outline how to do it but not do it to
its final answer. The activity of a sample (counts rate) is an
exponential function: *A*(*t*)=*A*0exp(-l*t*) where *A*(*t*)
is the activity at time *t* and l is the decay constant related to the halflife by t=ln(2)/l. Since you know *A*
at two times (I would call the first one* t*=0), this equation is
actually two equations for two unknowns (*A*_{0} and l), so you can solve for l which gives you t.

**QUESTION: **

WHEN A 1,000 POUND PLANE HAS
WINGS THAT ARE BANKED AT 45* DURING A LEVEL TURN, THE CENTRIPETAL FORCE
ON THE PLANE IS EQUAL TO THE WEIGHT OF THE PLANE. USE THE PYTHAGOREAN
THEOREM TO FIND THE LOAD ON THE PLANE. [LOAD=WEIGHT+(CENTRIPETAL
FORCE)]

A. ABOUT 2,000 POUNDS

B. ABOUT 707 POUNDS

C. ABOUT 1,414 POUNDS

D. ABOUT 500 POUNDS

**ANSWER:**

This looks suspiciously like a homework
problem to me which are forbidden by the groundrules. However, it is
sort of interesting to me because it doesn't make a lot of sense. I
would have thought that load would be defined as the net force on the
plane. However, load is defined here to be the horizontal component of
the force the air exerts on the plane plus the weight (which is, of
course, vertical). This force has a magnitude of the square root of
10002+10002, so C is the answer with the direction pointing 450 below
horizontal. If the load were the force the air exerts on the plane, the
answer would still have a magnitude of 1414 lb but would be in a
direction 450 above horizontal. If the load were the net force on
the plane the answer would be 1000 lb horizontal.

**QUESTION: **

Does the wavelength of light
affect how brightly it shines?

**ANSWER:**

No, "brightly" is determined
by the amplitude of the wave and not by its wavelength.

**QUESTION: **

What is light?

**ANSWER:**

Wow, that is a concise question. The answer
is not! The nature of light has been of great interest over the ages.
Once science became a legitimate pursuit (as separate from philosophy)
the debate centered around whether light is some kind of wave or some
kind of particle. Newton thought it was a particle; it was later
demonstrated (in the early 19^{th} century}, however, that
light behaves like a wave; see my earlier answer to a
similar question for more background. What was actually doing the
waving was a mystery until later in the 19^{th} century when
Maxwell showed that light is waving electric and magnetic fields;
again, see my earlier answer.
Finally, at the beginning of the 20^{th} century Einstein, in
explaining the photoelectric effect, found that light exists in
quantities no less than what is called a photon, one quantum of the
electromagnetic field. Hence, light really is like particles, a swarm
of photons. We finally understand that light is both, a situation
called the wave/particle duality; if you look for a wave you will find
one and if you look for a particle you will find that also.

**QUESTION: **

do all orbits in space
deteriorate? If not, why? Is it possible that the Earth's orbit could
deteriorate (as well as Mars, etc.) and cause global warming trends?

**ANSWER:**

For an orbit to "deterioate" (we usually use
decay to describe this), the orbiting object must lose energy. It can
do this by colliding with stuff, mainly gas and dust so that the energy
loss could be thought of like air friction on earth only much smaller.
An orbiting object will also lose energy by radiating gravitational
waves; this has been seen for some binary star systems. But, for the
earth, these are totally negligible and certainly have no effect on
global warming. The distance to the sun is much less influential than
the angle that the rays from the sun hit us; we are actually farthest
from the sun during summer.

**QUESTION: **

what would happen if there
was too much air pressure?

**ANSWER:**

Well, you don't stipulate what "too much"
is, so I will address an extremely increased pressure. The pressure due
to the atmosphere is about 1 ton per square foot. So why doesn't this
pressure crush you? The reason is that we have evolved in this
environment so that the pressure inside our bodies is about one
atmosphere; every cell in your body has a pressure inside which keeps
it from being collapsed. Now suppose that you double the pressure
outside. The pressure inside does not change and so you are crushed by
the net force in on you. One of the first things to go is your eardrums
which should not surprise you if you have ever dived to the bottom of a
swimming pool where pressure increases fairly dramatically.

**QUESTION: **

My questions pertain to
gravitational potential energy. Sepcifically, I'm a little confused
about how it works. My understanding is that when an object is moved
away from the earth (upwards) it gains gravitational potential energy
that is transformed to kinetic energy if and when it falls back toward
the earth. This understanding leads me to two questions. First, what
happens to that potential energy once an object moves beyond the
gravitational feild of the earth? Does that object still retain the
potential energy it gained as it moved away from the earth? Second, why
must I exert energy to hold something in a constant position relative
to the earth? for example, why must I exert energy to hold a text book
above my head. It is not moving towards or away from the earth, so is
not gaining potential energy, yet I am exerting energy by holding it up
against the force of gravity. On the other hand, a table does not exert
any energy in accomplishing the same feat. So w hat gives? where does
that energy go? Am I totally off base here?

**ANSWER:**

Your questions:

- An object in a gravitational
field never moves beyond the field since the strength of the field is
proportional to 1/
*r*^{2} where *r* is the distance
from the center of the earth. So there is never a place where the field
is zero, just very small. The potential energy you are probably
familiar with is *mgy* where *y* is the distance vertically
from where you have chosen *y*=0. This works fine (but only
approxiately) as long as *y* is much smaller than the radius of
the earth; The correct potential energy is proportional to -1/r so as *r
*becomes very large the potential energy goes to zero;
but, note the minus sign: the potential energy gets smaller (more
negative) as *r* gets smaller, so the potential energy becomes
biggest when you are infinitely far away.
- You are totally confused
about what energy is. The way you impart energy to something is to do
work on it, and work is a force exerted over a distance. You are
exerting a force on the thing you hold over your head, but that force
is not acting over a distance so you are not changing any energy. It
makes no sense, from a physics point of view, to say that you "exert
energy".

**QUESTION: **

Is it true or not that one
can make larger structures such as planes, spacecraft (rotating) if we
make the walls thicker? Does making the walls thicker enable one to
build larger structures, without making them fall appart or deform?

**ANSWER:**

There is no answer to this question since
what is necessary to make something bigger depends on what the thing
is, what its location is, what it is made of, *etc*.

**QUESTION: **

This may seem like a strange
question and one that cannot be answered without some sort of bias
(religion, etc.), but if energy cannot be created or destroyed, where
does the energy in a living creature go upon death? What other forms of
energy is it transformed into, and what happens to the electrical
signals in the brain and other parts of the nervous system?

**ANSWER:**

What energy is there in a living being? It
is almost all bound up in the chemicals which make up the body. When it
dies, the chemical energy either stays there or ends up as heat if the
object decays. Regarding the electrical signals, an analogous question
would be what happens to the light coming from a light bulb when you
turn off the switch? The only reason the light bulb continues to glow
is that there is a source of energy pushing electrons through it and
when that source is removed the electric current simply ceases.

**QUESTION: **

OK, I have a sealed box with
a 60W electrical fan inside. The fan just circulates the air inside the
box. Does this box give off 60W of heat?

**ANSWER:**

A 60 W appliance is one
which consumes 60 W of power, that is it consumes 60 J of energy each
second. The appliance then converts this energy to another form of
energy. For example, a toaster will convert most of the energy to heat
(because it is designed to do that). A fan is designed to not convert
energy into heat, but rather into kinetic energy (of both the fan and
the air); the electric motor will heat up but not nearly as much as a
60 W toaster but probably more than a 60 flourescent light which is
designed to convert as much energy as possible into light. But if your
box is truly isolated from the rest of the world, much of the energy
initially converted into kinetic energy of the air will end up as heat
in the box and its walls.

**QUESTION: **

What is the
math/calculations to transform volts/meter into newtons/coulomb?

**ANSWER:**

A volt is a joule/coulomb, 1 V=1 J/C. A
joule is 1 kg m^{2}/s^{2}, so 1 V/m=1 kg m^{2}/s^{2}/m/C=1
kg m/(Cs^{2}).

A Newton
is 1 kg m/s^{2}, so 1 N/C=1 kg m/s^{2}/C=1
kg m/(Cs^{2}).

So, 1 V/m=1N/C.

**QUESTION: **

why does the d- block in the
periodic table have two valence electrons?

**ANSWER:**

This is really chemistry, not physics. I
believe it is due to the following:

The first 20 elements have s-
and p-shells. Beyond that, the ordering is not what you might expect.
For example, you might expect, after 1s, 2s, 2p, 3s, 3p, are filled
that next would come 3d. However, the 4s happens to have lower energy
than the 3d so it fills first. Therefore, as the nd-shell is filling
there are two electrons in the (n+1)s shell and these have wave
functions which extend farther out than the d-orbitals and thus are
more influential in determining the chemistry.

**QUESTION: **

How to shield an electronic
circuit or laboratory from stray electric fields, and why does this
work?

**ANSWER:**

Completely surround the circuit with a
conductor. The reason that this works is that the electrons are free to
move in a conductor. When the conductor is put into an electric field,
the electrons move around in the conductor. All such charge (or lack
thereof where electrons have left) will reside on the outside surface
of the conductor and be arranged in such a way that the field due to
these "induced" charges will exactly cancel out the field which induced
them inside the volume enclosed by the conductor. This is called a
Faraday cage (named after Michael Faraday who first constructed one).
If what you want to shield is quite large, just enclosing it with a
conducting mesh does a very good job as well. You should realize that
this is true only for static fields; if the field changes with time,
there will be fields inside the cage.

**QUESTION: **

If there was no cyntrifical
force on planets... would there still be gravity?

**ANSWER:**

First of all, there is no
such thing as a centrifugal force; I have repeatedly discussed that on
this site and you can read a bit about it by going to older answers and searching (do a
CTRL F) on centrifugal. The existence of the force of gravity is
universal and the gravitational attraction between two objects is
unaltered by anything else. Gravitational force between two objects
results from their masses and nothing else. What you may be thinking of
is that the apparent force of gravity is lessened somewhat by the
earth's rotation. Imagine standing at the equator: you have an
acceleration pointed toward the center of the earth of *v*^{2}/*R*
where *v* is the tangential speed due to the rotation (2p*R*/24
hr)=7.3x10^{-5}*R* and *R=*6.4x10^{6}* *m*
*is the radius of the earth. Putting in the numbers, your
acceleration would be *a*=3.4x10^{-2} m/s^{2}. A
force of *ma* is needed to keep you going around in circular
motion and the source of this force is gravity. The result is that your
apparent weight, the weight you read on a scale (which is actually not
measuring your weight but is measuring the force the floor pushes up on
you) would be slightly less than your actual weight. Since weight
is *mg*=9.8*m *your apparent weight would be (9.8-0.034)*m*,
about 0.3% less. If the earth rotated faster on its axis, this effect
would be bigger and eventually your weight would not be sufficient to
keep you in your circular motion and you would drift off into space.
But the point is that your weight is always the same regardless of
anything else--gravity is constant.

**QUESTION: **

how is the stella parallax
angle of a distant planet or star calculated?

**ANSWER:**

I presume you mean stellar parallax. I
recommend
this site for a brief animated tutorial.

**QUESTION: **

When chemical bonds form,
energy is released. Therefore, does water release energy as heat when
it freezes? If yes, does this explain why it is warmer when it snows?
Does the change of water from a gas to a liquid to a solid cause the
ambient temperature to increase?

**ANSWER:**

You must add energy to melt ice. Therefore
you must remove energy to freeze water. So, yes, water does release
energy when it freezes. Similarly, water vapor releases energy when it
condenses. However I doubt that these effects have any measurable
effect on air temperatures. It is often warmer when it snows because
the weather conditions favorable for snow (clouds, low barometric
pressure) cause it to be warmer; in other words, the warmer (less cold)
weather results in snow, not the other way around.

**QUESTION: **

While researching I found
out At one time it was proposed to launch satellite directly into a
circular orbit at a constant distant from earth using a giant WW
cannon. Can you pleas tell me why this proposal would not work

**ANSWER:**

Assuming that we had a cannon capable of
launching a projectile with sufficient speed (at least about 18,000
mi/hr), how would we aim it? One possibilty is horizontally. In
principle, this could work. It was actually Newton himself who first
imagined artificial earth satellites by proposing shooting a projectile
off the top of a high mountain with sufficient speed. There is a good
website where you can play around with launching satellites; if you
set the speed to 16,000 mi/hr you should see a nice circular orbit. In
practice this could not work, however, because the air friction due to
the atmosphere at such a high speed would either burn the projectile up
or cause it to slow down and hit the ground. If you aimed it up at some
angle, the resulting elliptical orbit would intersect with the surface
of the earth, that is it would crash before one complete orbit was
completed. What you need to do is first lift your satellite above the
atmosphere and then give it a horizontal speed with rockets on the
satellite. So a simple projectile will not work.

**QUESTION: **

what would happen if a
planet identical to Earth were to lie tangential to the earth, assume
that there is no impact between the two
heavenly bodies, one just appears. what would happen to gravity, the
planets,
the oceans, etc?

**CLARIFICATION: **

I meant that the crusts of
both planets would be just barely touching.

**ANSWER:**

The gravitational field due to two spheres
is the vector sum of the fields of each sphere. Hence, you could easily
calculate the gravitational force at any point in space (in particular,
of interest to you, on the surface of the earth) by just adding the
forces due to each planet. A few simple examples would be:

- At the point of contact the
gravitational force would be zero, so if you were located close to this
point you would be weightless.
- Along a line tangent to both
spheres and passing through the point of contact the force on an object
of mass
*m* (i.e. the weight) would be directed exactly toward
the point of contact and wold have a magnitude of 2*GMmd*/(*d*^{2}*+R*^{2})^{3/2}
where *G* is the universal gravitational constant, *d* is
the distance from the point of contact, *R* is the radius of the
earth and *M* is the mass of the earth. Note that this is zero if*
d*=0 and approximately 2*GMm*/*d*^{2} if *d*
is much larger than *R*.
- At the point opposite the
point of contact, the weight of an object would be have a weight 10/9
times larger than if the new planet were not there and point vertically
down.
- At other points the weight
would not point vertically down anymore because of the force from the
other planet.

To compute these results you
need to know that the gravitational force due to a uniform sphere of
mass *M* on a point mass *m* a distance *r* from the
center of the sphere points straight to the center of the sphere and
has magnitude *GMm*/*r*^{2} where *G*=6.67x10^{-11}
Nm^{2}/kg^{2} (only true if you are outside the sphere).

**QUESTION: **

The core of the earth is
'energized' by the compression of mass, since energy can be neither
created or destroyed, where prior did this energy exist?

**ANSWER:**

The simple answer to your question is
gravity. As a mass decreases in size its gravitational potential energy
decreases and this energy loss is made up by energy gain, kinetic
energy of the mass, that is it gets hotter. This is also how stars gain
enough energy (temperature) to "ignite", gravitational collapse. It is
thought, however, that part of the energy for heating the earth's core
comes from the decay of radioactive
nuclei in the core.

**QUESTION: **

Further on the "pull one end of a rope" idea - Do individual
elemental particles with mass behave the same way? That is, do they
have a "diameter", such that a force applied to say, the "right side"
of say, a quark, will be "felt" on the "left side" of the quark an
attosecond (or whatever) later?

**ANSWER:**

You have to be careful in
extending classical ideas into the realm of the very small. In quantum
mechanics, the appropriate way to describe subatomic physics, it turns
out that the idea of force is not very useful. Rather we use the ideas
of fields and potential energy. In classical physics, potential energy
is easily related to force associated with the field. There is no
useful way to define left and right but certainly the propogation of a
field, responsible for forces, is not instantaneous.

**QUESTION: **

In the article here --
www.iop.org/EJ/article/0143-0807/27/2/017/ejp6_2_017.pdf -- the authors
describe a process whereby sunlight is concentrated using the well
known parabolic dish method, but afterwards is directed into a large
sphere with a completely reflective interior. If one were to direct
solar energy into a sphere of this nature, and closed the "hole", could
one actually "store" the sunlight, and then let it out when needed?

**ANSWER:**

Well, I find I have no access to that
article since I am not a subscriber to the journal. However, I do not
need to see the article to answer your question. The answer is no, it
is not practical to store light using mirrors. The reason is that a
"completely reflective interior" is simply not possible and the light
is quickly absorbed. To get some idea of the numbers involved, see one
of my previous answers.

**QUESTION: **

In reference to
singularities, etc., I do not understand the concept of "nothing".
Since "nothing" is only understood as related or opposite to
"something" it would seem that "something" is primary and "nothing" is
imaginary. "Something" can be shown, while "nothing" can not be shown
except in a relative sense. "Nothing" is only useful in a limited sense
as a technique such as "zero". I think physicists use of "nothing"
shows nonsense. "Nothing" is nonsense in and of itself since the
thought of it alone, vis a vis "something", dissolves from the
imagination. Therefore, the singularity is truly something but as yet
not rationally described.

**ANSWER:**

I have no idea what your rant is about. I
have never heard a physicist refer to a singularity as nothing. It has
zero size but infinite density (for example if we think of a model for
a black hole). And physicists were the first to realize that a vacuum
is not empty at all but filled with virtual particles popping into and
out of existence (see vacuum
polarization). I should also note that most physicists I know do
not believe that a true mathematical singularity is a physical thing
because, although we might find "nothing" to be unphysical, we find the
notion of something being infinite as abhorrent! However, the use of
singularities in models is extremely useful and helps make our theories
comprehensible.

**QUESTION: **

If I want to create a higher
vacuum pressure in a container, than my vacuum pump can deliver, could
I create that vacuum pressure by placing both the pump and container
inside a second larger container, use the pump to evacuate both
containers, seal the larger container off and then pump out the smaller
container once more into the evacuated larger container. If my
understanding of vacuum pumps is correct, they create a difference in
pressure between the inside and outside of a given space, therefore it
should be possible by placing one evacuated chamber inside another to
multiply the pumps capability.

**ANSWER:**

The way a simple pump works
is that it pumps an amount of air out, compresses it, and expells it.
What determines the vacuum achievable is the rate at which air is
leaking in (or outgassing from inside the vessel) since when you reach
the point where the amount you take out in a cycle equals the amount
that leaks in. It is not the pressure differential which is most
important. The catch, however, is that if the vessel you are evacuating
is in a low pressure environment, less gas will leak in. So my answer
is yes and no--how's that for a hedge?

**QUESTION: **

Which will travel further
when kicked a soccer ball or an american football. They are roughly the
same weight, 410-450grams for a soccer ball and 421 for a football. I
am assuming that the drag caused by the odd shape of the football will
cause it to travel a lesser distance. Is there a way to calculate how
much less either as a distance or percentage?

**ANSWER:**

This depends on a lot of
things. However, the considerations I have thought of give the football
an edge over a soccer ball. I will assume that each is launched with
the same initial speed and angle. Were there no air drag, it would
surely be a tie. Now, I assume that the football has been punted by a
skilled kicker such that it spirals, that is spins around its lolng
axis of symmetry. When this happens, as you probably know, it goes
through the air pointy end first and is thus more aerodynamic than the
spherical soccer ball. In addition, the soccer ball is relatively
smooth whereas the football is knubbly. Although it is partly
nonintuitive, a rough ball suffers less air resistance than a smooth
ball because the rough surface carries a layer of air along with it
called the boundary layer which helps reduce air friction; this, in
fact, is why golf balls have dimples and tennis balls have fuzz.
Finally, I can think of one way the soccer ball might have an edge: if
the ball has a lot of spin in the right direction, lift will be
generated (like in an airplane wing, or more analogously, a curveball
in baseball). I doubt, however, that this effect will be as large as
the effects which make the football go farther.

**QUESTION: **

What keeps an electron from
crashing into a proton in an an atom?

**ANSWER:**

See my answer to an earlier question.

**QUESTION: **

If I google "einstein field
equations" and go into the Wikipedia site, the bottem of the first page
has "contents." I proceed to the section "The cosmological constant"
and therein find a version of EFE with Lamda in it. It looks like this:
Ruv - 1/2 R g uv + Lamda (guv) = 8 pi T uv. My question is this: Can I,
in a mathematically valid (algebraic) sense, move every thing except
Lamda from the left to the right side of the equation? More to the
point, is it mathematically valid to say: l=(8
p
T_{uv} + 1/2 R g_{uv} -R_{uv}) /g_{uv}
I don't know if I'm breaking any geometric convention. Thank you for
your thought.

**ANSWER:**

No, you may not do this. It is a matrix
equation and you cannot divide by a matrix.

**QUESTION: **

How can force carriers
affect two particles differently? For example: A virtual photon
interaction between two electrons causes them to repel, but an
interaction between an electron and an up quark causes them to attract.
The photons are the same, so what is different about those two
interactions that can cause different results?
(I asked this question on another website, and I was told only that I
was simplifying things too much. If I'm describing the process poorly,
please let me know!)

**ANSWER:**

You are indeed simplifying things too much.
The idea of particles passing photons back and forth is only a rough
schematic picture of what happens. The particles, quanta, which convey
a force (like photons do for the electromagnetic force) are not real
particles (photons) but rather virtual particles. They are photons
which cannot be directly seen, that is you could not stick a detector
between the two charged particles and be able to detect them. Their
existence defies energy conservation but that is ok as long as they
"exist" for a short enough time; the reason is that it is, according to
the uncertainty principle, ok for D*E* of energy to appear as long as it disappears
within a time D*t
*where D*E*D*t* is less
(approximately) than Planck's constant. There is a very nice discussion
about virtual particles at
http://math.ucr.edu/home/baez/physics/Quantum/virtual_particles.html

**QUESTION: **

Concerning gravity. I'm very
confused (NB I,m 59 yr old NOT a student!)
In a sphere (like a planet) if every atom is fully surrounded by
similar atoms then, except at the surface, shouldn't gravity effects
cancel out?
OK, the heavier atoms will 'fall' to the centre but don't EM effects or
the smaller atomic radii of metal atoms (so they will move through the
planets core more easily) explain this?
If centre of planet is a plasma, what does this 'do' to gravity?
Has gravitational force of 'weightless' objects towards each other (eg
in a spaceship) ever been measured? (OK I know it's very weak).

**ANSWER: **

Whoa, too many questions.
The site groundrules state only single, well-focused questions, but I
will go ahead this time and address some of your questions.

- Imagine that you are the atom and you are one
mile deep into the earth. Then if you look "up" you will see many fewer
atoms than if you look down because it is a lot more than one mile
through the whole rest of the earth. So you will still feel a force
toward the center of the earth; it will however, be less than your
weight on the surface. It is easy to calculate the weight of something
inside the earth by the following trick: only that part of the earth
*
inside* where you are exerts a force on you. Hence, if the earth
were hollow you would feel no force inside. Incidentally, your question
is related to one of the most famous problems in the history of
science. Newton delayed publishing his theory of gravitation for years
because he could not be sure that the force between two spheres was the
same as the force between two point masses at their centers. It is a
very difficult problem and part of the reason he had to invent calculus
was to solve this problem.
- Regarding
your second question: heavier atoms do not preferentially fall toward
the center of the earth. If they did then lead and uranium would be at
the core, then lighter and lighter atoms like onion shells as you went
out until the lightest would be on the surface. This is not how it is.
The reason is that all objects, regardless of their mass move the same
way (with the same acceleration) in a gravitational field.
- It does not
matter what the composition of the center is as far a gravity is
concerned.
- You do not
need to make the objects weightless to do this experiment. You just
have to be careful to make sure that all other forces on the objects
add up to zero. This experiment has been done many times. The classic
experiment was that of Eötvös (see inset picture) done in the
very early 20
^{th} century. A group at the University of
Washington has made many modern and very accurate measurements.

**QUESTION: **

I have a bunch of lasers and
the manuals all say that the tubes will last longer if they are run a
few hours a month. I used to work in analytical chemistry at an
undergraduate lab and the chemist said that the gas filled tubes for
the Atomic Absorption machine went bad if they weren't run all the
time. However, I pulled out a hollow cathode tube that looked like it
had never been used but was in a box that looked 30 or 40 years old and
it was very strong.
What is the physical reason for saying that gas filled tubes last
longer if they are run "A few hours a month"? I have a degree in
physics and have asked a number of PhD phycists and chemists this
question and have not received even an attempt at an answer.

**ANSWER:
(Courtesy of Chad
Fertig)**

Running a discharge tube generates pumping
action due to sputtering of the filament. This pumps away (some of the)
background gasses that inevitably leak into the tube. An Ar/Kr Ion
laser tube which hasn't been used in a long while will often need to be
run at low-ish current (low enough to prevent overheating) until the
pressure drops and the laser stabilizes to its normal operating
parameters.
If the background gas pressure gets __too__ high, one may not be
able to light the tube and __not__ trip the overcurrent protection
circuits. The laser engineers I have spoken with tell me that the shock
of lighting a tube at high-pressure can be enough to kill the tube
entirely.
I don't know how much of this discussion applies to small atomic
spectroscopy discharge tubes -- my experience is mainly with Ar/Kr Ion
laser tubes.

**ANSWER:
(Courtesy of Uwe
Happek)**

One should run the laser periodically to activate a getter
pump that traps unwanted aroms that slowly diffuse into the tube.

**QUESTION: **

If EVERYTHING in the
Universe doubled in size...?
.....would anybody notice?
What about the square-cube ratio?
The surface area of objects increases by the square, while volume
increases by the cube. If you doubled the diameter of a planet and the
height of the man standing on it, his mass would increase by a factor
of eight and the mass of the planet by a similar factor.
So the mans weight would be something like 64 times as much as
before.while the cross section of his legs would only be 4 times as
much.
The burden on each square inch of his legs would be about 16 times the
prior burden, without the extra strength to support it.
It would be like suddenly standing on Jupiter. He would collapse and
die very quickly by being 'squashed' to death by gravity!
Obviously this is a purely theoretical question but if the 'known' Laws
of Physics were applied to this, what would the answer be?
I may have twisted my knowledge because it has been years since I
studied. Simply take it that the universe has doubled (by magic?! :~}
). Would there be noticable consequences?

**ANSWER:**

I would not presume to make
a blanket statement one way or the other for this question (because we
physicists don't deal in magic!) I can, however, refute your specific
example. You have forgotten that the radius of the earth would double
and, since the weight is inversely proportional to the square of the
distance, the weight would be only 16 times greater (64/4). Hence your
new body would be ideally engineered to exist in your new environment.

**QUESTION: **

Light is massless and as
such is the only thing can can travel at this speed. For any object
with mass, it would take an infinite amount of energy to reach the
speed of light. Therefore the speed of light is an unattainable goal!
However, light can be caught by a Black Hole (I'm sure you know the
phrase - the gravity is so strong that not even light can escape!).
If light is without mass, how can it be caught by ANY gravity well?
Astronomers have also proved that light 'bends' around black holes in a
measurable and observable way.
What can the gravity be 'pulling in' if there is no mass to light? Am I
missing something?

**ANSWER:**

You are missing something--classical
gravitational theory, where the force is proportional to the mass, is
incorrect. Einstein's general theory of relativity is a theory of
gravity which has withstood all experimental tests so far. The central
idea of this theory is the equivalence principle which states that
there is no experiment you can do by which you can determine whether
you are in a gravitational field or an accelerating reference frame.
For example, suppose that you are inside a box with no windows and you
drop a ball and it accelerates down with an acceleration *g*=9.8
m/s^{2}. Are you at the surface of the earth or in the middle
of empty space in a box which is accelerating with an acceleration *g*
in a direction opposite the direction you see the ball accelerate?
There is no way you can know without looking out a window. Now do a
similar experiment where you stand at one side of the box and shine a
beam of light across the box; it will follow a parabolic trajectory
down if the box is accelerating up, that's for sure (although for such
a small acceleration, it would be very difficult to observe; see one of
my earlier answers). The
equivalence principle thus asserts that the beam of light will "fall"
in a gravitational field.

**QUESTION: **

There is
a rope, say 20 mile long, and a person pulls the rope from one end,
point A.
Question: Will the other end, point B, move instantly or will it take
time?

**ANSWER:**

It takes time. Basically,
atoms in the rope are held together by the electromagnetic forces
between atoms and electric fields propogate with the speed of light, so
a very rigid strong rope would take a pretty short time for the other
end to start moving. A more stretchable rope would take longer.

**QUESTION: **

How many tons of TNT would
it take to be able to stop an asteroid with a mass of 7.2e15 kg moving
at 2436 m/s? Would we assume that the collision is ellastic or
inellastic and would we use the priniciples of the conservation of
energy or conservation of momentum?

**ANSWER:**

You are approaching this question in such a
way that there is no way to answer. It depends entirely how the "bomb"
of TNT is configured and is a very complicated question. You can do
some calculations:

- the kinetic energy of the
asteroid is about 2 x 10
^{22} J
- the linear momentum of the
asteroid is about 1.8 x 10
^{19} kg m/s
- the energy content of TNT is
about 4 x 10
^{9} J/ton

Probably the best way to
approach how to stop the asteroid is to consider momentum. The time
rate of change of momentum is equal to the force applied, so suppose
you pushed on the asteroid for a year with a constant force such that
it stopped at the end of the year. Then the force would be (1.8x10^{19})/3.2x10^{7})=5.6x10^{11}
N=1.26x10^{11} lb. The rate at which energy is expended is the
energy change divided by one year, (2x10^{22}/3.2x10^{7})=6.3x10^{14}
W. This is bigger than the entire energy consumption rate of the US,
about 10^{13} W.

What you should be figuring out
by now is that it is totally impractical to talk about stopping this
asteroid. When people discuss how to protect us from collisions from
asteroids, the idea is always to make a very small change in its path a
relatively long time before it would hit us. That means a rather small
change in momentum thereby requiring much less force. For example,
suppose you wanted to change this asteroid's trajectory by 0.01^{0}.
Then the momentum change would be about sin(0.01)x1.8x10^{19}=3x10^{15}
kg m/s. If you had an explosion which lasted 10 s, it would have to
supply a force of 3x10^{15}/10=3x10^{14} N=6.7x10^{14}
lb. This is still a pretty big force, you will agree. Here the energy
increase would be about 6.5x10^{14} J so the power over the ten
seconds would be 6.3x10^{13} W which, although still pretty
huge, could probably be achieved with a thermonuclear device over a few
seconds. I guess my message here is that making big changes in the
motion of something as large as an asteroid using brute force methods
are simply not possible with technology we have .

**QUESTION: **

If the maximum velocity of
any particle or electromagnetic radiation is the speed of light and if
light and other forms of electromagnetic radiation cannot escape a
black hole, then how could Hawking radiation be possible?

**ANSWER:**

Hawking radiation has nothing to do with
what the speed of the radiation is. The radiation, the existence of
which is still controversial, is due to esoteric quantum effects which
are too technical for this site.

**QUESTION: **

Is it possible for a
material to act as a superconductor at absolute zero. I understand that
matter can become superconductive at temperetures around absolute zero,
but I am unable to find a definative answer as to whether or not this
happens at absolute zero.

**ANSWER:**

Well, acheiving absolute
zero is not physically possible, so you need not concern yourself with
what happens there. However, you may approach arbitrarily close, so it
is meaningful to ask what happens in the limit of very small
temperature approaching zero. If the material is known to be
superconducting it has undergone what is called a phase change where
the resisitivity of the material suddenly drops to zero at some
temperature. Then the resisitivity would remain zero as temperature
approached zero. If the material did not undergo a phase change, it
would not be superconducting in the limit as temperature approaches
zero.

**QUESTION: **

How much one cubic inch of
sugar cube weigh?

**ANSWER:**

I looked up the density of granulated sugar,
from which sugar cubes are made, and found 849 kg/m^{3}. From
this you can find, by using standard conversion factors, that the mass
of one cubic inch of sugar is 13.9 g or a weight of 0.491 oz.

**QUESTION: **

If you took a radio antenna
and had the technology to generate a eletrical AC signal across the
antenna with a frequency of around 6*10^{14} Hz, would you see
visible light coming from the antenna, or would it just be a really
fast oscillation of energy between eletric and magnetic fields?
If it would produce visible light, would similar frequencies give IR
and UV and so forth?

**ANSWER:**

You would see nothing. There might be some
EM radiation in the visible region but the intensity would be too small
to "see". The problem is that the antenna must have a size comparable
to the wavelength corresponding to the frequency for it to have any
appreciable intensity. The wavelengths for visible light are hundreds
of nanometers and so you would need to have an antenna comparable to
the size of an atom. In fact, atoms do act like little antennae and
that is where we normally get visible light.

**QUESTION: **

If a fine liquid filled
capillary tube is place horizontally and both ends are immersed in the
same liquid as that filling it, is the pressure at the midpoint of the
tube larger than that at the ends?

**ANSWER:**

Although I do not know a lot about
capillaries, I do know Newton's first law. If the pressure were greater
in the center than the left end, the fluid in the left half of the tube
would have a net force to the left which it cannot since it would be in
equilibrium. What I do know about capillaries is that they depend on
the meniscus to drive the fluid through the tube and there would be no
meniscus under the conditions you state.

**QUESTION: **

I actually have an idea that
isn't possible currently, but I'd still like to suggest it to you,
because I'm vey concerned about the effect of the greenhouse effect on
mankind. Seeing how things are going with it right now, time for all
life on earth may be running out faster than we think, and we MUST do
something more than just fighting oil companies emissions...
Now to the point - I't is finally time that people in the physics
community would take a chance at designing and building at least a
working model of an ozone particle regenerating machine. For the sake
of the earth and mankind, I think it's at least worth a good try.

**ANSWER:**

The ozone problem and the greenhouse effect
are not the same thing. The greenhouse effect comes from too much CO_{2}
in the atmosphere which traps the energy which light brings from the
sun. The ozone problem is that ozone is needed as a shield against
incoming ultraviolet radiation from the sun but is depleted by
introduction of chemicals which interact with it (like chlorofluorocarbons in older refridgerants). I
believe that restrictions on these chemicals is making noticable
effects in solving the ozone problem. Regarding your suggestion,
building any machine which can have any kind of effect on something as
huge as our atmosphere would be an undertaking which would cost our
entire GDP and more!

**QUESTION: **

Why is a 45 degree angle the
best angle to shoot a water baloon to get it to
go the fartherest distance?

**ANSWER: **

See my earlier answer
pertaining to projectile motion. Inasmuch as the range* R* of a
projectile may be shown to be *R*=*v*^{2}sin(2*A*)/*g
*where *v*
is the speed at launch, *A* is the angle of launch, and *g*
is the acceleration due to gravity, you can see that the range is
proportional to the sine of twice the launch angle. At 45^{0}
the sin(2x45)=sin(90)=1 which is the biggest the sine can be.

**QUESTION: **

What exactly do scientists
mean by "folding a spectrum through a filter transmission profile" ?
What is folding?

**ANSWER: (Courtesy
of J. Scott
Shaw)**

In astronomy it means multiplying the
intensity of the spectrum by the transmission % of the filter at each
wavelength to get the resulting intensity at the detector. Or you can
do it from the detector to the spectrum, depending on how you need to
see the problem.

**ANSWER: (Courtesy
of Richard S.
Meltzer)**

I think this refers to the alteration of the
actual spectrum by the transmission of a filter so that what is
observed is so modified by the filter transmission. If one knows the
transmission of the filter as a function of frequency, one can deduce
the actual spectrum from the observed spectrum by dividing the observed
spectrum by the transmission of the filter.

**QUESTION: **

a light bulb uses 60J of
energy to give 6J of useful heat energy. true or false???

**ANSWER: **

False. An incandescent light bulb is only
about 5% efficient, that is 95% of the energy goes into heat. Your
question is sort of strange because I wouldn't call heat useful energy.
We usually use a light bulb for light, not heat, so it is the light
which would be thought of as useful. If the question had said "useful
light energy" instead, it would not have been far off.

**QUESTION: **

Can you tell me the
wavelength of the EM wave that would correspond to the photon emitted
when a hydrogen atom's electron falls from the n2 to the n1 energy
level?

**ANSWER: **

121.566 nm. See
http://hyperphysics.phy-astr.gsu.edu/hbase/tables/hydspec.html

**QUESTION: **

I am learning about
half-lives and am curious: is it possible to shorten the half-life of
radioactive decay?

**ANSWER: **

The short and practical answer to your
question is no. The half life for the transition from one state of a
system to another is determined only by the wave functions before and
after (a wave function is a mathematical construct which contains all
the information about the system). However, if you were able to change
the wave functions by changing the environment, you could change the
half life; for example if you put the radioactive nuclei in a very
strong electric field you would change the wave functions. However, the
force which holds the nucleus together is so strong, it would be
virtually impossible to make a noticable change in this way. What is
more conveniently done is to transmute the original nucleus: for
example, if you add a neutron to a radioactive nucleus you would likely
form a new radioactive nucleus but with a very different half life.
This has been discussed as a way of dealing with radioactive waste from
reactors.

**QUESTION: **

Is there any very important
reason too why a coulomb is 6.24x10 exponent 18 electrons? i do not
know very much about the coulomb

**ANSWER: **

The Coulomb (C) is defined in terms of the
Ampere (A). The Ampere is an electric current carrying 1 C/s. The
Ampere is operationally defined in terms of the magnetic force between
two current carrying wires. So the answer is that the fact that there
are a certain number of electrons in a Coulomb has no significance.

**QUESTION: **

In nuclear reactions, when
they are bombarding atoms with a neutron n for example, How do they get
just a neutron (fission) by itself to hit at a certain velocity?

**ANSWER: **

You are referring to nuclear
fission reactions in a reactor, I presume. Every time one of the fuel
nuclei splits into two pieces, it also releases several fast neutrons.
These neutrons may then be used to cause other nuclei to split and so
forth. This is called a self sustaining reaction--once you get it
started, it will keep going as long as one or more neutron, on average,
causes another fission. The problem is that fast neutrons have a very
low probability of being captured by a nucleus and are most likely to
just fly away; if we slow them down, however, they have a high
probability of causing another fission (simply because a slow neutron
spends more time passing through a nucleus than a fast one). So we must
slow them down for the reactor to work. The way that this is done is to
introduce a moderator which is efficient in slowing them down. Good
moderators are water or graphite.

**QUESTION: **

Besides being released in
beta decay and making up for the excess of mass when a proton+electron
are froce to bcome a neutron what does the elementary particle
"neutrino" actually do??

**ANSWER: **

What do you mean by "do"? The question is
more appropriately "what are the neutrino's properties?" To get a full
discussion of neutrinos I would recommend the Wikepedia article.

**QUESTION: **

What is the formula for the
range of a projectile?

**ANSWER: **

Neglecting air friction and assuming that it
lands at the same height at which it was launched, *R*=*v*^{2}sin(2*A*)/*g
*where *v* is the speed at launch, *A* is the
angle of launch, and *g* is the acceleration due to gravity (9.8
m/s^{2}). You can find plenty of derivations of this formula on
the web by googling "projectile range".

**QUESTION: ;**

We say that centripital
force is centre-seeking and that it pulls the rotating object to the
centre of rotation. If this is the case then what force is responsible
for pulling the object outwards. For example, with a yo-yo rotating in
a horizontal plain. The tention in the string pulls the yo-yo inward,
keeping it from flying off. However, what is the force that causes the
yo-yo to extend outard? Is this the centripital force? If so then
doesn't this mean that centripital force pulls outward on the yo-yo
while the force of tension pulls inward on the yoyo?

**ANSWER: **

A ball going around in a circle has an
acceleration pointing toward the center of the circle. Newton's second
law thus says there must be a force pointing toward the center of the
circle and this is called the centripetal force. Any number of forces
with components in that direction may contribute to the centripetal
force, but the simple example you give has just the tension in the
string providing the centripetal force. There are no other forces (in
the horizontal plane) acting on the yoyo. Your statement referring to
the yoyo "extending out" makes no sense; if the string breaks the yoyo
does not fly radially outward but continues in the direction of its
motion at the instant the string breaks. If you imagine yourself to be
the string, there will be a force outward on you which is equal in
magnitude to the tension in the string. This is because of Newton's
third law: if one object (string) exerts a force on another object
(yoyo) then the other (yoyo) exerts an equal and opposite on the first
(string). But this outward force is not on the yoyo.

**QUESTION: **

According to Einstein's
special theory of relativity ,velocity of light is a universal constent
.It does not change with respect to observers velocity relative to the
source of light .But I had
heard that Doppler effect occurs due to the relative velocity between
the source and the observer .Then if relativity theory is true,why
doppler effect occurs?

**ANSWER: **

You have answered the question yourself. The
postulate says that the speed is constant, not that the frequency or
wavelength are. The frequency or wavelength of light does depend on the
motion of the observer.

**QUESTION: **

I am a teacher and I was
wondering how I can address students' misconception that weight does ot
affect accleration due to gravity.
We did several controlled experiments to determine the variables that
affect the speed of a car rolling down a ramp. In one experiment with a
car and ramp, the weight was changed as the car was timed from point A
to point B. Some groups of students found that sometimes the more
weight added to the car, the faster it acclerated down the ramp, while
other groups found that the more weight added, the slower the car
rolled down a ramp. So now they are confused. How can I steer them away
from this misconception?

**ANSWER: **

The design of the experiment must take into
account all the variables. One of the most troublesome variables in
doing mechanics problems is friction and I am sure that changes in
friction as you change other variables is what is causing trouble here.
So, I propose the simplest of all experiments to convince them that
acceleration is independent of mass if it is the only (nonnegligible)
force present: just do Galileo's experiment of dropping a marble and a
bowling ball (or some similar pair) simultaneously and see them hit
simultaneously. This would be most effective out of a second floor
window, but you can drop them from six feet in the classroom and have a
pretty convincing experiment. Of course, you could also use a feather
and a bowling ball but the feather would be the loser by far, not
because of its (smaller) weight but because of its (larger) frictional
force. At a nearby college or university you might be able to borrow an
apparatus in which there is a feather and a marble inside a glass tube
which, if you pump the air out, the two will fall with the same
acceleration. If your students understand Newton's second law you might
find my previous discussion of this problem helpful. Another experiment you
could do if you have access to an air table is to use it for your races
and minimize friction.

I helped my son with a pinewood
derby a couple of years ago and I can tell you that it is not easy to
understand the physics of these little cars. One thing which is often
noted is that the fraction of the wheels rubbing on the axels is quite
important and using graphite as a lubricant often speeds them up.

**QUESTION: **

How much evergy is released,
when a drop of water changes its shape from a cube to a sphere of the
same volume? How much is the drop getting warmer as a consequence of it?

**ANSWER: **

The work done in changing the surface area
by *d**A*
is *y**d**A* where y is the surface tension which, for
water-air interface near 20^{o} C is about 73x10^{-3}
N/m. The surface area of the cube is about 24% larger than the sphere
with equal volume (which I am assuming is easy for you to show). So the
energy released is about 0.24x73x10^{-3}x*A* where A is
the area (4p*r*^{2})
of the sphere. For a sphere of water with radius 1 mm I estimate an
energy of about 2.3x10^{-7} J. I will leave it to you to
compute the temperature change for this amount of water when this
amount of energy is added; you just need to calculate the mass *m*
of the drop and set the energy equal to *mc**D**T* where *c*
is specific heat of water and *DT* is the temperature
change.

**QUESTION: **

I made this question up
myself when pondering how to teach Newton's 3rd law:
A pulse of electricity through a wire produces an electromagnetic field
that travels outward at the speed of light. This field encounters a
charge and exerts the appropriate forces on it. While the forces are
occuring on the charge, on what is the reactionary 3rd law force? I
believe that the closed loop nature of the fields would render the net
work done as zero.

**ANSWER: **

Here is a dirty little secret we never
reveal to our students in introductory physics: Newton's third law is
not always true! Particularly in electrodynamics, it is rather easy to
see in simple examples. The culprit, as you seem to have intuited, is
the magnetic forces. As a simple example suppose you have a particle
(#1) of charge *q* moving in the positive *x-*direction
with speed *v* along the positive *x*-axis and a particle
(#2) of charge *q* moving in the positive *y *direction
with speed *v* along the positive *y*-axis. Particle 1 sees
a magnetic field pointing in the negative z-direction due to particle 2
so it experiences a force in the positive *y*-direction; particle
2 sees a magnetic field pointing in the positive z-direction due to
particle 1 so it experiences a force in the positive *x*-direction.
Of course, each particle also experiences a repulsive electrostatic
force but these do obey Newton's third law. But the net force does not.
If the magnetic forces involved were due to magnetostatic forces, long
steady currents, Newton's third law would be obeyed (as in the well
known force between two long parallel current carrying wires on which
the definition of the Ampere is based). It turns out that for the
electromagnetic field, one must include energy and momentum densities
of the fields themselves to do Newtonian mechanics and then all is
well. If you want to pursue this further, I would recommend the
intermediate-level E&M book by Griffiths.

**QUESTION: **

My question regards a
discrepancy between answers I get when I work a problem using two
different approaches. This problem was given to me several years ago,
and although I got the right answer then, I was told that I could have
also used a different approach. I have tried several times since to do
this problem the other way, but have had no luck. The problem is this:
if a pole of length L is stood on end and released, if the initial
velocity is neglegible, what is the final velocity of a point at the
end of the pole when it hits the ground. I believe I originally solved
this problem using the concept of the potential energy being converted
to kinetic energy (mgL=(1/2)mv2), getting an answer of
v=(2(g)(L))^(1/2). I am now trying to solve it using calculus by
integrating the equation v2=2ad over all da from 0 to 9.81m/s2 (where d
is the arc length of the falling pole), and taking the square root of
both sides. When I do this I end up with an answer of v=((
PI)(g)(L))^(1/2). What am I doing wrong?

**ANSWER: **

Neither of your methods is correct. The
second method, using *v*^{2}=2*ad* is wrong because
this equation is valid only if the point has uniform acceleration which
it does not. The first method is incorrect because you treat the
stick as a point mass at the end of the stick falling straight down
which is not what is happening. The only way to solve this problem in
closed form is to use energy conservation as you have tried to do;
however, you must use rotational dynamics to do this. So the potential
energy at the beginning is *mgL*/2 because the center of mass of
the body is located halfway up the stick; the kinetic energy when the
stick hits the ground is *I**w*^{2}/2 where
*I *is the moment of inertia of a the stick about its end
(which is* ML*^{2}/3 for a uniform stick of mass *M*
and length *L*) and * w* is the angular velocity of the stick (which
is *v*/*L* if *v* is the speed of the point at the
end). If you now equate the energies before and after and do the
algebra, you will find *v*=(3*gL*)^{1/2}.

**QUESTION: **

Do physicists believe that
the world is continuous or discrete? In other words, is there a
smallest distance a particle can travel and/or a smallest increment in
time?

**ANSWER: **

This is an open question. Although nobody
has seen any evidence for the discreteness of space or time, many
serious theorists, particularly those working in quantum gravity,
believe that there does exist a distance which is the smallest possible
distance called the Planck length. This length is on the order of 10^{-35}
m so it is not surprising that there is no experimental evidence for it
since this is 10^{-20} times the size of a proton! Similarly,
time is thought to have the smallest possible duration which is the
time it would take light to travel the Planck length, also very small.

**QUESTION: **

What guarantees that human
made particle colliders won't create black holes eventualy as they
reach higher and higher collision energys? I ask this because if i
understand it correctley, black holes aren't created only out of the
large mass of the stars that go supernova, but they are created by the
large density that the large mass of the star creates in it's center
when the atoms if its center collapse. What i mean is: The star that
went supernova was heavier than the black hole it creates, yet it is
not a black hole. So this means that black holes are created by their
large density and not their large mass. This is why i want to know
wether particle colliders could create a (dangerous) balck hole here on
eart, beacause they also, like supernovas make atoms collapse into
great densitys.

**ANSWER: **

The possibility of a black hole being
created is still speculative, but there is the real possibility that a
tiny black hole (say 300 proton masses) may be created. However, black
holes do radiate energy (called Hawking radiation) and such a black
hole, if it were to exist, would totally evaporate in an unimaginably
short amount of time, before it would have time to suck up any mass.

**QUESTION: **

If you were in a black room
with no doors/windows/external light sources and every part of your
body was the same shade of black as the room and you lit a match, would
you see your shadow? Would you see your own hand?

**ANSWER: **

I presume that by "black" you mean something
which is a perfect absorber of electromagnetic radiation. In that case
you would not be able to tell if light is falling on it or not by using
your eyes as you usually do, *i.e*. by seeing the reflected
light. On the other hand, the energy carried by the light would have to
go somewhere and it would show up in increased temperature of whatever
absorbed it. Now, all objects radiate electromagnetic energy but, in
your example, things look black not because they are not emitting any
electromagnetic waves but rather that nearly all this radiation is
outside what eyes can see (in the infrared). But the catch is that a
perfect absorber is also a perfect radiator, so all the energy from the
lighted match will be reradiated but mainly in the infrared so you
couldn't see it. If you had an infrared detector you would be able to
"see" the shadow, *etc*.

**QUESTION: **

I just moved to an area with
snow and find that whenever it is snowing in the night, there is always
this orange-ish "ambient light" that seems particularly bright, bright
enough that one can see fairly well to the point where one can drive
slowly without headlights in unlit areas. i am wondering what is the
source of this light. i am fairly sure that it is not moonlight (there
is light even when the sky is covered with clouds, and the intensity of
the light does not seem to change during with moonphase). It might be
street lights reflecting off the snow, since the color of the light is
orange-ish, but then again you can see this light even when you are
dozens of miles away from big cities, and the intensity of the light
does not seem to change as you travel further from big cities.

**ANSWER: **

I feel pretty sure that what you are seeing
is what astronomers call light polution. The characteristic orange
color you are seeing would indicate that the source is sodium vapor
lamps, often used for city street lights. The light, particularly if it
is not directed toward the ground and is transmitted upward can scatter
from snow, water vapor, dust, smoke, *etc*. in the air so that
you can see it quite readily even at surprisingly large distances from
the city of its source.

**QUESTION: **

All of the physics examples
for gravity and projectiles depict freefall or horizontal/angular from
fixed start locations, eg: a ball dropping over a cliff or a cannon
shooting a ball. And I understand the results.
However, I have been unable to find any answer regarding specific
vertical scenarios.
For example, if we are standing in an elevator that is not moving, and
drop a ball, it freefalls at 9.8 m/s/s. So we can easily calculate the
time from when it is dropped to when it hits the floor.
But what would occur if the elevator were moving upwards at a constant
velocity (not accelerating) of 2.5 m/s (the average elevator speed),
and you dropped a ball.
Would the time for both balls to hit the floor be identical?
If the ball in the upward moving elevator maintained a constant
vertical velocity of 2.5 m/s during its freefall lifetime in addition
to the applied force of gravity I would think that they would...
However, I would assume that the vertical velocity of 2.5 m/s would not
remain constant for the lifetime of the ball's fall, as gravity is
directly opposing that upward velocity. The ball's vertical upward
velocity should decrease as a curve due to the gravitational force
applied in the exact opposite direction.
Similar to what would occur with a projectile that is fired vertically,
the upward velocity decreases and it then falls back down accelerating
due to gravity.
Now since the elevator's floor is still moving upward at 2.5 m/s, the
ball dropped in the moving elevator should hit the floor first.

**ANSWER: **

The motion of the ball is the same in any
frame of reference which moves with constant velocity relative to the
stationary elevator. The dropped ball in the moving elevator takes
precisely the same time to reach the floor as it did when the elevator
was not moving. To help you understand this, keep in mind that when the
ball was released in the moving elevator, it had a speed of 2.5 m/s
upward as seen from the ground. Basically, you are touching on what is
called the principle of relativity, namely the laws of physics are the
same in all inertial frames of reference; an inertial frame of
reference is any frame which moves with constant velocity with respect
to a frame of reference (for example your stationary elevator) in which
the laws of physics are true. If your elevator had been accelerating
upward with an acceleration of 2.5 m/s/s it would have been a different
story. In this case, the ball would appear to fall with an acceleration
of (9.8+2.5) m/s/s and hit the floor sooner.

**QUESTION: **

I have a question regaurding
light and energy. It is known that it is impossible to accelerate a
particle as fast as the speed of light due to the fact that it would
take an infinite amount of energy. However, a photon's energy is
difined as E=hf, where h is the product of Planck's constand and f is
the frequency of the photon. So, why can light have a finite amount of
energy whereas an accelerating particle can not?

**ANSWER: **

The photon has no mass and therefore it is
exempt from this rule (as is any massless particle). All massless
particles necessarily travel with the speed of light and they are not
accelerated to get there, they are created already going that speed.

**QUESTION: **

Okay, hypothetically
speaking, if there was a chain strong enough to not break under the
ridiculous amount of stress and the chain was attached to the moon and
the earth (probably by a mad scientist) what would happen? Would the
moon slowly be drawn into the earth? Would the earth wind itself up in
the chain as it rotates upon it's axis and how fast would it wind up?
would the chain have to be built on the moon and lowered to earth? How
would the chain be affected by earth's gravity when it first hit the
atmosphere? If it was possible what type of material would the chain be
and how thick would it need to be? Would it heat up as it cut through
earth's atmoshpere?

**ANSWER: **

When you first start, there is no need for
the chain to be strong because the moon is held in its orbit by gravity
and any additional force (the tension in the chain) would disrupt that
orbit. To see this, imagine the earth and moon to be point masses and
there is a weightless chain between them;there is no tension in
the chain. Now, let's get a little more real: no chain is weightless
and so there would be tension in it just to support its weight but it
would vary from point to point and still exert no force on the earth or
the moon which would continue to orbit each other as if the chain were
not there. Now, let the earth become its normal size. Since the earth
rotates once on its axis every 24 hours but the moon goes once around
the earth every 28 days, the chain would pull the moon down like a
fishing reel. There is an analogous thing which has been discussed,
having an "elevator" into space (not as far as the moon, but farther
than where communication satellites are). Here, both to support its own
weight and the weight it carries up, the cable would have to be very
strong. It has been suggested that perhaps the cable could be fabricated of carbon nanotubes. You
might be interested in the Wikepedia article
on space elevators.

**QUESTION: **

I know that the length of an
organ pipe (as well as the speed of sound in air) determines the
frequency of sound produced within it. Does the diameter of the pipe
have any effect on the sound produced?

**ANSWER: **

What the length determines is the
fundamental frequency, but no musical instrument contains just the
fundamental. each note played by each instrument also contains what are
called overtones, other frequencies, usually simple multiples of the
fundamental. The relative intensities of the many frequencies produced
is called the timbre and it is what allows you to tell the difference
between an A played on a violin or an organ or a trumpet *etc*.
Geometrical properties of organ pipes other than its length determine
its timbre; design of organ pipes has evolved from trial and error and,
as such, is more an art than a science.

**QUESTION: **

What exactly is oscilating
when we're talking about the wave nature of a particle?
What are the bounds in which between it oscilates?

**ANSWER: **

There is not a physical wave which you can
visualize. It happens that something called the wave function, which is
intimately related to the probability of the particle being found at
some place at some time, satisfies a wave equation. This equation,
however, is not the usual one since its solutions are necessarily
complex, that is they contain both real and imaginary parts. An
imaginary number, the square root of negative one, cannot be physical
but often is very useful mathematically in describing the physical
world. To extract what you actually observe in nature from the
mathematics requires having techniques which remove the imaginary parts
of quantities. So, the oscillating is of a complex quantity and, as
such, is not visualizable.

**QUESTION: **

Suppose you are given two
iron rods, and you are told that one is a magnet and the other is not.
Using ONLY those two rods, how would you determine which was a magnet
and which was not?

**ANSWER: **

If you, at some distance
away, align one bar (A) perpendicular to the other (B) and pointed
toward B's center and bring it closer it will experience a strong force
along its direction if it is the magnet; this is because it will
attract B and Newton's third law says that A will feel an equal and
opposite force. On the other hand, if A is not the magnet, it will find
itself in a magnetic field which is nearly uniform and perpendicular to
its length, so it will become magnetized in the direction of the field;
however, a magnet in a uniform field feels no force so it will
experience very little force. I am assuming that the magnetized bar is
a simple dipole, that is one end is north and the other south.

**QUESTION: **

what keeps electrons
energetically orbiting a nucleus?

**ANSWER: **

What keeps a satellite orbiting the earth?
What keeps the moon going around the earth or the earth going around
the sun? In all cases, once you give an object the energy required for
a particular orbit, conservation of energy keeps it from changing. If
the earth were to suddenly stop moving and drop into the sun, it would
have far less energy; where did that energy go? To change the orbit you
need to add or subtract energy to/from the object. What is particularly
interesting about an electron in an atom is that an electric charge
running around in a circle radiates energy (that is what an antenna is)
and so the energy should radiate away and the electron fall into the
nucleus. However, it does not and this observation started the whole
branch of physics called quantum mechanics: one of the laws of nature
is that bound objects are allowed to exist only in specific (quantized)
energy states and therefore, if in such a state, a particle cannot
radiate its energy away except all at once by going to a lower energy
state. There is, however, a lowest state (called the ground state) and
if the atom is in that state, it must stay there.

**QUESTION: **

- Is nanomolecular technology
able to create a dimond saw blade from the carbon in the air?
- Are nanobots able to create
things out of carbon?
- What would happen if Carbon
was broken down again? (that is, carbon is an element, but can you
destroy or break it down futher?)

**ANSWER: **

- The only way to make diamond
is under extremely high pressures, so one could not just coat a saw
blade with carbon in the air and expect it to be diamond.
- Nanobots are still in a very
experimental stage and so what they can or cannot do is open to
question and interpretation. Most nanobots which exist have the purpose
of detection of something, for example bacteria or particular
chemicals. I don't think there would be a reason why, someday, a
nanobot couldn't fabricate things out of carbon or anything else.
- Normal carbon
^{ }(^{12}C)^{ }is
composed of 6 protons, 6 neutrons, and 6 electrons. You could make
anything you like out of those 18 particles. Some examples:
- 6 hydrogen atoms and 6 free neutrons.
- 3 helium atoms
- 6 "heavy hydrogen" atoms

However, this kind of
rearrangement takes much more energy than chemistry and is not easy to
do. The reason is that the force which holds a nucleus together is the
strongest force in nature so it is tough to break nuclei apart. You
could do some "chemical" type breaking apart with much less energy by
ionizing the atom, for example remove one electron and you have a
singly ionized carbon ion. You might find the Wikepedia article on
nanobots interesting.

**QUESTION: **

When accelerating from a
stop with your car door open, the door swings shut. Now given that the
force applied to the door is thru its pivot point there should not be a
net torque on the door, so it shouldn't move. To idealize the situation
I have imagined an axle with a rectangular mass attached accelerated
(normal to the axle) in deep space to negate gravity and air
resistance. I'm thinking the "door" would not pivot in this case, so
that the pivoting experienced in the original case is due to air
resistance, some kind of unbalance of applied forces, or maybe even the
fact that the car is not an inertial frame.

**ANSWER: **

Idealize the hinge to be frictionless. Then
there is no torque about the hinge. However, the hinge can exert a
force on the door (or else it would be left behind when the car
accelerated). The direction of this force is forward so that, according
to Newton's second law, the center of mass will accelerate forward, as
you know to be the case. Now, ask yourself if there are any torques __about
the center of mass__ of the door. There is the forward force which
the hinge exerts and this exerts a torque which will cause an angular
acceleration about the center of mass. If you sketch that force, you
will see that the torque will tend to close the door. You were right to
be suspicious of whether the car and the door not being inertial frames
might be a problem. You may not apply Newton's laws in noninertial
frames but there are special exceptions, the most important being if
you ask about what happens in a frame attached to the center of mass;
even though not inertial, Newton's laws remain vaild in this frame.
That is why, after asking what forces there were on the door, I
switched to the center-of-mass frame.

**QUESTION: **

I am teaching physics at a
Kansas high school, and my students and I were debating over a problem.
The problem is as follows:
Two 20-N boxes are placed on both ends of an ideal rope. The rope is
then passed over two pulleys fixed on each of the two edges of a fixed
table, so that one 20-N box hangs on one pulley, and the other 20-N box
hangs on the other pulley (the rope being continuous over the two
pulleys).
We have been debating over the value of the tension in the rope,
whether it's 20 N or 40 N. Half of the class agrees with me that the
tension is going to be 20 N, but I cannot convince the rest of the
class that the tension is not 40 N, but rather, 20 N. (Or is it me
who's wrong?)

**ANSWER: **

Breathe easy--you are right! The tension in
this rope is 20 N. The tension at a point in a rope is defined as the
force which it exerts on what it is attached to. So you need to focus
on one box or the other. You now say, what are all the forces on that
box? One is its own weight which we know to be 20 N vertically down.
Another is the force which the rope exerts on it; technically we know
neither the magnitude nor direction of this force, but it is called the
tension in the rope at the point of attachment. There are no other
forces on the box. Since it is in equlibrium, all (both) forces must
add to zero, so the tension is 20 N straight up. And, for a rope of
negligible mass the tension must be the same everywhere on the rope;
otherwise if you inserted a tiny mass in the rope and the tension were
different on one side than the other, the tiny mass would not be in
equilibrium.

**QUESTION: **

I attached magnets (round,
penny-size, strong) magnets to each of the three blades of my small
wind turbine and a two-inch opposite magnet stick to the pole for more
power to push the blades. Then I placed the wind turbine into a wind
tunnel to test if if it generates more energy than without. It did
generate less energy...please explain why. Do I need a stronger magnet
stick ?

**ANSWER: **

As each magnet on the turbine approaches the
stationary magnet it is attracted but as it goes away from the
stationary magnet it is still attracted, so this force will cause the
turbine to alternately speed up and slow down so you will get no net
work from the magnets. Technically, you should have gotten the same
energy output but your experiment probably increased the friction of
the turbine and so you lost energy there.

**QUESTION: **

if you are in a train
traveling half the speed of light, and another train on a separate,
parallel track, was approaching you, also at half the speed of light,
would you see the passing train travel past you at the speed of light?

**ANSWER: **

Classically, that is what
you would think. But the theory of special relativity shows that
velocity addition in classical physics is wrong but you can only easily
see that it is wrong at very high speeds and half the speed of light
certainly qualifies! The speed you would see the other train
approaching would be 80% the speed of light.

**QUESTION: **

When boiling distilled water
in a pot, bubbles rise from the bottom. What is within those bubbles?
Would it be oxygen? If so, is the oxygen extracted from the water? What
happens to the hydrogen excess?

**ANSWER: **

When a liquid is heated enough it transforms
into a gas (this is called a phase transition). The bubbles you see in
a boiling liquid are simply little volumes of gas within the liquid, so
in your question there is just water vapor inside the bubbles.

**QUESTION: **

If you were to drop an ice
cube and a shot glass from 4 feet up, which would land and break first?
Why?

**QUESTION: **

My question to you involves
the feather and bowling ball freefall experiement in a vacuum. Now I
understand that by removing the factors of air resistance that you free
up the feather to fall much faster than it normally would. But the part
I'm having trouble with is that they do indeed fall, gravity is
obviously still involved and the ball still outweighs the feather many
times over. In fact the term "weight" is defined by the amount of force
gravity exerts on an object's mass. (not totally clueless, I just look
like I am) So by that term should not the ball fall much more quickly
since gravity has that much influence on it?

**ANSWER: **

Since these two questions are so similar, I
will answer them with one answer. Ignoring or removing air friction
results in all falling objects as having the same vertical
acceleration, 9.8 m/s/s; that is the speed of any freely falling object
increases by 9.8 m/s as each second ticks by. Hence, the ice cube and
the shot glass and the feather and the bowling ball will all hit
simultaneously. To understand the "why" you need to know two things:

- Newton's second law states
that the acceleration of an object is proportional to the force it
experiences and inversely proportional to its mass; if we define a unit
of force to be that which causes one kilogram to have an acceleration
of 1 m/s/s, then
*a=F/m *if *F *is in Newtons.
- An object's weight, the force
which the earth exerts on it, is proportional to its mass. So we can
write that
*W=mg* where, for now, *g* is just some
constant; if we measure the weight in Newtons and the mass in
kilograms, then we find (by simply measuring) that *g*=9.8 m/s/s.

Putting these two things
together for the case where the force in Newton's second law is the
weight of an object, then *a=W/m=mg/m=g*. Note that *m*
cancels out; this is the key to understanding. Although the weight is
proportional to the mass, the inertia (resistance to acceleration) is
also proportional to the mass, so all objects have the same
acceleration.

**QUESTION: **

Water is attracted to each
other right. So when you cut through ice are breaking this attraction.
I mean what happens when you break something or cut something at the
atomic/molecular level.

**ANSWER: **

In a solid, each molecule is bonded to its
nearest neighbors. The nature of the bond is very complicated, but is
similar to the bonds which bind molecules together. When you break a
solid, you break all such bonds which were along surfaces which appear.

**QUESTION: **

I am writing in the interest
of hopefully resolving a question which had arisen in my workplace. One
gentleman poses the hypothetical situation of a motionless tank sitting
on solid ice which he describes as "very slick and smooth - so much so
that if one were to toss a penny across the surface then it would glide
on endlessly." He posits that the tank is then started and attempts to
move forward. His position is that the tank will not be able to move as
the treads would simply spin on the ice. His detractor posits that the
treads are moved by the wheels inside the treads and that this would be
able to propel the tank forward. So, would this tank be able to move
forward or not? If so, what propertys of physics would make it be able
to move and, if not, why would this tank not be able to move forward?
The gentleman's scenario also posits that there is no friction between
the tank treads and the ice. Is it realistic, physically speaking, to
posit these two surfaces touching and no friction existing between them?

**ANSWER: **

How genteel you are! The gentleman who says
that the tank will not move forward if the ice is perfectly
frictionless is correct. It is the force of friction which accelerates
the tank forward, not the force which the wheels exert on the treads;
if the wheels exert a force on the treads, then Newton's third law says
the treads exert an equal and opposite force on the wheels so the two
cancell each other out. No it is not possible to have a perfectly
frictionless surface; it is possible to get a good enough
approximation, however, to do an experiment which should convince the
second gentleman.

**QUESTION: **

I assume that the "big bang"
theory is correct, but to accomodate the concept of infinity, it must
be that this process is repeated or cyclical. After the universe
expands for quite some time, gravitational pull will eventaully slow
down the speed of expansion until it stops, and then gravity will
create an accelerating contraction when all matter returns to a single
space and time, when another "big bang" takes place. While the universe
is contracting, history and time go backwards, and we live our lives
again in reverse, and all cosmological events are repeated in reverse
order.
This theory provides for infinity, and also for the concept of "eternal
life", that would be a cyclical event, half the time going backward,
but repeated for all eternity. Eternal life in this way may not be just
a religious belief. I don't know the math involed, but this may be the
"unified theory" unsolved by Einstein.

**ANSWER: **

Your basic premise, that the universe is
fated to collapse back on itself is not necessarily true. If the
universe has more than a critical amount of mass, it will eventually
fall back; if it has less than that amount of total mass, it will keep
going forever. Determining which of these possibilities describes our
physical universe has been one of the main quests of astrophysics for
many years. However, recently observations have been made that the
expansion of the universe is actually accelerating, so it seems more
likely that the universe will not collapse as you posit.

**QUESTION: **

What happens to all the
light photons that enter your eyes?

**ANSWER: **

For the most part, they vanish giving their
energy to heat or chemical reactions which initiate nerve impulses
which your brain detects and interprets.

**QUESTION: **

Why do high voltage devices
(power lines, transformers, etc) hum? They have no moving parts to
vibrate, so what causes the humming?

**ANSWER: **

If there is sound, then
obviously something must be moving. The hum you hear is usually 60
cycles (since that is the standard for AC) and results from electric
currents interacting with magnetic fields. Suppose you have a thick
wire which carries a current; then there will be a magnetic field
everywhere around that wire, including inside it. The current will
interact with the field and will experience a force which causes it to
move and since the frequency of the field is 50 Hz, so is the motion
(in response the the force) of the wire.

**QUESTION: **

if two people are moving
past each other at a constant speed in an infinite empty space, to
either one the universe would be static and the other person would be
in motion (relativisticly).
if two people were at a constant unmoving distance from each other, but
one of them was rotating at a constant speed, to either one the
universe would be static and the other person would be in motion,
correct?
so if they were far enough apart, wouldn't the rotating person see
their friend travelling faster than the speed of light (tengentially)?

**ANSWER: **

The two situations are not equivalent.
Assuming that in your first scenario each was an inertial frame (one in
which Newton's first law is true), then both are inertial frames and
each can rightly claim that he is at rest. In the second scenario, if
one is an inertial frame then the other (revolving around it) is not,
so the rotating frame cannot claim to be at rest.

**QUESTION: **

I recently heard that if you
shoot a bullet straight out with one hand and drop a bullet to the
ground from the same height with the other hand then both bullets will
hit the ground at the same time. Is this true and why. It would seem
that the bullet being shot would have much more energy behind it abd
take longer to expend that energy and hit the ground.

**ANSWER: **

This is what happens
assuming that there is no air friction (which is actually a pretty poor
approximation for something going as fast as a bullet). But, if there
were no air, they would hit simultaneously. The reason is that they
both move identically in the vertical direction, that is they both have
the same acceleration vertically whereas the one shot moves with
constant speed horizontally. So, imagine having a horizontal spotlight
which cast a shadow of the shot bullet on a screen, a way of looking
separately at its vertically motion. The shadow would move in exactly
the same way as the dropped bullet.

**QUESTION: **

If the earth were to see an
extreme increase in mass, would it colapse and form a black hole?

**ANSWER: **

That depends on how big an
increase of mass. If big enough it could collapse because of the
gravitational force.

**QUESTION: **

i am working on a pendulum
and i want to know how the shorter the lenght of string the quicker a
pendulum completes a period? Could you also tell me how the lenght of
the string affects the period of a pendulum?

**ANSWER: **

The pendulum is a standard problem which any
elementary physics text will explain in detail. If the amplitude is
small (it does not swing through too big an angle), the period is
approximately proportional to the square root of the length; for
example, if you make the length 4 times longer, the period will be
twice as long.

**QUESTION: **

If one places a lightbulb
inside of a mirrored chamber, such that all surfaces other than the
lightbulb itself are made of the best mirrors available, then turns the
lightbulb on, does the chamber get brighter and brighter? What will
happen eventually? During this process, if one open the chamber, will
he see a flash of light?

**ANSWER: **

The answer to your question is that, even if
the mirrors were extremely reflective, say 99.9% of the light was
reflected, and since light travels so incredibly fast, a pulse of light
is gone before almost any time has elapsed. It might be helpful for you
to read an answer to an earlier
question sort of like yours.

**QUESTION: **

My friend and I are arguing
over which science one should study first. I say chemistry because it
is a "central science" which helps one understand other sciences, but
he says physics does this. Any thoughts?

**ANSWER: **

Physics is more fundamental
than chemistry; scientists generally say that if you understand
something in terms of the laws of physics, you understand it from
"first principles". So you are right, from a philosophical perspective
and physics should be studied first. Chemistry may be thought of as
applied atomic and molecular physics. But, most educators would agree
with your friend as can be seen in any high school science curriculum;
chemistry should be taken first. The argument for this point of view is
that physics requires much more mathematics to do properly, that is,
chemistry can be understood empirically without knowing a lot of
mathematical details. If you are good at math and have had enough of
it, then physics might be better to take first. Actually, I took
physics first in high school and fell in love with it!

**QUESTION: **

I was recently watching a
programme about the Hubble Space Telescope and the pictures it had
captured. It mentioned that the pictures it captured were of galaxies
forming millions of years ago-If this is so- Could it then be possible
for man, should he a find a way to manipulate space travel, be able to
position himself at a certain area of space, at a certain distance and
witness the birth of the milkyway itself? or indeed the birth of
Earth?..........perhaps even the birth of man?

**ANSWER: **

Suppose that something happened here on
earth 500 years ago and you were located at a distance of 500 light
years from the earth with a very good telescope. Then you would be able
to witness that event right now. But, here is the rub. You cannot get
there from here before the light from the event reached there because
it is physically impossible to travel faster than the speed of light;
in other words, you could get there in just under 500 years and you
would be able to witness what happened here tomorrow.

**QUESTION: **

My family is astounded with
long thin projections of ice that form regularly and randomly on top of
ice cubes since I began placing the ice cube trays in the freezer door.
Even when the door is unopened from the time the trays are filled until
the time the ice is well hardened, the needle like spears that usually
slant in various directions at about a 45 degree angle, still form.
Some of these projections reach a length of about an inch. On some
cubes there are large fat lumps that raise up somewhat like a low
volcano. The trays are stacked one on top of the other and the cubes in
the bottom one does not, of course, have these curious growths. Can you
explain how this happens?I

**ANSWER: **(Thanks
to Professor Craig
Wiegert)

I've also witnessed this phenomenon.
(Unfortunately, automatic ice
makers seem to be largely immune to this curiosity, so it's been
several
years.) The creation of these ice spikes has to do with the fact that
the ice cube freezes from the outside in. The top surface starts to
"crust over" first, with the ice growing outward from the edges of the
cube (in the same way that lakes freeze over in colder climes).
Meanwhile, the sides and bottom of the cube also start to freeze.
Because ice is less dense than water, the growing "skin" of ice starts
to crowd out the unfrozen water at the center of the cube. The water
has nowhere to go but up. If the top surface of the cube is mostly
frozen except for a thin spot in the middle, the water will be pushed
out of that opening to form a bump. When the conditions are right, the
"bump" will instead become an ice tube (freezing from the outside in,
remember) and the water will be able to rise even higher. The end
result is the ice spike.
Better descriptions, with lots of nice photos, movies, and some
experimental results, are available at:

http://www.its.caltech.edu/~atomic/snowcrystals/icespikes/icespikes.htm

and

http://www.physics.utoronto.ca/~smorris/edl/icespikes/icespikes.html

The best example I ever saw was in my family's backyard birdbath when
we
lived in Oregon. A cold front had swept through overnight, and the next
morning we found an ice spike at least 4 inches tall protruding from
the
center of the basin. There's probably a picture tucked away somewhere
in a family photo album...

**QUESTION: **

In deriving the equation for
pressure of an ideal gas, is the force exerted by a gas molecule on the
wall given by change in momentum/time between coliisions or change in
momentum /collision time?

**ANSWER: **

You do not actually want the force delivered
by an individual molecule but the average force per molecule averaged
over many collisions. If you knew the time per collision, you could add
many collisions, divide by the number, and find the average force per
molecule. But, if you watch a single molecule and find the time between
collisions for that molecule, you will find the same result without
having to know the details of the collision itself. You get momentum
transfer per unit time which is force due to that molecule.

**QUESTION: **

When matter and anti-matter
come into contact,is the destruction complete.Do no elementry particles
remain?? Is it just "gone"?

**ANSWER: **

Many different things can happen. The best
known matter/antimatter annihilation is when an electron and a
positron, both at rest, annihilate. In order to conserve energy, two
photons come out (photons are essentially light, electromagnetic
radiation but with no mass). Since physicists think of photons as
elementary particles (even though massless), the answer to your
question is no. If one or both of the electrons have energy (are
moving), it is possible for new particles (with mass) to be created in
the process. The most important thing is that the energy (including
mass energy, *mc*^{2}) must be identical before and after
the "destruction".

**QUESTION: **

If you were to drop two
equal boxes of equal dimensions built with the same material and you
filled one with ping pong balls and the other with bricks. You than
proceded to drop them both simaltaneously out of an airplane at 2000
feet. Which one would hit the ground first and why?

**ANSWER: **

In an elementary physics course you are
taught that all objects have the same acceleration, so from that
perspective the motion of the two boxes would be identical and they
would therefore hit the ground simultaneously. However, in the real
world there is air friction which is normally neglected when you first
learn about free fall. However, air friction is not negligible
particularly if speeds get very large. So, as you stipulate, the
geometries of the two objects are the same, they will both have equal
air friction for a given speed. However, when the air friction force
equals the weight of the object, it will stop accelerating and fall at
constant speed; therefore the lighter box will stop accelerating sooner
and therefore hit the ground later.

**QUESTION: **

Hi! Why doesnt an electron
emit radiation as it goes around the atom
is it not really accelerating?
Does the equal + and - charges make the dipole invisible.

**ANSWER: **

This may be an unsatisfying answer, but it
doesn't because it doesn't! The problem is that our laws of classical
physics do not work at very small distances (or at very large speeds).
It turns out that an object must be described in terms of its "wave
function" which is, essentially, a statement of the probability of
finding it somewhere. When you do the calculations using the branch of
physics called quantum mechanics, the wave function is zero unless the
electron is in only certain states (including the ground state), so the
probability of finding it in a slightly less energetic orbit (as it
would tend toward if radiating energy away) is zero; hence, no
radiation. An alternative way to look at it is to say that the
electron should be thought of as a wave; it turns out that the
wavelength of the wave is exactly right to fit in the orbit so the wave
interferes constructively with itself (just like a vibrating guitar
string). However, for a different orbit, the wave each time around
"destroys" itself.

**QUESTION: **

My wife and I were in a car
accident last night and I want to know how many G's our bodies
withstood. I weigh 175 and she 140. We were hit from behind at a speed
of 65-70 mph while at a complete stop. I was driving a 4Runner and the
woman who hit us was driving a Dodge Caravan. I'm afraid I don't have
the exact weight of each vehicle.

**ANSWER: **

That question cannot be answered. It depends
on how long the collision lasted, whether the cars stuck together, how
fast each car was going after the collision, *etc*. The
information you have given me is mainly irrelevant to computing your
acceleration (g's). Here is how you could make a rough estimate:
suppose that after a quarter of a second you were going 20 miles per
hour having started from rest. Then your average acceleration would
have been (20 mi/hr)x(1 hr/3600 s)x(5208 ft/1 mi)x(1 *g*/32 ft/s^{2})/(0.25
s)=3.7* g.*

**QUESTION: **

I’m a PhD student in
philosophy interested (but not working in) the philosophical
foundations of relativity. I have a couple of questions dealing with
the speed of light and special relativity. The main question is number
3, the other two are auxiliary. Your response would be greatly
appreciated. I will also greatly appreciate it if you could let me know
whether there is some bibliography available dealing with this kind of
issues.

- Why is the relativistic
length contraction – as it appears in the Lorentz transformation – a
function of the speed of light?
- Conceptually, it is possible
that the speed of light had a different value than it actually has. How
would that have affected special relativity (in particular length
contraction for fast-moving bodies)? I recommend your looking into the
Mr. Tompkins in Wonderland books by George Gamow.
- Suppose we will discover a
“form of light” (call it light*, symbolized c*) whose speed is double
the speed of light, and it is also invariant. This would enable us to
send signals at this speed and to use these signals to synchronize
clocks so that we may provide an empirically meaningful definition of
simultaneity. Do we need to revise special relativity and base the
Lorentz transformation for length on this new value (c*), instead of c?
Which of the following possible responses should be the case and why:
a) we can do that; b) is it impossible to do that; c) we must do that.

**ANSWER: **

- The answer is that the fact
that light has the same speed in all frames of reference leads to this
result. It is simple algebra and, if you are seriously interested, you
should take the time to learn the basics of special relativity.
- Special relativity would have
the same form it does. If the speed of light were 100 miles/hr, effects
like time dilation and length contraction would be everyday phenomena
which we would not find puzzling at all. I recommend your looking into
the
* Mr.
Tompkins in Wonderland* books by George Gamow.
- This seems extremely unlikely
since light is just a manifestation of electromagnetism and its speed
is predicted by Maxwell's equations. For a new kind of invariant speed
to exist, there would have to be another fundamental force in nature
the theory of which predicts radiation of that speed. Since there is no
good quantum theory of gravity, that is a remote possibility; gravity
waves, however, have never been directly observed although their
existence has been inferred from energy loss of binary systems. It is
usually assumed that gravity waves move with the speed of light, but
that is unverified. Regarding your simultaneity question, there is
never any problem defining when two events are simultaneous. The
problem is that events simultaneous in one frame of reference are not
simultaneous in other frames; having some other universal speed is not
going to change that.

**QUESTION: **

Why there is a
weightlessness in an artificial satellite?

**ANSWER: **

See the answer to the following question.

**QUESTION: **

I always wondered about this
question and was hoping you can shed some light on it for me.
I noticed on Star Trek, they have gravity on their spaceships. I know
this is a sci-fi program and realize its all fictional based on some
scientific facts. But, I always wondered , why can't we put gravity on
the spacestation we have orbiting our planet now?
I know we have simulated 0 gravity on earth. Why can't gravity be
simulated on a spacestation in space?

**ANSWER: **

The only way we know to "simulate gravity"
is to be in an accelerating frame of reference. If you are in a frame
accelerating down with an acceleration of 9.8 m/s^{2} near the
earth (e.g. a freely falling elevator) you will feel weightless. That
is why you are weightless in the space station because it is in free
fall, just like the elevator but it is a free falling projectile. To
create "gravity" you would have to have a local acceleration of 9.8 m/s^{2};
the way to do this is to have a very large donut shaped space station
(say maybe a few hundred meters across) which is rotating with the
right speed so that you could walk around the inside of the outer
surface feeling as if there were gravity.

**QUESTION: **

Suppose a star is 2 light
years from earth. A ship leaves earth and travels to the star and then
returns to earth. If the ship travels at very close to the speed of
light , it should take close to 2 years for the trip, as measured by
someone on earth. But would the time for the trip be close to 0 , as
measured by someone on the ship? Mathematically, if t is the time for
the trip, as measured by someone on the ship, and v is the velocity of
the ship, does t tend to 0 as v tends to c ?

**ANSWER: **

The answer to your questions are "yes" and
"yes". Of course, you made a small mistake in that it would about take
4 years to make the round trip at close to the speed of light. You
might be interested in my previous discussion of the twin paradox.

**QUESTION: **

Why does light travel faster
than sound? In Grade 11 physics, I am learning that everything that
goes through the same medium should travel at the same speed.

**ANSWER: **

It is incorrect to say that everything that
goes through the same medium has the same speed. When I walk through
air, I don't go at the speed of sound. Maybe what the idea is is that
all waves traveling in a particular medium have the same speed. The
medium through which sound travels is air and all sound waves go
(approximately) the same speed. However, when light passes through air,
air is not the medium through which allows it to travel, that is if we
take away the air, the light will still go through but the sound will
not. Finally I should note that even the statement that all waves in a
medium have the same speed is incorrect. The speed which a wave moves
through a medium depends on its frequency; this is called dispersion
and is why a prism splits white light into a rainbow.

**QUESTION: **

According the Law of
Conservation of Mass (or matter), matter is neither created nor
destroyed, it simply changes form. So, when a baby is gestating, where
do the atoms that make up that fetus come from? My thought is that the
matter is coming from two sources: the sperm and egg to begin with, and
from the food that the mother is ingesting to nourish the fetus. (And I
suppose the air she is breathing contributes to the nourishment of the
fetus.) Would that be correct? I figure that's where new plants come
from....they pull atoms of nourishment from the ground and that helps
build the plant itself.

**ANSWER: **

First of all, there is no such thing as
conservation of mass. Energy is what is conserved and matter is a kind
of energy (you know, *E=mc*^{2}). The idea of
conservation of mass is a 19th century concept and comes from chemistry
where it is generally assumed that if you have a certain mass of
hydrogen and the appropriate mass of oxygen and if they combine to form
water, the mass of the water will equal the sum of the masses of
hydrogen and oxygen. However, if you could make an accurate enough
measurement, you would find that the water had a little less mass than
the hydrogen plus oxygen (because you must put energy in to break the
water apart and it shows up as mass in the end). That said, the forces
holding molecules together are incredibly weak and so the change of
mass in chemical reactions is incredibly small, so, for all intents and
purposes, mass is conserved. And therefore, you are right that the
mother supplies all the mass (after conception). And, yes, plants get
their mass for growth from the ground and the air.

**QUESTION: **

I am investigating a factor
that affects the period of a conical pendulum, so after a little
theoritical work* I decided to vary the lenght of the cord while
keeping other variables constant. My question is "does the initial
speed affect the period?" and What is the best way to design this
experiment using simple lab equipments?

* I came up with this formula>

T = 2pi*sqrt(L*cos(a)/g)

T = period

sqrt = square root of ()

L = lenght of the cord

a = angle between the cord and the vertical

**ANSWER: **

Your equation is right. The
initial speed does not appear in the equation, but the motion certainly
depends on it because for the pendulum to be a conical pendulum with a
particular angle *a*, it is necessary that the speed be just
right. Hence, *v* is "hiding" in *a*. In fact, you should
be able to show that *v*=sqrt[(*Lg* sin^{2}(*a*)/cos(*a*))].
Design your experiment so that you can vary *L* as well as *a*
so that you can measure *T* and compare experiment with theory.
The tricky part might be launching it with the right speed at each
angle; trial and error is probably ok.

**QUESTION: **

The Heisenberg Uncertainty
Principle states for a photon that: (certainty of energy)*(certainty of
lifetime)=k
If a photon's speed is always = c, then a photon can't age. My question
is: if photons don't age, then how can there be uncertainty about their
lifetime?

**ANSWER: **

"Aging" has nothing to do with anything
here. Also, you should state the uncertainty principle in terms of
uncertainties, not certainties. In the case of a photon, its energy is
exactly *hf *where *h* is Planck's constant and *f*
is the frequency of the associated electromagnetic wave. Hence, the
uncertainty of the energy is zero, so to obey the uncertainty
principle, the uncertainty of the lifetime is infinite; as you know,
photons are stable particles.

**QUESTION: **

Electrons have two possible
states, spin up and spin down; no one electron is forbidden from
changing from one state to the other, yet how does an electron create
the energy from within to change states?

**ANSWER: **

For an isolated electron,
there is no energy difference between the two states.

**QUESTION: **

if i understand correctly
light travels at a fixed speed, and so it takes, for example, 8 minutes
for sunlight to travel to earth.
if this is so, is everything is see in the past, allowing for the
light's travel time?
and if so, is an object i see at 50 metres closer in time than an
object seen at 100 metres?

**ANSWER: **

This is certainly right. In simple physical
terms, when you make a physical measurement you must make allowance for
the time of transit of the information to you.

**QUESTION: **

When I studied the force of
gravity in a college physics class, I always wondered how one object
could exert a force on another object or how one "knew" the other was
there. Later, in trying to understand Einstein's general theory of
relativity I came to understand that gravity is not due to objects
acting upon each other but rather from a distortion that occurs in the
geometry of space-time (like the bowling ball on the trampoline idea)
which results in the illusion of an attraction. More recently, I've
been reading about a particle called the graviton which physicists
hypothesize travels back and forth between massive objects at the speed
of light resulting in the "attraction". So, which one is it? The
distortion of space-time or the "messenger" particles zipping back and
forth? Or both? And if both, how do the two concepts fit together?

**ANSWER: **

The operative word here is "hypothesize".
The idea of a graviton is based on expectations that we should be able
to understand gravity from the perspective of quantum physics. However,
there is no remotely successful theory of quantum gravity and it
remains one of physics' "holy grails". The theory of general relativity
is very successful but not reconcilable with quantum mechanics.

**QUESTION: **

The discussion is if there
was such a thing as a indoor wakeboard training facility would the
hydro dynamics be such that if water speed was equal in the following
scenarios could equal amounts of 'big air' be obtained.

- A 200# wake boarder is being
towed behind a boat at a distance of 60' at 20 mph. The wake height is
24" high and has a 45 degree angle on the outside of the wake. The wake
boarder has sufficient skill to cut in from outside the wake and obtain
a height of 36" and travel 20'. Rope mounting height is 36" above water
level.
- The same 200# wake boarder is
in a wave pool capable of creating the same water conditions as being
towed behind a boat at a distance of 60' at 20 mph. Same wake
characteristics and same skill level from the same wake boarder. Will
the Wake boarder be able to obtain the same height and distance as he
would behind a boat? Same rope, rope height same everything.

Some of us say yes some say no.
Some are of the opinion that forward momentum generated by the boat
would enable greater distances to be obtained. Others say that the
height and distance would be equal because it is the speed of the water
going by and the ability to generate speed perpendicular to the
direction of the water that provides the speed to obtain height and
distance.

**ANSWER: **

You are going to have the water going by in
#2 with the same speed as the boat in #1--good. You are going to have a
wake with the same characteristics (same height and motion relative to
the wakeboarder)--good, although I am not convinced that it would be
easy to actually do this since the wake shape has to be essentially at
rest relative to the wakeboarder whereas the water per se is not. What
you do not talk about is the air. In #1 there is a significant wind in
the face of the wakeboarder so you better have a big fan for #2. I
believe that air friction will play a very important role after he
lifts off, that is he will essentially fly like a ski jumper. I think
that if you don't forget the air, it will be a pretty good simulation.
Incidentally, the boat has nothing to do with the mechanics of
the wakeboarder because they are not in contact so the boat cannot
exert any forces on him. Whatever happens to the wakeboarder depends
only on his interactions with water, air, and rope (and, of course
gravity).

**QUESTION: **

around 1930, Dirac solved
electron spin and magnetic moment by treated the electron as a point
particle. i ask, is the electron a point? what is meant by a point
particle?

**ANSWER: **

To the best of my knowledge, nobody has
measured a structure of an electron, that is it really appears to be a
point particle, something which occupies zero space. However, most
scientists I know are uncomfortable with infinities in nature and such
a particle would be infinitely small and have infinitely large density
(because it has nonzero mass). Another aspect of your question is that
elementary particles all, as you know, exhibit wave-like properties and
as such the meaning of "size" becomes sort of fuzzy.

**QUESTION: **

Regarding the Stern-Gerlach
experiment of 1922 concerning space quantization, does this mean that
electrons come in two flavors, spin up and spin down?

**ANSWER: **

Spin up and spin down have meaning only if
up and down have a meaning. Hence, you must first choose a coordinate
system in which to make measurements. When you do this, you may say
that electrons have two possible states, spin up and spin down.
However, a particular electron may be in a state which is a combination
of some probability of each. Quantum mechanics is weird!

**QUESTION: **

Given the length of a column
of air in a musical instrument changes the frequency of the note
(shorter column, higher pitch), I assumed that this was why adding
water to a wineglass changed its frequency when made to "sing".
However, on reflection, adding more water to a wineglass lowers the
pitch. Given adding more water decreased the length of the column of
air, this can't be the correct explanation (shorter column of are
should increase the frequency).
Moreover, I've done the same "experiment" with the wineglass submerged
to the same depth as it was previously filled (ie., water is at the
same height on the outside, as it was previously on the inside). The
pitch was the same in both cases.
I've also noted that the same volume of water at a higher temperature
increases the pitch of the note. My question is what is the correct
explanation for the change of pitch of a "singing" wineglass? (I think
that is must be something to do with the damping effect of the water in
direct contact with the glass. This makes sense given at a higher temp,
the density of the water is lower, therefore the absorption of sound
energy is less for the same height of water in contact with the glass.
Less absorption, less change in frequency.)

**ANSWER: **

The reason is that it is not the air column
but rather the glass which is resonating. Think of a mass on a spring:
if you increase the mass (inertia) you decrease the frequency and I
think that is what you are doing by adding water, increasing inertia
against vibration. In that light, it is not surprising that you get the
same frequency whether the water is inside or outside the glass
(although I would not expect them to be precisely the same). The
temperature effect may simply be that you are changing the elasticity
(spring constant) of the glass by changing the temperature; try heating
the glass without adding water.

**QUESTION: **

Since the speed of light is
a finite number why would it take an infinite amount of energy for a
spacecraft to trave at the speed of light? *i understand that the
faster you go the more massive you become, but you cannot be infinitely
massive to reach a finite speed. It doesn't make sense to me.
Maybe Infinite mass and infinite energy should be replaced by "unknown"?

**ANSWER: **

You are thinking about this all wrong. What
you have to do, once you understand relativity, is to compute the total
amount of work which you must do in order to acquire a speed v for a
particle whose mass is *m*. In classical physics this turns out
to be *mv*^{2}/2, but classical physics is only
approximately true and becomes invalid for high speeds. The correct
expression for the kinetic energy, the work you do, is* mc*^{2}/(1-*v*^{2}/*c*^{2})^{1/2}-*mc*^{2}.
(Here *m* is the mass of the object at rest.) This expression may
be shown to reduce to *mv*^{2}/2 for *v* much
smaller than * c* but clearly becomes infinite for *v=c*.
Thus, to accelerate a particle to the speed of light requires an
infinite amount of work (energy).

**QUESTION: **

I am a 16 year old student
currently enrolled in Physics at my high school. I was given an extra
credit assignment in which I have to figure out all the steps to
convert meters per second to miles per hour. I need to know every
single step in completing the conversion. I have done research, and
have found nothing that has helped me out. Thank you for your time.

**ANSWER: **

The trick to unit conversion is to
repeatedly multiply by 1.0 (we can always do that, right?) until the
units are what we want. Since I will not do your homework for you (it
violates the groundrules of this site!), I will work out an analogous
problem. Suppose that I want to convert a pressure expressed in pounds
per square inch (psi) to the more "scientific" expression of newtons per square meter. For
a concrete example, let's do 14.7 psi which is about atmospheric
pressure:

14.7 (lb/in^{2})x(1 in/
2.54 cm)^{2}x(100 cm/1 m)^{2}x(1 N/.225 lb)=1.01x10^{5}
N/m^{2}.

**QUESTION: **

How much helium does it take
to fill a standard balloon ? Is there a way to measure helium ?

**ANSWER: **

First your second question: there is
certainly a way to measure helium, or anything for that matter. One way
is to simply measure its mass (in grams or kilograms). Another, often
more useful way, is to measure its molecular weight in moles where you
have one mole unit for each molecular weight unit. For example, atomic
hydrogen has molecular weight of 1 but it normally occurs as the H_{2}
molecule, which is two hydrogen atoms bound together so its molecular
weight is 2. Hence, one mole of H_{2} gas has a mass of 2
grams. Helium has a molecular weight of 4, so one mole of hydrogen has
a mass of 4 grams. The reason that a mole is useful is that 1 mole of
any material has the same number of molecules, about 6 x 10^{23}
which is called Avagadro's number. Of course once you know Avagadro's
number, you could also measure the amount of helium by stating the
total number of atoms in the sample.

Now, to your first question: I
do not think there is such a thing as a "standard" balloon, and it
depends on how much you blow it up. Suppose we have a balloon which has
a volume of about one gallon which would be about 4 liters which is *V*=4
x 10^{-3} m^{3}. The pressure would have to be bigger
than atmospheric, so let's say that it is about 2 times atmospheric
pressure which would be about *P*=2 x 10^{5} N/m^{2}.
Suppose that the temperature is room temperature, about 20^{0}C
which is, in absolute temperature (kelvin) about *T*=273^{0}K.
Now there is a very useful equation called the ideal gas law, which
works extremely well for most gasses at normal conditions which is *PV=nRT*
where *n* is the number of moles of the gas and *R* is
called the universal gas constant and has a value of about 8.3 for the
units of things I have used here. So, *n=PV/RT*=0.35 moles. So,
since a mole is 4 grams, the mass is about 1.4 grams. This answers your
question. By the way, 0.35 moles is about 2.1 x 10^{23} atoms.

**QUESTION: **

I was just wondering, could
the principle of superposition of waves be used to muffle or even
silence a noise projecting from a sound source? So, perhaps if a source
of sound was project a particular frequency, and i places another
source of the same frequency and ampilitude in another position, say
half a wavelength behind, could the original noise be silenced?

**ANSWER: **

Yes. In fact, that is how noise-cancelling
headphones work--the external sounds are captured by a microphone,
flipped, and added back to the incoming sounds. Then you hear only
(almost) the sounds being sent to the headphones, music, talk, *etc*.
Pilots often use this device so that the hear only other crew members,
ground controllers, *etc*. The answer to your second question is
also yes but you must also take care that the two speakers are in
phase. This kind of destructive interference is responsible for "dead
spots" in concert halls.

**QUESTION: **

Why is heavy water (D_{2}O)
used in moderators of Nuclear Power Plants instead of normal water (H_{2}O)?
If heavy water (D_{2}O) absorbs and slows down the neutrons
emmited in fission what happens to it?

**ANSWER: **

The purpose of a moderator is to slow
neutrons down so that they will be more probable to be absorbed by a
fuel nucleus (*e.g. *uranium) and cause a new fission. And each
new fission becomes the source of more neutrons, but they are fast and
the moderator slows them down. If you use something like lead as a
moderator, it would work poorly because the scattered neutrons would
have almost no loss in speed (think of bb's bouncing off bowling
balls). But, if you use something light, like hydrogen, then you are
bouncing neutrons off something about the same mass which will quickly
slow them down (think of a head-on collision between two billiard balls
where the cue ball stops dead). So, hydrogen gas or liquid would be the
best moderator, but hydrogen is very explosive, so we use something
rich in hydrogen, water. But the problem is that a single proton can
easily combine with a slow neutron (to create a deuteron) but that
removes the neutron which we want to use to cause more fissions. The
purpose of the moderator is __not__ to remove neutrons, so we try
the next lightest atom, deuterium, which is chemically identical to
hydrogen but has a mass about twice as big. It is not quite such a good
moderator, but it has a very small probability of absorbing neutrons.
In the event that it does absorb a neutron, it becomes hydrogen with
one proton and two neutrons and is called tritium. Tritium is
radioactive and harmful to the environment.

**QUESTION: **

I've
heard of this experiment: Two parallel mirrors are set up and a laser
is fired perpendicularly between them. It is then possible to view the
beam of laser light (maybe with some dust or smoke between the mirrors)
falling towards the earth with an acceleration of -9.8 m/s/s. Is this
possible? If so, has this ever been performed?

**ANSWER: **

It is true that light will
fall with an acceleration of 9.8 m/s^{2 }(but retaining a
constant speed, that is the vertical component of the velocity would
increase), so in principle your device would work. But, think about the
scale of things. If the mirrors were 3 m apart, it would take 10^{-8}
s for the light to go from one to the other. In this time the light
would "fall" 9.8 x (10^{-8})^{2}/2 m which is about 5 x
10^{-15} m, about the size of a nucleus! I reckon (gt^{2}/2)
that it would take about a hundredth of a second to fall 1 mm, right?
But in this time, light travels 3 x 10^{8} x 10^{-2} =
3,000,000 m, a million reflections in our device. But no real mirror is
completely reflective; an amazingly good mirror would be 99.9%
reflective, but a million reflections would leave you with about 10^{-435}
(.999^{1,000,000}) of the initial intensity! Clearly, this
seems to be an impossible experiment and I very much doubt that any
variation of it has been done.

**QUESTION: **

Would a type of nuclear
reaction take place if a proton entered a specific atom at a certain
rate, or if a neutron entered at a certain rate? Is this considered the
splitting of an atom or just one atom becomming another atom? Would
there be any kind of an explosion? What happens to the gluons in each
case?

**ANSWER: **

Just about anything which is energetically
possible can happen. Take some examples: a proton could be absorbed by
the nucleus and stay there creating the next element in the periodic
table; it could knock out a proton while passing through creating the
previous element in the periodic table; it could knock out a neutron
creating the next lightest isotope; the struck nucleus could split into
two heavy, but much lighter than the target, nuclei (called fission);
and just about anything you can think of, as long as there is enough
energy carried in by the proton to do it. "Splitting of an atom" is a
qualitative term but usually refers to fission. Neutrons are better for
causing nuclear reactions since slow neutrons can interact easily with
the nuclei whereas, since the proton and the nucleus both have positive
charge so it takes a much faster proton to get close enough to the
nucleus to interact with it (the nuclear force is very short-ranged).
Anything you can do which involves a single atom will not cause what
you would call an "explosion", but if you make many things happen at
once so that a large number of nuclei participate, you could get
something observable on a macroscopic scale. That is how an atomic bomb
works (or a reactor): one neutron causes a fission, but a fission
releases several other neutrons and some of those will create new
fissions, and so on and so on. There is no reason that a third grader
needs to be thinking about gluons!

**QUESTION: **

Assume two identical objects
A & B, with a rest mass of m, moving relative to each other at a
velocity V. The question is this: what is the energy equivalent of A?
According to relativity theory, the energy of A = mc^{2}, where
I assume, m is the mass of the object from the point of view of an
observer in the same frame of reference as A.
BUT, also according to relativity theory, when an object moves, its
mass increases, which we will call M [capital M). So the the energy of
A, since it is moving relative to B, = Mc^{2}.
There then appears to be a paradox: the energy equivalent of mass A is
two different amounts, depending on whether the observer is in the
frame of reference of A (stationary) or B (who sees A moving at
velocity V). The object itself has no way of knowing whether it is
moving, so it seems there should be only one correct answer.
Is this a paradox?

**ANSWER: **

You do not have to do
special relativity to answer this question. Energy is a relative thing,
its absolute value has no meaning; all that matters is the amount by
which it changes when things happen. Take a book which sits on the
table (and I am doing this nonrelativistically). If I choose the
position of the table top as the level of zero gravitational potential
energy, then this book has zero energy. If I run past it, however, it
moves relative to me with some speed* v* and therefore has energy
of *mv*^{2}/2 (kinetic energy). If I raise it some
distance above the table top it now has some amount of potential
energy. It is always the same book but with just about any amount of
energy I like. No paradox. In relativity, *mc*^{2 }(with
*m* the mass of the object at rest is called the restmass
energy). If an object moves its energy is *Mc*^{2} (with *M*
the mass it has when moving). The kinetic energy is by definition *Mc*^{2}-*mc*^{2}
and this will be approximately *mv*^{2}/2 if *v *is
very small compared to *c*.

**QUESTION: **

V=IR

Either increase R or I Voltage(V) will increase

Which of the two we are increasing in a step up transformer while
increasing the voltage as far as I know Current (I) decreases while
stepping up the voltage than is it the R that we are increasing?

**ANSWER: **

A transformer is not an "Ohmic device" and
so Ohm's law is not true. The reason that* I* decreases when the
voltage increases is that energy must be conserved and the power, the
rate at which energy is consumed (or delivered) is *P=IV*. So *P*_{input}=*P*_{output.}

**QUESTION: **

In Global Warming, I
understand there is a shifting of visible energy to longer wavelengths
by the land mass and oceans which then radiates this energy to the
greenhouse gases in the atmosphere which in turn re-radiates the energy
back to earth. 1. What accounts for the shifting of the energy from the
shorter 400- 700 nm range) to the longer IR & ‘heat” wavelengths?
Is it analogous to Fluorescence spectral shifting phenomena? 2. In a
theoretical situation, if only pure visible wavelength energy fell on a
perfect black body, would the black body absorb all of this energy,
raise its temperature and reradiate it (at longer wavelengths) outward?

**ANSWER: **

Question number 1: Matter
absorbs electromagnetic energy and the result is that it heats up; a
hot object radiates energy but mostly in the infrared region.

Question number 2: Yes, except
that the radiated spectrum would depend on the final temperature of the
black body. *I.e*., if the black body were originally very hot
such that most of its energy was at short wavelengths, the final
spectrum would be hotter and peak at even shorter wavelengths.

**QUESTION: **

How does a ballon gain
positive charge?

**ANSWER: **

What normally happens, since it is
negatively charged electrons which can be moved around most easily in
normal matter, is that an object becomes positively charged by losing
electrons.

**QUESTION: **

if you shot a bullet
directly up, when it came back down would its speed be the same as when
it left the gun or does terminal velocity prevent that.

**ANSWER: **

If there were no air friction, the speed
would be the same. But there is significant air friction which takes
kinetic energy away from the bullet, so it is going more slowly when it
hits the ground. Incidentally, because the earth is rotating, the
bullet would not hit precisely at the point from where it was fired
straight up.

**QUESTION: **

So we move with the earth
through space as it both orbits the sun and rotates on it's axis. Now
the closer we get to the speed of light the slower time passes for us.
Does this mean even when stationary on the ground our perception of the
passage of time is altered because the earth is moving fairly fast
through space? If so how much faster do we move through time then
someone not moving along with the earth or anything else. If not why?

**ANSWER: **

In your own frame, time will progress at a
perfectly normal rate. It is only the rate of your clocks relative to
clocks in motion with respect to you which run slower. See my
discussion of the twin paradox in an earlier
question. Incidentally, the motion of the earth is far too slow
for any easily measurable effects to be observed since the earth's
speed relative to any other clock you are likely to compare it to is
very small compared to the speed of light.

**QUESTION: **

Does the Heisenberg
Uncertainty Principle say (a) that particles have a definate position
and momentum, but we are incapable of ever knowing them both
simultaneously or (b) that particles do not have a definate position
and momentum at all?

**ANSWER: **

Technically, one may know one (position or
momentum) with perfect precision if we are totally ignorant of the
other. However, we can never be totally ignorant of either in practice
(for example, surely the particle in question is somewhere in the
universe). So, both your (a) and your (b) are correct, but (b) cannot
be by itself a statement of the principle because the degree to which
we can know one is determined by the degree to which we know the other.

**QUESTION: **

What is the shortest
wavelength (I assume in the gamma range) that has ever been
experimentally observed.

**ANSWER: **

The most energetic photon which I could find
reference to was a cosmic ray of energy 3.2 x 10^{20} eV
(observed in 2004 by the Fly's Eye Detector). Since *E=hf* and *f=c/**l*, *l*=*ch/E=*(3
x 10^{8} m/s)(4.1 x 10^{-15} eV s)/(3.2 x 10^{20}
eV)=3.8 x 10^{-27 }m. Here, *h* is Planck's constant and*
c* is the speed of light.

**QUESTION: **

Can you tell me if anyone
has studied the conection between gravity waves and bremmstralung? For
example if a charged mass were orbiting a significantly larger mass it
would emit both gravitational waves, (at least according to general
relativity) and electromagnetic waves. Has anyone studied at least the
theoretical model
of this? How would the energy radiated by one field compare to the
other, both separately and simultaneously?Would they radiate less
energy when simultaneous?

**ANSWER: **

Electromagnetism and General
Relativity are separate theories. In the case you suggest, both gravity
waves and electromagnetic waves would be emitted and would have nothing
to do with each other as far as we know (although some have suggested
that general relativity may have effects on electromagnetism). Both
phenomena have been fully explored theoretically. I should of course
include a disclaimer here: nobody has ever directly observed a gravity
wave but some physicists are trying very hard.

**QUESTION: **

can matter at absolute zero
be seen ?
could dark matter be this ?
i mean, if matter was at absoulte zero,
is it possible it still has mass but we
cannot see it ?

**ANSWER: **

Matter exactly at absolute zero cannot be
because of several laws of physics. However, let's suppose that there
were a chunk of matter at absolute zero. Could it be "seen", that is
detected? Well, if it were just sitting there by itself in totally
empty space we could not "see" it but then we could not see a nearby
piece of matter at any temperature. If light were to strike it, I do
not see why the light would not be either reflected or absorbed, and in
either case we could detect that so we could "see" it.

**QUESTION: **

Why does light travel in a
srtaright line and sound don't?

**ANSWER: **

Light does not travel in a straight line
necessarily any more than sound does. The simplest example is a mirror
which clearly changes the direction of light. Light is also bent by
entering a different medium which is how lenses work. Light is also
bent (ever so slightly) by gravity. Light is also bend by diffraction
(for example, you can never make a perfectly sharp shadow of something
because light bends as it passes the edges.

**QUESTION: **

I have a problem with the
standard explanation of atmospheric pressure as beeing caused by the
weight of the air lying above.
If i have a hermetic closed bowl of glass (or something else), so there
is no way forces can be transmitted from the inside to the outside, how
am I to explain the pressure in the bowl as caused by the weight of the
air above ?

**ANSWER: **

What matters is the environment when you
close the bowl. If you simply close it in atmospheric pressure, there
will be atmospheric pressure inside it. If you were then to pump the
atmosphere away, the pressure inside the bowl would still be the same.
If you were to pump more air into the bowl, the pressure would increase
and pumping it out would decrease the pressure. These subsequent
changes would be due to you, not the atmosphere.

**QUESTION: **

I'm not quite sure that I
understand the theory of relativity. Is it true that light NEVER slows
down; that instead, time is slowing down? (such that the m/s speed of
light is the same as always, but a second becomes longer)

**ANSWER: **

The speed of light in a vacuum is always the
same, regardless of the motion of the source or the observer. As a
consequence of this, moving clocks run slowly (which is called "time
dilation"). Light does move more slowly in a medium (say glass, air,
water,...) which is responsible for optical instruments like
eyeglasses, cameras, telescopes, * etc*. working.

**QUESTION: **

If the half life period for
say Uranium is constant then it should be that every atom of particular
mass of Uranium degrade simultaneously and say after the half life for
one atom whole number of atoms in that mass should get degraded and
hence no more remians mass of Uranium but some thing else. Is it so?

**ANSWER: **

What half life means is that at that time
half the number of original atoms will be converted into something
else. It is useful only for a very large number of atoms because
radioactive decay is a statistical process and you cannot know when any
given nucleus will decay, only what the probability for decay is. After
many half lives almost all the uranium will be gone.

**QUESTION: **

What generates more energy?
A explosion or an implosion? Also, which takes more energy to create?

**ANSWER: **

This question has no meaning in physics. In
the overall picture, energy is conserved in any case. Take a
conventional bomb (TNT): Energy is chemically released from the
explosive TNT and reappears as light, heat, sound, and the kinetic
energy of the fragments. The same is true for the case of implosion:
Chemistry provides energy but there are no fragments flying out so more
of the original energy ends up as heat, light, and sound than in the
case of the explosion. In all cases, something provides a certain
amount of energy and it shows up somewhere else.

**QUESTION: **

How does beta particle
radiation produce heat energy? Does it do it by merely striking a
nucleus and increasing the movement of the atom? I have never read
material that explains that a beta particle strikes a nucleus and
increases the vibration or movement of the atom itself.
Or is the heat energy produced when the beta particle knocks an
electron off of an atom and then the atom later picks up another
electron and so produces heat in an indirect fashion (an exothermic
reaction where the atom picks up an electron)? To me that would be the
conversion of kinetic energy of the beta particle to heat energy.

**ANSWER: **

The beta particle is just an
electron (or positron) and loses its energy almost entirely by
interacting with the atomic electrons, not the nuclei. Atoms become
excited or ionize, then deexcite and emit electromagnetic radiation
(light, x-rays, *etc*.) which gets reabsorbed and eventually ends
up as heat, increased kinetic energy of the absorber atoms.

**QUESTION: **

Using the electron flow
model is it correct to assume that flow is from the earth to the
generator?Is it correct to assume that the earth is negative in regards
to the generator?Or is the generator more negative than ground?

**ANSWER: **

One of the most important points about
electric potential is that its zero is arbitrary. We usually call the
point where we define zero potential to be "ground" or "earth", but
that point need not be the actual physical earth. The one thing which
you may be certain of is that electrons will always flow from low
potential to high potential. Thus, if you call the earth zero potential
and if your generator is at +5 volts, then electrons will flow to the
generator. On the other hand, if the generator happens to be at -5
volts, electrons will flow from the generator.

**QUESTION: **

I am fascinated by
magnetism, most likely because I do not understand its limits. I
recently read somewhere that it has been determined that gravity
"flows" at the speed of light (i.e. if the sun were to inexplicably
vanish, it would still take eight minutes for it to disappear from the
sky and for the earth to drift from it's orbit). Does a magnetic field
behave similarly, or is it instantaneous in effect?

**ANSWER: **

Electromagnetic fields all
propogate at the speed of light. Thus, if you created a magnet on the
sun, it would take 8 minutes before you saw the magnetic field on the
earth.

**QUESTION: **

What is equivalent of 250
rpm in x gravity?

**ANSWER: **

I presume that you want to know how many g's
of acceleration 250 rpm is. Well, you have not given me enough
information because the acceleration depends on the radius of the
circle the object is moving in. The acceleration of an object with
speed *v* moving in a circle of radius *R* is *v*^{2}/*R*.
So the acceleration of an moving at 250 rpm which is 250/60 rps=4.17 s^{-1}.
So, the speed would be *v*=2p*R* x 4.17=26.2*R* m/s. So, the
acceleration would be *a*=(26.2*R*)^{2}/*R*=685*R
*with the answer being in m/s^{2} if* R *is
expressed in m*. *The acceleration due to gravity is 9.8 m/s^{2},
so a=685*R*/9.8=69.9*R* in g's. So, for example if *R*=0.5
m, *a*=35 g's.

**QUESTION: **

If e=mc2 than what does
happen when --e=-mc2. Will time stand still? If you go backward and
time is always trying to catch up would you not be caught in in a loop.

**ANSWER: **

Sorry, this question doesn't really make any
sense. You might want to study some about Dirac who postulated a filled
"negative energy sea". When a particle is elevated from this sea to the
realm of positive energy it leaves a hole behind. This hole is an
antiparticle.

Note to this
questioner: I cannot answer your questions about a career in physics
because the email address you gave me does not work. Also questions of
this sort I will often answer but not here because this site should be
reserved for physics questions.

**QUESTION: **

During the past several
months, I have been working my way thru an "Elementary Modern Physics"
by Weidner & Sells (circa 1962). For the most part, I been able to
handle the majority of the problems, but have slammed into several that
I can't breakdown. One of these is as follows:
"What is the mimimum speed of a particle such that its kinetic energy
can be written as its total energy E, and therefore as pc, with an
error in total energy no greater than 1%?" This implies that this is in
the extreme region where E~pc (momentum) & this confirmed by the
solution below.
I have not been able to set-up the equation required to yeild the
solution = 0.9995c. What seemed routine at first has become
something else.
At least one author said to ignore the rest mass energy in the extreme
region, but when I do that I get E=pc or mc^2 = mvc , hence v=c &
this not correct. There has to be some small factor (~1 in 2,000) to
achieve the text's solution. However, when I write E = Eo + KE &
try to work it thru I get "bogged down" in the algerba with
(1-beta^2)^0.5 factor.
I'm about out of bullets & to the point of frustration. It's clear
to me that I have missed something in my understanding of the set-up of
the initial equation. I am asking for any coaching & direction you
or perhaps a graduate student might have.
I'm also working thru a similar one that has a different twist
......."it asks what's the maximum speed a particle can move so that
its KE can be written as 1/2 Mo*v^2?" If I can solve the one above then
I think this one will fall out.

**ANSWER: **

A detailed answer may be read here.

**FOLLOWUP
QUESTIONS:**

- You indicated that m always
refers to rest mass (Mo), and I assume that
the momentum (p) in these equations refers to the classical momentum
p=Mo*v,
- otherwise the terms would not cancel out? I did not see
any use of
the gamma term. Am I correct?
- also, since you knew that this was "slow speed relative to
c "...........
is this the reason to use classical in this application?

**ANSWERS: **

- No,
*p* is relativistic momentum, mu/sqrt(1-*u*^{2}/*c*^{2})
where *u* is particle speed.
- The gamma is in
*p*. I view linear momentum as the
thing that is redefined in relativistic mechanics, not mass. It must be
redefined to have momentum conserved in an isolated system.
- What I know is that in the limit of small
*u* special
relativity must reduce to Newtonian mechanics. Hence, we must have *T*=.5*mv*^{2}
for *u<<c* or equivalently *pc<<mc*^{2}.

**QUESTION: **

If there was a circular race track, and it had three
lanes; one car on the inside lane and one car on the outside lane.
Would the centrifugal (or is it centripetal) force of the cars be equal
if it takes the same time for them to complete a lap. Because while the
one on the outside lane is traveling faster; it has a softer angle. The
one in the inside lane is travelling slower but with a sharper angle.
I thought of this when tryingt o go to sleep in the car and feeling the
centrifugal force when going round bends.

**ANSWER: **

First let's get straight the difference
between centripetal and centrifugal forces: an object moving with speed
*v* in a circle of radius *R *will have an
acceleration (called centripetal acceleration) *v*^{2}/*R*.
Because of Newton's second law, a force must cause this acceleration,
so *F*=*mv*^{2}/*R*. If you are riding in a car
and leaning on the outer door, the door pushes on you with with this
force, called the centripetal force. Because of this __ real__
push, you have the perception of being pushed against the door with a
force equal to the centripetal force; you are not really being pushed
into the door, you just feel that way. In physics this is what we call
a "fictitious force" and, in this case it is called the centrifugal
force. Another example is when the car is accelerating you feel that
you are being pushed back into your seat but what is really happening
is that the seat is pushing forward on you.

Now to your question: Since the
speed *v*=2*pR*/*T* if the
period is* T, *the centrifugal and centripetal forces (*mv*^{2}/*R*)
will not be the same for both cars because *v*^{2} is
proportional to *R*^{2}. The ratio of the forces would be
*F*_{out}/*F*_{in}*=R*_{out}/*R*_{in},
that is the outer track would have larger force.

**QUESTION: **

What are colours, does it have any physical mass?

**ANSWER: **

Color is a qualitative way to describe the
differences between wavelengths of visible light as perceived by our
eyes and brain. It is not an object, so to ask if it has mass is
meaningless. Photons, from which light is composed, have energy but no
mass.

**QUESTION: **

if there is an object with zero inertia, and there are
enormous forces of the same strength pulling at it from all directions,
so the all cancel out. will it take some effort to move this object? or
will the object be like.. nothing?

**ANSWER: **

Dynamically, an object with zero net force
on it (as you describe) is identical to one with no forces on it, so we
need only ask ourselves what happens when we exert a force on an object
with zero mass. It will experience infinite acceleration because a=F/m;
by the same token, an object with zero mass can have an acceleration
when there is no net force on it. This all sounds quite bizarre, but
keep in mind that there is nothing with zero mass (photons do not count
because classical mechanics does not apply to them.) We often talk
about objects with zero mass in elementary physics problems, for
example "...the pulley is massless and frictionless" but these should
be understood as approximations, that is the mass of the pulley is very
small compared to other masses in the problem. A force acting on an
object with very small force will result in a very large acceleration.

**QUESTION: **

Do photons have mass?
In one of your answers you say no. My penquin dictionary of science
says, no mass. However, in the September 2006 issue of ASTRONOMY, the
article, ASK ASTRO page 63. It is stated that the photon's mass is less
than 10(-50)kilograms. Or 14 orders of magnitude smaller than a
neutrino. Very low mass, yes, but there is mass. Is a photon massless?

**ANSWER: **

When we say that photons have no mass, we
mean that every measurement we have ever made is consistent with their
having no mass. However, it is often of interest to test the limits of
our knowledge: how accurately do we know that the photon is massless?
Most likely the article you were reading put an upper limit on what the
mass of a photon could be based on experiments, 10^{-50} kg.

**QUESTION: **

I was wondering whether or not one could accelerate a mass
of about 1 kilogram in a large particle accelerator to nearly the speed
of light. If this is possible, how fast would the mass go, how large
would the particle acclerator have to be, and how much energy would be
needed to acclerate the mass? Also, what type of energy is released
when two particles or in this case one kilogram objects collide or what
percent would be light and what percent would be heat.

**ANSWER: **

It is not feasible to accelerate a 1 kg mass
in a particle accelerator because the 1 kg mass is not charged. Even if
you caused it to become highly charged, the force of gravity on it (its
own weight) would be larger than any electrostatic force you could
exert on it so the accelerator would not work. The speed, if close to
the speed of light as you stipulate, would be about 3x10^{8}
m/s. The energy would be about 10^{26} times larger than the
energy of a proton having the same speed. The energy of 1 kg going 99%
the speed of light would be about 6.4x10^{20} Joules. If you
accelerated it to this energy over the time of one year, you would have
to continuously supply over the year about 20,000 Gigawatts of power!
There is no way to know exactly what will happen when two objects
collide.

**QUESTION: **

Do electrons contain photons? Electrons emit photons when
elevated to higher energy level. E=mc^{2}. Photons are massless
but are energy. Does not all energy have mass? What happens to photons
in a beam of light in a dark room when the beam is switched off?

**ANSWER: **

We do not think of electrons as "containing" photons
although they are thought to be surrounded by a cloud of virtual
photons popping into and out of existence. The emission of photons from
excited atoms is due to a creation of a photon, not the "release" of
one. Not all energy has mass, the photon being the perfect example.
Every object has a total energy part of which is due to its mass and
part of which is due to its motion (kinetic energy). Photons get
absorbed by the walls in a dark room.

In future, please note that one
of the groundrules for this site is to ask __single, well-focused__
questions.

**QUESTION: **

Could the comparison of an atom and a solar system exist
with the current understanding of nano science. I.e. do electrons orbit
the nucleus of an atom in relation with a nuclei's weight or mass? Do
the nucleus' of atoms emit light?

**ANSWER: **

No. Gravity is not the force which holds the
electrons in their orbit. It is the electrostatic force (the attraction
between the negatively charged electrons and positively charged
nucleus) which does it. Gravitational forces in an atom are entirely
negligible compared to the electrostatic force. Mass, however, is not
irrelevant, however. The mass of an electron is very small compared to
the mass of the nucleus, so the nucleus, for all intents and purposes,
remains fixed as the electrons orbit. If the mass of an electron and a
proton in a hydrogen atom were equal, the two would orbit about a point
halfway between them, much like a binary star.

Regarding your second question,
yes a nucleus emits "light" but not light you could see. When an atom
emits light it is often within the visible spectrum. The
electromagnetic (called gamma rays) waves emitted from nuclei are much
more energetic and thus of a far shorter wavelength than your eye can
see.

**QUESTION: **

I'm a photographer. I take photos that take advantage of
what I call 'gravitational lensing'. I set up a black rod between the
camera and the subject. If I get just the right 'focus' setting on the
camera I can get the the background and the rods out of focus but the
areas of overlap seem to come into focus. My guess is that, when the
photons travel from the background to the camera they are pulled closer
together by the mass of the rod and therefor they appear in more focus.
The best examples are images #0518a and #0512 at http://www.morgan-anderson.com/artwork/2005Works.html
I've been working with this phenomenon for a couple years and, while I
have a cursory understanding of it, I'd like to know for certain what
I'm doing. So My question is: what is the physics behind this?

**ANSWER: **

Let's first dispense with what the
explanation cannot be. Since the gravitational pull on light is so
incredibly weak, there is no possibility that the mass of the rod can
have any observable effect on light; deflection of light passing close
to the sun, with huge mass, is extremely small and difficult to
observe. For this reason, you should probably not call, even
whimsically, what you are seeing "gravitational lensing" because,
whatever it is, it certainly has nothing to do with gravity. What it
most looks like is diffraction. When you put an obstacle in the way of
light, the light which comes from either side of the object interferes
and results in light and dark fringes. What worries me about this
explanation, however, is that diffraction is usually hard to see except
for monochromatic light and what you see seems to come from the whole
spectrum. So maybe there is some explanation from geometrical optics
(optics which does not depend on the wave nature of light), but I would
need more information to make any further guess: how thick are the
rods, is there more than one of them, where are they relative to the
camera, where is the focus of the camera when you see these effects?
Being a photographer, you should probably take it upon yourself to
learn about diffraction.

**QUESTION: **

I teach Science in Oconee County, Georgia. In class one
day we were discussing the Northern Lights and they are "cosmic
radiation" that is being burned up in our atmosphere at the poles due
to the high concentration of magetism from the earth's magnetic field.
I had two questions, wondering if you guys might be able to help me
answer the questions:

- I wanted to make sure I was correct in the cause for the
northern and southern lights.
- I had a student ask, why we couldn't use large magnets or
even the magnetic north/south pole to stop large scale radiation type
attacks, ie. whether it be a nuclear war, an atomic bomb, or even to
help clean up something like the leak at the Russian nuclear plant?

**ANSWER: **

Referring to northern lights as
"radiation...being burned up" is inaccurate. Here is a brief
explanation: There is a constant stream of electrons and protons which
come from the sun called the "solar wind". (During times of intense
sunspot activity the intensity of these particles increases.) If the
earth did not have a magnetic field, these particles would simply plow
through the earth's atmosphere (ionizing and exciting atoms as they
went) and then hit the ground where they would lose all their energy.
But, because the earth is like a giant bar magnet, these incoming
charged particles get deflected and their tendency, because of the
nature of the magnetic force, is to spiral around the magnetic field
lines toward the poles. Hence, there is a concentration of these
charged particles around the poles (which is why the aurora phenomena
are usually very far north or south) and as they follow the field lines
down, they strike the upper atmosphere. When these energetic particles
hit the air, they ionize (knock off an electron or two) the atoms along
the way and when these ions recombine with electrons, light is
emmitted--hence the "lights" part of the phenomenon. So,
you see, it is not really a case of radiation being "cleaned up" at
all. The cases you refer to are nuclear radiation and there the most
damaging radiation is usually gamma radiation which is very energetic
electromagnetic radiation (like x-rays but even more energetic); since
gamma rays have no electric charge, they are totally unaffected by
magnetic fields.

**QUESTION: **

Does the refractive index of salt solution change with its
concerntration? If yes, what is the best way to determine it?

**ANSWER: **

I can't imagine that it would not vary.
There are numerous ways to measure index of refraction, too many to
enumerate here. Generally, you need to have a setup which allows you to
measure the angle of refraction for a known incident angle and use
Snell's law. Another way to do it is to measure the critical angle of
total internal reflection.

**QUESTION: **

I know that we see the colors of the visible spectrum from
the interaction of the different frequencies of visible light as seen
from our eye and our brain. In other words, there is no intrinsic
"color" property for a specific frequency of light. My question is
this. If our eyes were sensitive to say the ultraviolet region of the
EM spectrum instead of the visible region and the things around in our
environment (i.e. trees, concrete, buildings) reflected and absorbed
the uv light like they do visible light, would our eyes discern
different "colors" for different frequencies within the uv region? In
other words, is there anything special about the visible section of the
spectrum or is it simply that our eyes were made to see this region?

**ANSWER: **

The idea of color is, as I see it, a purely
subjective thing. In fact, how do I even know that what you see as
green is the same as I see as green? The only thing, from a physics
perspective, which matters is that you and I are able to distinguish
between different wavelengths of the spectrum to which our eyes are
sensitive (assuming that neither of us is color blind). Also, it is
necessary from a scientific point of view, that our observations be
repeatable, that is green, once I have learned it, will never look red
to me. Animals have a variety of color sensitivity which you can learn
about on the web by googling "color vision in animals". Insects, which
have an entirely different eye structure from other animals, use
primarily ultraviolet light since the resolution of their eye is
maximized for very short wavelengths. There is no simple answer to your
question since it depends on the detailed structure of your eye (rods,
cones, etc.), but there is no reason why, had our eyes evolved like the
insects to see ultraviolet light, we could not, in principle,
distinguish between different wavelengths of ultraviolet light.

**QUESTION: **

Usually when I get bored, I spin my chair. First I take a
spin with my legs in. When I strech my legs out, the speed decreases,
which is abvious because of the laws of the centrifugal force. The
weird think, though, is when I retract my legs again, the speed
INcreases after it has decreased. I asked my scince teacher about this
conundrum, and her suggestion was that perhaps I retracted my feet fast
enough to give my spin energy enough to spin faster. To me that just
doesn't seem right.

**ANSWER: **

First of all, there is no such thing as "the
laws of the centrifugal force", so though it may be obvious to you that
you slow down, it should not be! What you are experiencing here is
conservation of angular momentum. Angular momentum is the product of
the angular velocity (for example, the number of revolutions per
second) and the moment of inertia the object has relative to the axis
about which it is rotating. Moment of inertia is essentially a measure
of how far away, on average, the mass of the object is from the axis of
rotation. So, when your legs are in your moment of inertia is smaller
than when your legs are out. The angular momentum of an object remains
constant (is conserved) if there are no external torques on the system.
You and the chair spinning can be approximated as having no torque,
although there is some due to friction which will eventually, as you
know, cause your angular momentum to vanish (because you stop
spinning). But, over the short term, your angular momentum stays about
the same, so if you put your legs out your angular velocity must
decrease and if you pull them in, it must increase. This is the same
principle dancers and skaters use to increase their spin rate by
pulling in their arms.

**QUESTION: **

Classical physics texts all have common problems where a
horizontal force acts on a triangular wedge with a rectangular block
(of smaller mass) sitting on the wedge's incline (the net force
accelerates both masses). Some problems have the surface between wedge
& block as frictionless & some don't. However, in all the
problems I've seen, the surface between the wedge & horizontal
surface supporting it are frictionless. Is this done to avoid the so
called 3 body problem, or is there another reason? Just curious.

**ANSWER: **

I am a stickler on the way you state
problems like this, so first let me reprimand (!) you for a conceptual
problem: The force pushes on the block and not the wedge and therefore
the force does not accelerate the wedge, the block (which is touching
it) does. The only thing you must make sure of is that there are not
more unknowns than equations. If you add friction to the table surface,
you have not added an unknown since it is proportional to the normal
force between the wedge and the table. So, if you can do the
frictionless problem you can do the one with friction. It has nothing
to do with the 3-body problem in which you cannot write an analytical
solution to the motion of three bodies mutually interacting via central
forces (like a planet with two moons).

**QUESTION: **

I am trying to find the launch angle required for a ball
to clear the net of a tennis game. For example if I want to perform a
drop shot no matter where I stand in the court, I want to place the
ball so that it lands close to the net at the opposite side while
making sure that it clears the net.
I manage to work out the formula for calculating the initial start
velocity required for the ball to reach the destination but I can't
quite figure out the formula required to clear the net. There is one
in-efficient solution I came up with, that is that I can just check if
it manage to clear the net, and if the ball failed to clear the net I
can increase the launch angle... but there got to be a better solution
for this.

**ANSWER: **

You seem to have too many unknowns as far as
I can figure out what you want to do. Here is what you can do: you can
choose a particular distance from the net, an initial velocity, and an
unknown launch angle, and an initial height from the ground. Then,
stipulating that the ball just clears the net, you should be able to
solve for the angle. You will get two answers: one corresponds to a
fairly low trajectory and one corresponds to a lob. The lob will hit
closer to the net.

**QUESTION: **

In my readings about relativity, much is made of the
equivalence of gravity from a mass, and acceleration due to thrust,
such as a space ship either sitting at sea level on a planet vs. the
same space ship accelerating at the equivalent rate in free space. In
fact, these two situations are supposed to be indistinguishable by
experimenter or experimenters within the space ship.
However, wouldn't they be able to discern which by using two
plumb-bobs, which in the case of being under thrust would be parallel
to each other but at rest on a body of matter, would each point towards
the center of mass of the body, and therefore make an angle
(vanishingly small under realistic conditions, but this is a thought
experiment, after all) to each other?

**ANSWER: **

You are right, you could distinguish between
an accelerating frame and a nonuniform gravitational field, for example
from a planet. The adea you allude to assumes the
gravitational field to which you compare the accelerating frame is
uniform.

**QUESTION: **

Many references define gyroscopic precession as "a
phenomenon occurring in
rotating bodies in which an applied force is manifested 90 degrees
later in
the direction of rotation from where the force was applied." This does
not
jibe with my understanding, which is that gyroscopic precession is the
movement of a rotating body in a gravitational field, where the axel on
the
axis of rotation is secured at one end, and such axel sweeps out a
cone.
If my understanding is correct, what do we call the phenomenon
described
above? My old college physics text describes the phenomenon, and
obviously
mathematically models it (with vector cross-products), but does not
name the
phenomenon.

**ANSWER: **

Remember that Newton's second law for
translational motion may be expressed as force equals the time rate of
change of linear momentum. In rotational physics, the corresponding
statement is torque equals time rate of change of angular momentum.
Imagine a top spinning about an axis through its center of mass and in
empty space. Its angular momentum is along this axis and, since there
are no torques on the top, the spin axis stays fixed (no precession).
For example, the angular momentum of the earth points along the axis
and from south to north poles; the fact that this direction always
points to the north star demonstrates that the angular momentum is
constant (conserved). Now take the top and exert a torque on it (a
spinning top, unless standing straight up, has a torque due to its own
weight). The result, due to Newton's second law is that the angular
momentum vector will not remain constant; the way it changes is to
change its direction, hence precession. This is a simplified
explanation; the top problem is one of the classic problems in
classical mechanics to understand in all its gory detail. I hope this
gives you a better qualitative understanding.

**QUESTION: **

If two rockets of the same weight were placed at the same
height, and one was dropped in free fall and the other launched
horizontally, wouldn't the one dropped hit the ground before the one
flying would? (assume wind resistence is negligible)

**ANSWER: **

Yes, because I presume you mean by
"launched" that its rocket is burning; in principle, it could keep
going horizontally until it ran out of fuel. You are, I think,
confusing this with the situation where it is projected horizontally
but does not have a rocket engine. In this case, both hit the ground
simultaneously.

**QUESTION: **

Is the statement correct: "Today the temperature is 40
degrees Celsius and yesterday it was 20 degrees Celsius so it is twice
as hot today as it was yesterday"

**ANSWER: **

Although "as hot" is a qualitative
statement, physicists would say certainly not. It is the Kelvin
temperature which determines the energy content of something, and the
Kelvin temperature is 273 degrees below the Celcius temperature. Thus
the two temperatures would be 313^{o}K and 293^{o}K.
Maybe you could say that 40^{o}K is twice as hot as 20^{o}K

**QUESTION: **

What is the angular momentum of the spin axis of an atomic
nucleus? I have only heard about this in advanced physics. Is there any
way one could reverse the spin axis of the angular momentum of an atom?

**ANSWER: **

The angular momentum of a nucleus is the sum of the
angular momenta of its components. Each proton and each neutron has a
spin (always 1/2 in appropriate units) and an angular momentum due to
its orbital motion (always some integer in appropriate units); for each
particle, its total angular momentum is the sum of these (always a half
odd integer, *i.e.* 1/2, 3/2, 5/2...) If the nucleus has an even
number of protons and of neutrons, the ground state angular momentum is
always zero because it is energetically favorable for pairs to sum up
to zero angular momentum. Only nuclei with odd numbers of particles or
with an odd number of protons and neutrons have ground state angular
momenta. The total angular momentum of a nucleus is usually referred to
as its spin. To "reverse" the spin, you just need to flip the direction
of the spin vector. So you should think of taking a spinning object and
pointing its spin axis in the opposite direction, not stopping and
reversing it; the effect is the same.

**QUESTION: **

Does everything in the universe rotate in the same
direction?

**ANSWER: **

No. However, most things in the solar system
do; if viewed from the north star, most objects in the solar system
rotate counterclockwise.

**QUESTION: **

Lets say you had two rocket ships docked at a space
station. They decided to leave the space station at the exact same time
in completely opposite directions at 99% the speed of light. Both
rockets traveled for one year (relative to the rockets time) and then
at the exact same time reversed their directions and went back to the
space station. The space station has now "aged"... thousands of years
from when they left. Have the two rockets aged at the same rate? Would
they each only be two years older compared to each other then when they
left? Would the same apply if they traveled next to each or
perpendicular to each others direction? How does special relativity (I
think that is what it's called) effect these ships since you cannot say
that one ship is moving 198% the speed of light compared to another
ship which may be concided stationary.

**ANSWER: **

I have earlier answered just about
the same question.

**QUESTION: **

"energy is matter, and matter is energy"
Is this statement true?

**ANSWER: **

Matter is, indeed, a form of energy. This is
the famous *E=mc*^{2} relation of special relativity. I
do not think most physicists would say that energy is a form of matter,
however. That would sort of be like saying "horses are animals and
animals are horses"!

**QUESTION: **

Determine the distance to which the painter of weight "w"
can climb without causing the ladder to slip at its lower end. The top
of the 15kg ladder has a small roller and at the bottom of the ladder
the coefficinet of static friction is 0.25. The ladder is 1.5m away
from the bottom of the side wall.
I have drawn the free body diagram and realise that we need to be in
equilibrium, my problem is the last step, How do I use this information
to find the weight of the painter and how far from the wall it is?

**ANSWER: **

Although you do not specify it, I presume that you know
the length of the ladder. Your solution should have three equations:
one from setting the sum of the torques to zero and two from setting
the sum of the forces (x and y components) to zero. Thus you may find
three unknowns. You do not know the weight, the position of the
painter, the normal forces of the wall and floor on the ladder; the
frictional force by the floor, may be espressed in terms of the others
since *f=mN*_{floor}.
Seems to me that you have 4 unknowns and therefore cannot solve the
problem.

**QUESTION: **

can thermal expansion be stopped

**ANSWER: **

Of course, you just have to push on the
ends. This is analogous to containing a gas in a tin can and heat it
up; it wants to expand but cannot because the volume is constrained so
the pressure increases instead.

**QUESTION: **

I know that when I look at a flourescent bulb through a
diffraction grating, I see emission lines, but why, when I look at a
hot wire filament type bulb through a diffraction grating, do I not see
the absorbtion lines of our own atmosphere between the wire and the
grating? Why do I see a complete spectrum?

**ANSWER: **

Absorbtion is a relatively low probablilty
event and there is not enough air between you and the light bulb to
cause enough absorbtion to be seen.

**QUESTION: **

I was looking recently at old photos of the Space Shuttle
in orbit. In one particular photo, an astronaut is outside the
shuttle--untethered and over 300 feet from solid footing. He is, of
course, equiped with his jet pack (an EMU or something like that), but
my question is this: how, once the astronaut has exited the shuttle,
does he remain at the same speed as the shuttle is going? Let me
clarify....
The shuttle is going 17,000 mph or so in orbit, as anyone sitting
inside is also...what makes a person who leaves the shuttle while it is
in orbit stay in orbit along with the shuttle, despite having drifted
300 feet or so away from the departure point? The caption along with
the picture described the astronaut as a "literal human satalite." Why
doesn't the shuttle speed away from the man once he leaves?

**ANSWER: **

The only thing which determines the speed is the orbit in
which the satellite moves. When the astronaut originally leaves the
shuttle, he has the same orbit and moves with the same speed. But if he
does something which moves him 300 feet away (for example, 300 feet
farther away from the surface of the earth) he will now have a
different orbit and a different speed. However, his percentage change
in orbit radius is so incredibly small that the speed difference will
be incredibly small also. In principle, if you wait a long time the two
will get farther and farther apart.

**QUESTION: **

this is technically a "homework" question, but i disagree
with the answer given in the textbook--hopefully you can tell me why
their answer is valid. (or not)
"an electron travelling at 0.25c and of rest mass 9.11*10^{-31}
kg collides head on with a positron with the same mass but travelling
at 0.5c. when matter and antimatter meet in this way they anihilate
eachother to produce energy, how much energy is released" the answers
to the textbook just use E=mc^{2}, with the rest masses of the
particles eg:
E=2*9.11*10^{-31}*(3*10^{8})^{2}
E=1.64*10^{-12} J
However it seems illogical to me that the velocity of the particles
(significant fractions of the speed of light) doesent influece the
energy output. My initial reaction is that the relativistic mass (Mv)
should be used instead.

**ANSWER: **

I would tend to agree with you that you
should include the kinetic energy of the two particles in the total
energy released. Thus, E=9.11x10^{-31}x[(1-.25^{2})^{-1/2}+(1-.5^{2})^{-1/2}]x(3x10^{8})^{2}=1.79x10^{-13}
J. Then, for example, if the annihilation resulted in two photons (the
most common), their energy would sum to 1.79x10^{-13} J, not
1.64x10^{-13} J as the book has it (there must be an error of a
factor of 10 in your answer above).

**QUESTION: **

im a senior citizen who completed a short senior course on
physics so maybe this is stupid.

l. is a photon also an electron?

2. does an electron ever break down into another particle and are all
electrons charged?

**ANSWER: **

1. No. A photon is light, it has no mass and
no electric charge; an electron has both.

2. No, an electron is a stable particle. It is possible to collide
electrons with other particles and create new particles which do not
include any electrons.

**QUESTION: **

Is it true (as people say) that if you are out-of-doors
and trying to talk to a large group of people (e.g. a class of
students) that you should stand upwind of your listeners so that the
wind will carry the sound toward them rather than away? In other words,
in a moderately windy environment, does the direction of the wind have
an effect on how the sound travels through air?

1. I understand the Dopler effect, but that refers to a moving sound
source. My question is a about a stationary source and receiver.

2. For the sake of this question, let's *not* factor in that the
apparent sound of the wind changes when a person turns toward or away
from the wind source. That may have more to do with the shape of the
listeners ears. I am interested in the behavior of sound waves.

**ANSWER: **

The doppler effect refers to either a moving source __or__
a moving observer (the fomulas are different, but the qualitative
effects are the same). A wind is equivalent to a moving observer. If
you stand upwind of the receiver, the sound will be doppler shifted to
a lower frequency; downward to a higher frequency. But the intensity
will be unchanged. If you think of your sound as being directed at a
particular observer (like, for example a flashlight beam if it were
light), then you could get in trouble if you had a crosswind which
would result in the sound aimed at the observer missing him.

**QUESTION: **

Is is possible for something, a particle perhaps, to have
mass but no volume? Matter is defined as anything that has mass and
volume. But, is there anything that exists as a mass without volume?
Much Mahalo for your help,

**ANSWER: **

Yes, such a thing is called a "point mass"
or a "singularity". Black holes are thought to be singularities as are
electrons.

**QUESTION: **

I may be wrong, but it seems to me that a freezer full of
cold food is colder than the same freezer att he same temperature but
filled with air. Is one actually a few degrees colder than the other?

**ANSWER: **

"Colder" and "at the same temperature" are
contradictory. Colder means at a lower temperature.

**QUESTION: **

Would it be possible to engineer an antenna which could
radiate extremely short pulses of only 1 period ? (e.g. for a 1GHz
frequency, the pulse would last only 1 nanosecond )
Would it be possible to radiate a period and a half ? (e.g. for a 1 GHz
frequency, the pulse would last 1.5 nanoseconds )

**ANSWER: **

It is possible but the engineering is not
really the antenna but the electronics to generate the pulse. However,
is you take exactly one period of 1 GHz sine wave, what you are left
with is something which does not have a single well-defined frequency
but is rather made up of all frequencies with 1 GHz being the maximum
of the distribution. This is a classic example application of Fourier
analysis of waves. This kind of "chopping" is routinely done with
ultrashort laser pulses.

**QUESTION: **

Gravity and free fall. This is driving me crazy. Is the
moon really in free-fall? How does this relate to the notion that the
moon's "desire" to go straight is acted on by the earth's gravity and
results in an ellipse? And astronauts – are they really in free fall,
or just some metaphorical free-fall? Why don't the moon and astronauts
just..you know..fall? I keep reading websites on this, but I am still
confused.

**ANSWER: **

Is a stone which you throw horizonatlly in
free fall (neglecting air friction)? It is because anything which is
moving only under the influence of gravity is said to be in free fall.
Imagine your throwing the stone faster and faster; it will go farther
and farther until finally it goes all the way around the world and hits
you in the back! This is a satellite. (This is not my idea, but rather
was devised by Newton to understand the motion of satellites. Try it
yourself at
http://galileo.phys.virginia.edu/classes/109N/more_stuff/Applets/newt/newtmtn.html

**QUESTION: **

Imagine a man pushing a 10 kg cart horizontally across a
frictionless plane, accelerating it from 0 m/s to 20 m/s in 10 s. What
are the forces acting on the cart? I understand that there's F, the
man's push, and W, the cart's weight. What should F be? Is it just
simply: A) F = ma = (10 kg)(20 m/s - 0 m/s)/10 s = 20 N or B) F = ma +
W = (10 kg)(20 m/s - 0 m/s)/10 s + (10 kg)(9.8 m/s/s)= 20 N + 98 N =
118 N? Shouldn't W be simply neglected because it is perpendicular to
the direction of the object? Is the resistance the man feels when he
pushes simply the inertial mass, or inertial mass plus weight? (I know
you cannot add mass and force but well...)
If W isn't neglected, shouldn't the object dig diagonally into the
surface, by the usual addition of vectors?

**ANSWER: **

Your answer (A) is the right one. Your
reasoning is correct that this force is not in the direction of the
acceleration. What you have not noted is that the plane exerts an
upward force on the cart which is (for this problem) equal to the
weight so that the net force in the vertical direction is zero as it
must be since there is no acceleration in the vertical direction.
Weight is a force (which the earth exerts on a mass) and mass is mass,
so it is the inertial mass which is the *m* in *F=ma*.

**QUESTION: **

I was just wondering why when you rub two items together
(like your hand on carpet for example) heat is generated? Where does
that energy come from?

**ANSWER: **

It comes from you. When you cause the two
surfaces to move against each other you do work (a force acting over a
distance) and work adds energy to a system, in this case heat energy.

**QUESTION: **

A recent experiment which involved converting energy into
matter was accomplished at S.L.A.C. (short for Stanford Linear
Accelerator Center). But while converting matter into energy is an easy
feat, converting energy into matter is not so simple. Furthermore,
whenever matter is being converted into energy, some of it is
inevitably lost due to the second law of thermodynamics. However, you
could compensate by disintegrating some rocks and adding in that energy
too.

In Star Trek, the way the
transporter works is by separating crew members at the atomic level and
converting them into energy. Once they arrive at the appointed
destination, the process is reverse. Granted, Star Trek is just a tv
show, but let's say for the sake of argument that the transporter
operates by converting people into energy and vice-versa.

1) In order to convert a person
into energy, wouldn't that mean burning up that individual?

2) Would the person survive the
procedure, or would the individual ceased to exist and be replaced with
a replica, who was literally born into existence once the energy was
reconverted back into matter with the information? (Note: I know this
question sounds a bit philosophical but I'd be very interested in your
opinion anyway.)

**ANSWER: **

Several comments on your question.

- The second law does not allow energy conservation to be
violated.
- It is not really hard to convert energy into mass. If you
take a CO
_{2} molecule and pull it apart (adding energy by
doing work) it gets heavier; however, the amount of mass you make is
too small to measure because chemistry is a crummy way to get or store
energy. However, if you take the nucleus of an atom, say iron, and pull
apart all the protons and neutrons in it, it will get measurably
heavier.
- What is tough is to convert energy purely into mass. An
example of where this does happen is when a photon spontaneously
creates an electron positron pair. This may be made to happen provided
the photon has sufficient energy and it passes through a strong
electric field (
*e.g*. near some nucleus).
- In your star trek question, "burning up" is not turning the
person into pure energy, rather it is like the inverse of the CO
_{2}
example above. Carbon in the person combines with oxygen in the air to
make CO_{2} thereby releasing some energy, but all the carbon
and oxygen atoms are still there.
- Your question #2 is too far out to be physics, particularly
since there is no such thing as "beam me up Scotty".

**QUESTION: **

Hi. I've heard that particles (light, for instance) can be
sped up to speeds much higher than the normally travel at. Could a
similar process be used to accelerate the movement of radio waves?

**ANSWER: **

Particles may be accelerated to any velocity
slower than the speed of light* c* (assuming that you have the
energy to do it) but electromagnetic waves (including both light and
radio waves) travel through empty space move with a speed of c, no
faster, no slower.

**QUESTION: **

WHY COULDN'T INERTIA OR MOMENTUM BE CONSIDERED AS AN ETHER
WAKE? IF AN OBJECT GAINS MASS AS IT ACCERATES WHAT IS THIS MASS, WHERE
DOES IT COME FROM IF NOT SOME CONCEPT OF ETHER?

**ANSWER: **

I have no idea why you invoke the ether to explain mass
increase, particularly since it is generally acknowledged that there is
no such thing. Here is the orignin of "mass increase". If one defines
linear momentum as (rest) mass time velocity like we do in classical
physics, we find that the total linear momentum of an isolated system
is not conserved. this is a very bad situation from the perspective of
mechanics since the notion of a force is useless and the valuable ideas
of energy have no validity. However, if we redifine the linear momentum
as the quantity [1-(v^{2}/*c*^{2})]^{-1/2}
times mass times velocity, both the linear momentum of an isolated
system and its energy are conserved. So, you need not ever say that
mass increases, it is just that momentum must be redefined to be
useful. Many people choose to say that *m* is redefined and
momentum isn't (still mass times velocity but a new kind of mass), but
that is a point of view, not some kind of law.

**QUESTION: **

A recently published book on baseball pitching claims that
an arm/hand assembly travelling at 31 mph will allow for a ball to be
released at 95 mph. The author's contention is that, because of the law
of conservation of momentum, the larger mass of the arm travelling at
31 mph will transfer momentum to the smaller mass of the ball, thus
causing it to accelerate to 95 mph in order to satisfy that law.
It is my contention that there can be no transfer of momentum unless
there is a sudden decrease in velocity of the carrier due to an
external force being applied, thus allowing the carrier to "give up"
it's momentum to the unconstrained object (the ball).
I proposed this question. What event has occurred from a point 1
millionth of a second prior to ball release and a second point 1
millionth of a second after release that causes momentum to be
transferred?
The masses of the arm and ball have not changed. Therefore, the only
variable in the momentum equation to change is velocity. If the
velocity is reduced by internal means, muscular relaxation, the
momentum will be not be transferred to the ball but dissipated within
the body. There is no external force, like a brick wall to stop the
arm, therefore there can be no transfer of momentum to the ball.
Am I correct here? Any help would be greatly appreciated.

**ANSWER: **

I feel quite certain that the speed of the
part of the "arm/hand assembly" (as you call it) which is in contact
with the ball is moving with the same speed as the ball when it is
released. It is totally fallacious to talk about the speed of the
"arm/hand assembly" because each part is moving with a different speed:

- the shoulder has a small speed due to motion forward of the
body
- the elbow has a speed which is the vector sum of the
velocity of the shoulder and the velocity of the elbow due to its
rotation about the shoulder
- the wrist has a speed which is the vector sum of the
velocity of the elbow and the velocity of the wrist due to its rotation
about the elbow
- the hand (and ball) has a speed which is the vector
sum of the velocity of the wrist and the velocity of the hand due to
its rotation about the wrist

So, you see, it is not so
simple.

**QUESTION: **

Studies over the years seem to indicate that lightspeed is
slowing down. If so, is it because photon emmisions are somehow
calibrated with the quanta about stable matter and is a result of those
particles being in a state of deceleration?

**ANSWER: **

I think that this is quite speculative and
not at all verified experimentally. Since the speed of light is what
physicists call a "fundamental constant", the question is an important
one in physics and philosophy since by definition, a constant cannot
change. At this point, trying to understand why a constant of nature
might change is perhaps premature.

**QUESTION: **

Why is the speed of light given by 1/sqrt(permittivity
*permeabillity)? What is the great mistery behind such a simple
relation?
How these two parameters combine to give the speed of light?
Why does the vacuum (nothing...) has physical properties such as
permittivity and permeability?

**ANSWER: **

This is the great triumph