Miscellaneous



With the recent publication of PHYSICS IS... there are now three Ask the Physicist books! Click on the book images below for information on the content of the books and for information on ordering.


QUESTION:
If the earth is curved how is it you can get a laser to hit a target at same height at sea level more then 8 km away? How is it that it's bent around the earth?

ANSWER:
First of all, light is not bent around the earth; it travels in a perfectly straight line and therefore, because the earth is curved, there is a maximum distance away for a target at the same altitude. What that distance is depends on the altitude of the laser. You say that the laser is exactly at sea level by which I presume you mean the surface of the earth; at this altitude you could not hit any target also at sea level. In the figure I have drawn the earth, radius R, a point a distance h above the earth's surface (laser location), and another point a distance h above the earth's surface (target location). The distance between them is 2d. Focus your attention on one of the triangles with hypotenuse (R+h).
From the Pythagorean theorem, d=√[(R+h)2-R2]=√[2Rh+h2]; if h<<R, d≈√(2Rh). For example, if h=10 km, about the height a commercial jet flies, 2d≈714 km is the most distant target at the same altitude which you could hit.


QUESTION:
I have always wondered how much energy do you do with if you let a kettle at 1800 W be running for two minutes? What is the approximate cost for this? this is not a homework question.. just a question i wonder =)

ANSWER:
A Watt is one Joule per second, 1 W=1 J/s. Energy consumed by an 1800 W kettle in 2 min is 1800x120=216,000 J. But, we are more used to measuring electrical energy in kilowatt hours, (1 kW
·hr)(1000 W/1 kW)(3600 s/1 hr)=360,000 J. So the energy used by the kettle is (216,000 J)/(360,000 J/kW·hr)=0.6 kW·hr. A kW·hr costs on the order of 5¢-15¢, so the cost would be between 3¢ and 9¢.


QUESTION:
This is odd, but My family has just moved into a huge house with little outdoor space. We live in a climate that is cold in the winter, and I want my children to get some exercise on a daily basis. We own a trampoline, and have space for it indoors on the Second floor of our house. The ceilings are 12 feet high, so there would be no problem with the kids hitting their heads on the ceiling. My question is whether or not the house would stand up to the force generated by the trampoline. The walls of the house are made of concrete (you can't nail into it.) I am assuming the floors are quite solid as well, as they must support the weight of the house. They are concrete as well. My Youngest child is quite large (6 ft, 260 lbs)--he is only twelve. We need the activity.

ANSWER:
First, a disclaimer: I can give you an idea of how much force the floor will experience. I cannot predict whether this will cause your floor to fail because I have no information about your floor other than that it might be concrete. I have watched some videos and it seems that the jumper never goes as high as h=2 m and the trampoline never goes down as far as s=1 m. So I will just do my calculations with those to get an upper limit on what force might be expected. Your son's mass is about m=120 kg. An object falling from h=2 m will hit the trampoline with a speed of about v=
√(2gh)≈√(2x10x2)=6.3 m/s. I will treat the trampoline as a simple spring so that I can write ½mv2ks2-mgs where k is the spring constant. Putting in m, v, and s and solving for k I find k=7200 N/m; since the force exerted by a spring is F=ks, the largest force the trampoline exerts on your son is about 7200 N=1600 lb; Newton's third law tells you that this is also the force your son exerts down on the trampoline. Therefore, the trampoline exerts a force down on the floor of 1600+W where W is the weight of the trampoline. This is a little more than the weight of a grand piano.Keep in mind that this is the greatest force and just for an instant; the average force over the collision time would be half this. This is a little more than the weight of a grand piano.


QUESTION:
hi, can and are earthquakes be caused by celestial alignments ie planets?

ANSWER:
Let's take a simple example. As seen from earth, Mars and Jupiter are aligned. I estimated the force on a 1 kg object which is sitting, let's say, on the San Andreas fault: F=3x10-11 N; the weight of that 1 kg object is about 10 N. I would say that putting a 1 kg object on the ground is a great deal more likely to cause an earthquake than those planets, wouldn't you?


QUESTION:
So there's a powerline outside my bedroom window, and I thought, huh. Turns out I'm sleeping with my head in a 6mG AC magnetic field (according to two meters). Help me use physics to stop caring. How do I estimate/calculate which puts more force on the charged particles (calcium, potassium, sodium) in my brain: a) An aqueous solution at 98.6 degrees Fahrenheit or b) a magnetic field acting on charged particles moving at some estimated speed in said aqueous solution. My hope here is that the force of (b) is like an order of magnitude or two, or something, below the "noise floor" of (a) and then I can stop caring forever.

ANSWER:
How about this: the earth's magnetic field is about 0.6 G, two orders of magnitude bigger than the field due to the power line, and you are exposed to it 24 hours a day. It is also possible that there is some other source of field closer by than the power line which, though a much smaller current, would produce a much bigger field. For example, if there were a wire in the wall carrying a typical household current of 1 A, the field 2 m away would be 1 mG. There is no good scientific evidence that any magnetic fields you are likely to encounter have any effect, good or bad, on the functioning of your body.


QUESTION:
Several years ago, I was caught in a massive windstorm in a skyscraper. I was on the 54th floor (approx. 756 feet from street level, full building height is 909 feet) , pulling cable, and I stopped for a break. I left a cable pulling string hanging from the ceiling (48 inches free hanging length) in the office, with a 1/4 lb weight attached, and when the storm hit, the weight began swinging like a pendulum. The arc was 16 inches (eyeballing it), and traversing the length of the arc took about 1 second. How can I calculate how far (full arc) the skyscraper was moving by observing what the pendulum in the building was doing?

ANSWER:
A 48" pendulum has a period of about 2.2 s, the time to swing over the arc and back. Since you were estimating, the pendulum was swinging with about the period it would if the building were not moving at all. I would conclude that either the pendulum got swinging somehow and the building was not perceptibly moving or that the period of the building's motion was about the same. If the building was swinging with a period significantly different from 2 s, the pendulum would be swinging with that same period; that is called a driven oscillator.


QUESTION:
How strong is 0.01 newton meters of torque? I want to build a motorized camera slider that will pull a Canon 5d mk 2 up a 45 degree slope. It weighs 1.5 kg. How much torque do I need? T
his is the motor I am thinking of buying:
Rated power 0.01 W
Rated speed:20 rpm
Rated torque:0.01 N·m

ANSWER:
I will work it out in general and then we will see if this motor can do the job. There are some things you have not told me, in particular the speed v you want the camera to move on the slope and the nature of how the camera moves on the surface (in particular coefficient of friction
μ). But the general solution will have those in there and you can calculate with them. You will want to attach a spool of some sort the the drive shaft of the motor to act as a reel to pull up the string attached to the camera, say its radius is R. The angular velocity of this motor is ω=20 rpmx(2π rad/1 rev)x(1 min/60 s)=2.1 s-1. The weight of the camera is mg=(1.5 kg)x(9.8 m/s2)=14.7 N. The angle of the incline is stipulated to be 450. The force necessary to pull the camera up the ramp with constant speed may be shown to be F=mg(1+μ)/√2; since the torque τ is the known quantity, FR=τ=mgR(1+μ)/√2. In order for the camera to move at speed v, the radius of the spool should be R=v/ω. If the speed of the camera is v and the force is F, the power being generated in the motor is P=Fv=mgv(1+μ)/√2. Let's do an example. Suppose you want the camera to move with a speed of v=1 cm/s=0.01 m/s and the friction is negligible, μ≈0. Then the spool has a radius R=0.01/2.1=0.0048 m=0.48 cm; the required torque would be τ=0.0048x14.7/√2=0.05 N·m; the required power would be P=14.7x0.01/√2=0.1 W. I am afraid that your proposed motor is inadequate.


QUESTION:
Unlike a submarine traveling in a horizontal line at 5 fathoms compared to 50 fathoms (the pressure in the vertical direction would be the same....) But in a vertical line I imagine from 50 fathoms it would rise slower in the first 5 fathoms than it would in its final 5 fathoms.... I.e in its first 5 fathoms of accent it had the external pressure of 50 fathoms descending (dropping to 49 fathoms pressure then 48 etc) compared to 5 fathoms pressure descending to 0 fathoms pressure as it ascends. Is this correct....

ANSWER:
As long as the water is considered incompressible (which it is for all intents and purposes), the net force on the submarine due to water pressure (called the buoyant force) is the same at every depth. Even though the pressure in the water is enormously bigger at great depths, the pressure difference between bottom and top of the submarine is the same. Therefore, if drag forces are neglected there will be a net force up on the submarine which is constant and equal to the buoyant force minus the weight of the submarine. However, the drag force is not negligible and is approximately proportional to the speed. So as the rising submarine speeds up the drag force down becomes bigger and bigger until it is eventually equal to the buoyant force minus the weight; hence the net force is zero and from that depth up to the surface the speed is constant. You might also be interested in a related earlier question about submarines.


QUESTION:
If you took two 1000 mile long metal bars, laid one horizontally on the ground and stood the other vertically, would they weight the same and if not, why?

ANSWER:
By weight we mean the force of attraction between the earth and the object. Therefore, they would not weigh the same because the vertical bar has most of its mass farther from the center of the earth than the horizontal rod does. The weight of a point mass on the surface of the earth is W1=mMG/R2 where M is the mass of the earth, R is the radius of the earth, G is the universal gravitational constant, and m is the mass of the point mass. This is usually written as W1=mg. But, if the point mass is a distance H above the surface, its weight is smaller, W2=mMG/(R+H)2=mg/(1+(H/R))2. If you know integral calculus it is not hard to show that the weight of a vertical uniform bar of length L and mass m is W3=mg/(1+(L/R)). In your example L=1000 mi is not small compared to R
≈4000 mi, so W3=mg/(1.25)=0.8W1. But, because L is so large, your horizontal bar does not have a weight of mg either unless it bends to conform with the curved surface of the earth. But, you can see from the figure that the distances from the center of the earth are much smaller than for the vertical bar, so it will surely have a larger weight, just not quite as big as mg.

ADDED THOUGHT:
Actually, even if the bar conformed to the surface of the earth, it would weigh less than mg because the components along the length of the bar of the forces on each piece of the rod would all cancel out. I think I will not calculate the exact answer for the horizontal bar, just say that is slightly smaller than mg.


QUESTION:
according to the formula of variation of g above the surface of earth g' = g(1+2h/R) and the radius of earth is 6400 km .If we put R/2=3200 in the previous formula,did it mean that after 3200 km space start ?

ANSWER:
First, let's see where your "formula" comes from. The acceleration due to gravity g may be written as g=MG/R2 where M is the mass of the earth, G is the gravitational constant, and R is the radius of the earth. For some height h above the earth, g'=MG/(R+h)2
. Therefore g'/g=R2/(R+h)2=(1+(h/R))-2. This is an exact expression and you can see that g' never becomes exactly zero but continues decreasing forever as h gets larger. (Note that your "formula" cannot be correct because g' gets bigger as h increases.) However, for many applications you want to know what g' is if h/R is very small; one can do a binomial expansion of g'/g, g'/g=(1+(h/R))-2≈1+(-2)(h/R)+…=1-2h/R. So your formula was almost right, just need to change the + to -. But this is only an approximation and will fail when h gets too big. The graph above compares the exact (black) and approximate solutions (red); as you can see, the approximation only works up to about 0.1R. The fact that the approximation goes to zero at h=R/2 has no meaning.


QUESTION:
Is a board suspended between two points and evenly weighted across it's length (by books, for instance), less likely to bend if the ends are clamped or nailed so they don't move? This is in contrast to if the ends simply rest on end supports.

ANSWER:
Yes. Keep in mind, though, that the board will be exerting a horizontal force on the support. Be sure the end supports are strongly attached to the walls.

FOLLOWUP QUESTION:
If the end points are dado slots (the boards are shelves for media storage), and the shelves and dados are cut so that the shelves fit the dado slots very precisely on all three sides, then horizontal travel and twisting could be eliminated, which would obviate the need to attach to the wall. Correct?

ANSWER:
For the board to bend, the ends are pulled toward the center and lifted up (see figure). I would anchor the ends.
 

FOLLOWUP QUESTION:
One more question though, and a more challenging one I hope. If one wanted to screw a square block of wood to a wall, where would the optimal places be to put the screws? Assume that the block of wood is 12" on a side, two edges are parallel to the floor and only two screws are used. The wood will be weight-bearing and the weight will be evenly distributed along the top edge of the block. Also, assume that the thickness of the wood is small relative to the other dimensions and that the screws can find equal purchase in the wall in back of the block of wood being fastened. My gut tells me that (a) the screws both should be put along a horizontal line parallel to the floor, and, (b) it doesn't matter where that line is, high or low, since the weight is evenly distributed. What I can't intuit, is if it's better to have the screws be 3" or 4" or some other distance from a vertical side, as long as they are symmetrically placed. In the general case, if N randomly placed screws are used, what is the math that tells me what percentage of the weight each screw bears according to its geometric placement?

ANSWER:
I really do not think it is worth worrying about. The reason is that it, paradoxically, is likely not the screws which keep the block from falling, it is the static friction between the wall and the block; the function of the screws is more to press the block against the wall than to hold up the weight. Therefore, regardless of where you put the screws, tighten them as tight as you can get them since the amount of frictional force you can get depends on the normal force, the force pressing the wall and block together.


QUESTION:
I have measured the thickness of steel pipes with a thickness meter (pocketmike) with a sound velocity of 5813 m/s. No I need to change my thickness values with a sound velocity of 5920 m/s. This because this value is more accurate for this steel pipes I measured... Which formula I need to use?

ANSWER:
I would assume that the device measures a time. In that case, the thickness T would be proportional to the product of the velocity v and the time t, T=cvt where c is some constant. So, if you change v to v' but keep t (measured) constant, the corrected thickness T' will be T'=cv't. Take the ratio of the two equations and solve for the thickness: T'=T(v/v')=(5813/5920)T=0.982T.


QUESTION:
What ideas are the basis of the special theory of relativity and what conservation laws does it preserve? This isn't from homework, but a class discussion that I didnt understand

ANSWER:
This could be called an unfocused question, but the answer is pretty brief so I will carry on. Most textbooks will tell you that you need to postulate that the laws of physics are the same in all inertial frames of reference and accept that the speed of light (electromagnetic radiation) is independent of the motion of the observer or of the source. My take on this is that only the first postulate is needed because Maxwell's equations are laws of physics and they predict that the speed of light depends only on two physical constants, not on the motion of the source or observer. All important conservation laws
—energy, linear momentum, angular momentum—are preserved but only if changes to the definition of these quantities are changed. E.g., kinetic energy is no longer ½mv2 and linear momentum is no longer mv; the new quantities, however, are approximately their classical values if the velocity is very small compared to the speed of light.


QUESTION:
This came up in a discussion about the use electro-magnetic rails guns whose power is contained in the speed of a given mass when it slams into a stationary object as there is no explosive material involved, the energy produces is converting the kinetic energy of the projectile into heat on impact.

  1. How much energy is contained in every stationary object on earth due to the rotation speed of the earth? I understand this this is only Potential energy and would require the object to be shielded from the earth's gravitational pull in order to release it but if a steel block weighing 100 kg were to no longer be held by gravity how much potential energy would it contain as it was flung from the earth rotational spin.

  2. Also, once released from the earth's gravitational attraction, would you also need to factor in the speed of the earth's rotation around the sun to the calculations? The mass was travelling in two different directions (planetary rotational and orbital rotational) at extremely high speeds before the gravitational ties were cut?

  3. And as a final factor, while trying to calculate this someone pointed out that the starting 100 kg piece of mass would instantly become a 0.KG piece of mass once it was no longer had any weight with respect to the Earth.

  4. At that point, we pretty much tossed in the towel. But, still feel that because we started with a 100 kg item that became weightless, that would not remove the potential energy it contained before gravity released it. If afterward it were to crash into the moon or some other object in its path, wouldn't the amount of destruction still be equal to the energy it contained when it was "fired from the planet" much as a bullet fired from a gun?

ANSWER:
You have many misconceptions, so I have edited your question(s) by itemizing the parts of your question. I will answer by parts.

  1. The most important misconception should be dealt with first. Energy is something which depends on your frame of reference. If a mass is on the surface of the earth it has zero kinetic energy if you are also on the surface of the earth. If you view that same mass from a frame moving along with the earth in its orbit but not rotating like the earth is, it has the kinetic energy you envision, that due to the earth's rotation. Kinetic energy is given by Kmv2 where m is the mass and v is the velocity you see it to have. The speed v of an object on the earth's surface depends on the latitude λ, v=Rωcos(λ) where R=6.4x106 m/s and ω=7.3x10-5 s-1 is the angular velocity of the earth. Let's just look at the equator where v is largest, v=Rω=6.4x106x7.3x10-5=470 m/s=1050 mph; you should note that this is not really that large. The kinetic energy of 100 kg flung into space with this speed is K=½x100x4702=1.1x107 J.

  2. By now you should appreciate that it depends on who is looking at your projectile. Someone who is at rest relative to the sun would need to calculate the speed and therefore add in the velocity of the earth around the sun, call it V. But, this would get complicated because it would depend on time of day the projectile was launched. If you are standing right on the orbit and the earth is coming toward you, the speed would be V+v an noon and V-v at midnight; at other times it would be somewhere between these two extremes.

  3. You have this all wrong. Weight is the gravitational force which the earth exerts on the mass; the weight does not "instantly" become zero when it is launched, it gradually decreases as it gets farther away from earth. But, that is beside the point because the kinetic energy depends on the mass, not the weight, and the mass stays the same regardless of whether there is any gravity or not.

  4. Whenever the projectile stikes something, like the moon in your question, all that matters is what its velocity is with respect to the moon.


QUESTION:
Due to the ideal gas law/approximation the speed of sound does not change with altitude or barometric pressure. Yet ask any long range shooter and they will tell you, from practical experience, that the lower the barometric pressure or the higher the altitude, the less drag there is on the bullet and therefore the bullet takes longer to slow resulting in less time for gravity to affect the bullet leading to less "drop" for the bullet over long ranges. Why then doesn't the ideal gas law apply to bullet trajectory?

ANSWER:
I do not know about the speed of sound, but I would certainly not assume that anything about sound could be applied to bullets. The drag force Fd of a bullet of speed v in air is well represented by Fd=
½Cρv2 where ρ is the density of the air and C is a constant determined only by the geometry of the bullet. As the density of the air gets smaller, the drag on a bullet gets smaller, in accord with your experience. There is really no need to invoke the ideal gas law at all, but if you want to connect density to the ideal gas law, PV=NRT, note that the density will be proportional to N/V, so ρP/T. For constant temperature, density is proportional to pressure—the lower the pressure, the lower the drag.


QUESTION:
Would it be possible for an 'average' human to throw a 500 g weight 40 ft but with only a 2 ft high corridor of travel without the projectile touching any of the corridor's sides? This isn't homework, it's a really ridiculous question that we can't physically try at work! We work in a theatre that has two people positioned 40 ft apart and roughly 30 ft up in the air near the ceiling. Ages ago someone said that they could throw a spanner from one person to the other person. Some people agreed, some said that it wasn't possible due to the arc needed. This question comes up every few months and I just wondered if you might have an answer.

ANSWER:
So the problem is, with what speed would you need to throw the spanner in order that it reach a maximum height of 2 ft above its starting height when it has gone 20 ft? This is a straightforward kinematics problem. You are probably not interested in the details, so I will just give you the final result. The necessary speed would be 57.7 ft/s=39.4 mph. A major league baseball pitcher can throw a fastball with a speed of around 100 mph, so there is probably somebody in your theater company who could throw the spanner with the necessary speed, but I would not want a 1.1 lb wrench coming at me with a speed of nearly 40 mph!


QUESTION:
In some of the more realistic space combat science fiction there is a concept called a 'BFR' (Big Fast Rock) which, mined from a dead world or asteroid, melted to molten and then reformed to a near-perfect density distribution with collars of ferrous metal impressed in it, is shot at some fraction of light speed from a large EML cannon running down the long axis of mile long ships. I would like to know how to calculate the impact force release for a 2,000 lb BFR moving at .10, .15 and .30 C. I'm assuming it's going to be in the high Megaton range and I don't know what the translative math per ton equivalence in TNT.

ANSWER:
What you want is the energy your projectile has when it hits. The energy in Joules is E=mγc2 where γ=
√(1-(v/c)2). In your case, 2000 lb=907 kg, c=3x108 m/s, γ=1.005, 1.011, and 1.048. The energies in Joules are E=8.204x1019, 8.253x1019, and 8.555x1019 J. There are about 4x109 J per ton of TNT, so the energies are 20.51, 20.63, and 21.39 Megatons of TNT. I might add that this is not actually very "realistic". Where are you going to get that much energy (you have to supply it somehow) in the middle of empty space? Or, look at it this way: I figure that for a mile-long gun the time to accelerate the BFR to 0.1c is about t=10-4 s. During that time the required power is about 8x1019/10-4=8x1023 W=8x1014 GW; the largest power plant on the earth is about 6 GW! Also, don't forget about the recoil of the ship which would likely destroy it.


QUESTION:
I have a question related to determining the force at impact. Here's the question in two parts:

  1. If a firefighter adds 45 pounds of gear to his overall weight, does it increase the impact force if he has no choice but to jump out a window and if so to what degree?

  2. What is the effect on impact force of jumping out a second floor window vs. 3rd floor and above?

This actually isn't homework. I'm 54 years old and advising a charitable organization that provides safety systems to firefighters. One of the challenges they face is fire departments who don't have high rise buildings and feel they don't need the bailout systems. So I'm trying to figure out what the impact is for a firefighter forced to jump out a second story or third story window. This will help inform how they talk to prospective donors. If you could help me with that (understanding/identifying the increase in impact force from 1st to 2nd to 3rd floors and then up) it would be greatly appreciated. I've done a lot of googling around calculating impact and g forces, but its not making sense to me (I'm not being lazy, just not understanding).

ANSWER:
The "force at impact" depends, essentially, on the time to stop. If she has a speed v, a mass m, and stops in a time t, the average force F during the stopping time is given by F=m(g+v/t) where g=32 ft/s2 is the acceleration due to gravity. So, yes, if you increase the mass you increase the force proportionally; I guess I would toss that extra 45 lb over before I jumped! Regarding your second question, call the height of one floor h. Jumping from the second floor would result in a speed of v2=
√(2gh); jumping from the third floor would result in a speed of v3=2√(gh) which is about 1.4 times larger than v2. In general, jumping from the nth floor would result in a speed vn=√[2(n-1)gh].

Maybe some numerical examples would be useful to you. You prefer Imperial units, which makes things a little complicated. The quantity mg is the weight. I will take mg=160 lb and h=12 ft for my numerical calculations, so when I need the mass I will use 160 lb/32 ft/s2=5 lb·s2/ft. (The unit of mass in Imperial units is called the slug, 1 slug=1 lb·s2/ft.) The speeds from second and third floors will then be v2=27.7 ft/s=18.9 mph and v3=39.2 ft/s=26.7 mph; these speeds are independent of the mass. Finally we must approximate the times to stop. If she lands feet first, she could extend, as parachutists do, her stopping time by bending her knees into a squat; I will estimate the distance s she will travel while stopping as s=3 ft. The time may be shown to be t=2s/v so t2=2x3/27.7=0.22 s and t3=2x3/39.2=0.15 s. Finally, the average forces during impact are F2=160+5x27.7/0.22=790 lb and F3=160+5x39.2/0.15=1467 lb. These are approximately 5 and 9 times her weight (g-forces of about 5g and 9g).


QUESTION:
I want to ask about the Mandela effect theory. I do not want detailed answers concerning blackholes and cosmology,instead i want to know if it's real. I personally do not believe in time travel and all the "clues" people have been providing don't seem credible enough. So please if it is true what is the exact physics background that proves it? And how can i have further information and dig deeper into this theory?

ANSWER:
I never heard of the Mandela effect. For readers who, like me, are similarly ignorant it is a special case of a psychiatric phenomenon called confabulation, defined as "the production of fabricated, distorted or misinterpreted memories about oneself or the world, without the conscious intention to deceive"; in other words, a "false memory". The Mandela effect is a confabulation where a large number of people have the same same false memory; it is apparently so called because there are many people who "remember" that Nelson Mandela died in 1980, not 2013. So, where is the physics in all this? A "paranormal consultant" named Fiona Broome suggested that such cases could be explained as "bleed through" from parallel universes. She is not a physicist and her speculation, maybe amusing, has no real basis in physics and there is no way to test it one way or another; therefore it should not be labeled as a "theory" since it is neither testable nor falsifiable. Snopes.com has a long article on the Mandela effect which you can read if you want to learn more.


QUESTION:
As surface tension means force acting on surface then why not its unit if force per unit area i.e N/m2. If it is N/m then which length will we have to take here.

ANSWER:
Think of the surface as an elastic sheet. What you want to call the surface tension is how hard you need to pull on this sheet in order to make it rip. The way this is usually measured is to create a film which is actually a very thin volume with surfaces on both sides; a simple device to do this is shown in the figure. Now, pull on the sliding side to stretch the film. When the film breaks, measure F. It is found, by doing many experiments, that F depends on L, but that the ratio F/L is always the same. Furthermore, it makes no difference what the shape of the film to the left of the slider is. We therefore define the surface tension for this fluid to be
γ=F/(2L) as determined by this experiment, the factor of ½ because there are two surfaces we are stretching.


QUESTION:
I just came across an ad saying that the earth's magnetic field keeps us healthy and strong, and saying that if we live in the world with no magnetic field, all life on earth will end (assume that sunlight / water / oxygen exist / and for some weird reason gravity still works) So my question is, is this valid? If there is no magnetic field, even though we have sunlight, water and air, we would perish?

ANSWER:
The magnetic field has no direct effect on you. There are many magnetic products touted as having miraculous beneficial effects on your health; do not buy them, they are a scam. There are important indirect effects of the magnetic field which help provide a healthy environment at the surface of the earth, though. Probably the most important is that the field extends far into space and protects the earth from the solar wind which is a stream of charged particles (mainly electrons and protons) which are deflected around the earth by the field. If there were no field, the effect of this "wind" would be to strip the upper atmosphere, including the ozone layer which protects you from intense ultraviolet radiation from the sun. But I do not think that buying a magnetic matress pad, for example, would help that issue! Lack of a magnetic field cannot result in our perishing, though, since it is well known that the field reverses direction periodically; the reversal would not be instaneous which would mean there would have been a period at least hundreds of years long when the field was negligibly small. The most recent reversal was about 780 million years ago when humans existed and we survived somehow. One thing about your question is strange: "
for some weird reason gravity still works…" The earth's gravity has nothing to do with its magnetic field.


QUESTION:
I
f you tow a boat from a tow path which is the best point to tie the rope onto the boat?

ANSWER:
The rope will exert a force on the boat, obviously. This force will tend to do three things: exert a torque which will tend to rotate the boat about a vertical axis through the center of gravity (you don't want this), have a component along the bank which will pull it along the canal (that is what you want), and have a component which will pull the boat toward the shore (you don't want this). To minimize the tendency of the boat to turn, attach the rope close to the center of gravity of the boat. To minimize the tendency to drift (not turn) to the bank, make the rope as long as possible so that most of its force will be exerted along the bank. Some tiller will be needed to make small corrections, but those should be minimal.


QUESTION:
Does water slow down gradually as it rises vertically out of a fountain? It would seem that it should, but that would mean the water behind would catch up and create a constantly wider jet. However it seems that the jet stays relatively consistent in width (subject to some splashing) until it reaches the top. At which point it splays and falls. This would suggest it is at a consistent speed all the way up until it suddenly decelerates and falls.

ANSWER:
Any "piece" of the water has a downward acceleration (slows down on the way up, speeds up on the way down) at all times; ignoring friction effects, each drop of the water follows the same trajectory as a thrown ball would follow. So, if one piece is slowing down, why doesn't the piece behind it catch up? Because it is slowing down too at exactly the same rate. If you threw two balls up, one right after the other, the second would never catch up. Of course, if the stream of water were going vertically up, the water falling from the top would collide with the water rising and, as you say, splay out.


QUESTION:
It's a question about R value, and directed to you partly because it appears you are in New Zealand. I'm looking at a video from an inventor in New Zealand who is recycling plastics into building blocks. I cannot find him on the net to ask what is the R value of these blocks. I know it is a long shot to ask you, but I wondered if there is a way to calculate R value, based on assumptions about physical properties of plastics such as milk jugs, trapped air and density in these blocks.

ANSWER:
There are tables where the R-value per inch of thickness is tabulated for various materials. But, these blocks are fabricated from a random mix of all classes of recyclable plastics. Furthermore, it is not clear how much air is trapped in them. Plastics seem to have R-values in the range of 3-5 ft2
·°F·h/BTU/in, so you could certainly take this range to estimate the value for a block of known thickness. If you are interested in the details of the physics of the R-value, you might be interested in an earlier answer.


QUESTION:
Heavy water is Deuterium oxide. Water is H2O. So is Deuterium oxide water with one Protium and one deuterium atom, or water with two deuterium atoms. If both hydrogens in water are actually deuterium, how did that come to be?

ANSWER:
Deuterium (D) is a naturally occuring isotope of hydrogen; approximately 0.015% of hydrogen atoms are deuterium, which is about 1:6,670. Therefore about 1:3,330 molecules of water would be HDO and approximately 1:44,400,000 (6,6702)would be D2O. The term "heavy water" refers to D2O and DHO is sometimes referred to as semiheavy water. You would think it would be a hopeless task to extract such a tiny fraction of D20 from natural water. I was very interested to learn that there is a much more clever way to get nearly pure heavy water. There are relatively many DHO molecules so it is much more practicable to use standard isotope separation techniques to get enriched DHO. So, for example, suppose that you enrich the water such that the hydrogen atoms present are 50% deuterium. Then it turns out that the water is 50% HDO, 25% H20, and 25% D2O. Where did all that D2O come from? It turns out that in water the hydrogen atoms (both isotopes) do not stay attached to the same oxygen atom, rather they move more or less freely around. By repeating whatever you did to get this far, you can get a higher and higher percentage of deuterium. Enrichments of 99.75% D2O are routinely achieved.


QUESTION:
Is it possible for a skydiver to not be strapped in to a parachute, just holding onto it, or even wrapping his arm into the straps. When he pops the schute, is it possible to hold on to it? Would his arm withstand the sudden deceleration or could it be torn from the shoulder socket?

ANSWER:
There is, of course, no simple answer to this question. It depends on how fast he is falling and the parachute design. It also depends on "luck" as the graph shows since the two graphs are for identical parachutes, weights, and speeds. The drag force (the force the parachute exerts up on him) as a function of time is shown in gs. One g would correspond to the weight of the parachutist. Both graphs end up after about 7 s at gforce=1 which means that the force up on him would be equal to his weight. For the "soft" deployment, about 3g is the maximum, so you would have to be able to hang from your hands from a stationary bar with three times your weight attached to you; you could probably do this briefly and it would certainly not tear the arm from its socket. For the "hard" deployment, almost 6g is the maximum, so you would have to be able to hang from your hands from a stationary bar with six times your weight attached to you. You could probably not do this but it still would probably not tear the arm from its socket. In any case, I would never depend on being able to hang on with my hands!


QUESTION:
If I have a .25 inch airtube in a 2 ft deep fish tank, how can I calculate the force necessary to expel the first bubble of air at the bottom of the tank if the other end of the tube is at the surface?

ANSWER:
The weight density of water is ρ=62.4 lb/ft3=0.0361 lb/in3. Therefore the gauge pressure 2 ft down is P=ρh=62.4x24=0.867 lb/in2 (psi). That pressure will just keep the tube filled with air all the way to the bottom. Any pressure greater than this will expel air into the water. This is probably the number you want; the force over the area of the tube is F=
0.867·π·(0.25/2)2=0.0426 lb=0.68 oz.


QUESTION:
I am an avid sports fan and I have often wondered if the experts may be wrong about the myth of the rising fastball in the game of baseball. I played baseball for over 20 years and I can tell you that the ball does appear to rise when certain pitchers throw hard put a heavy backspin on the ball. I have been told that experts say it is nothing more than a visual trick your eyes play on you because a rising fastball is considered to be physically impossible. I can tell you first hand that a softball pitcher I know can throw a ball that rises after being thrown on a straight trajectory. I suspect the Magnus effect may have something to do with the anit-gravitational behavior of the ball. Do you think this could be what causes the ball to appear to rise as it travels, or is it just our perception?

ANSWER:
There is such a thing as a rising fastball, but it does not actually rise; it simply falls more slowly than a nonspinning ball does. An experienced hitter knows intuitively what a normal fastball does and when presented with a rising fastball he will swear that it rose because it actually fell less. Incidentally, by rise or fall, I am talking about the direction of the acceleration. So a ball which is thrown at an angle above the horizontal is obviously rising but it rises at a decreasing rate of rise until it reaches the peak of its trajectory and then begins back down; the rising fastball will actually rise farther. Then why do we say it is a myth? It is easiest to understand by looking at a ball thrown purely horizontally. Can spin cause the ball to actually go upwards? To answer this, you need to think about all the forces on a pitched ball. There is the weight, FG, which points vertically down and causes the ball to accelerate downward (a horizontally thrown 90 mph fastball falls about 4 feet on the way to the plate); there is the drag FD which points opposite the direction of flight and tends to slow the ball down (a 90 mph fastball loses about 10 mph on the way to the plate); and there is the magnus force FM which, for a ball with backspin ω about a horizontal axis points perpendicular to the velocity and upward. If the ball is moving horizontally the only way it could rise is for the Magnus force to be larger than the weight. Measurements have been done in wind tunnels and it is found that if the rotation is 1800 rpm, about the most a pitcher could possibly put on it, the ball would have to be going over 130 mph for the Magnus force to be equal to the weight. When you say "thrown on a straight trajectory", you cannot mean it left his hand horizontally because it would hit the ground before it got to the plate; a fast pitch like that is impossible to accurately judge the initial angle of the trajectory.


QUESTION:
I'm learning about ideal gases in class and learning about the ideal gas law, but we also (very briefly) mentioned that at low temperatures and high pressures the ideal gas law no longer holds very well. We didn't go much pass that but I did a bit of research and an explanation included another set of constants calculated experimentally, but again only really explained very briefly that the size of the molecules become much greater and the inter molecular force between the molecules is no longer insignificant (as is a factor of the kinetic molecular theory of gases). I guess my question is, what is so substantial to the aspects of low temperatures and high pressures of ideal gases that causes them to follow a different set of parameters?

ANSWER:
V=NkT/P is the ideal gas law (IGL). I write it like this to emphasize what happens if T decreases and/or P increases while N stays the same—V decreases. (You may write it as V=nRT/P where n is the number of moles and R is the universal gas constant. For reasons of clarity in my answer, N is the number of molecules and k is Boltzmann's constant.) The IGL assumes that the volume occupied by the molecules is insignificant and that the molecules do not interact with each other. But, when the volume decreases the molecules get closer together so that their interactions start to matter and the total fraction of the volume which the molecules occupy is no longer a negligible fraction of the volume of the container. (You are incorrect when you say that "…the size of the molecules become much greater…"; the size stays the same but now occupies a larger fraction of the whole volume.) The first thing to do to correct the IGL is to replace V by V-Nv where v is the volume of a single molecule: P(V-Nv)=NkT. Although this improves the accuracy of the IGL, it still overestimates the pressure observed experimentally. The reason is that the effects of the intermolecular forces have not been included. It turns out by doing measurements that the pressure is proportional to the square of the number density, P∝(N/V)2; this makes some sense because the molecules interact by pairs and there are N(N-1)/2
N2/2 pairs because N is very large. So, finally, (P-c(N/V)2(V-Nv)=NkT where c is a proportionality constant which depends on what the particular gas is. This is sometimes called the van der Waal equation.


QUESTION:
When I had solar panels installed on my house the old fashioned meter ran backwards when the Sun was bright. They have now fitted a digital meter which can sense when energy is being sent into the grid. I can see how this could be done with DC, but how does it work with AC? In AC the current is switching direction at 50 Hz. How can the meter sense the 'direction' of the energy flow?

ANSWER:
You are right, the average current is zero. However, the current is not the power
—the power is the product of the current and the voltage. Both current and voltage are sinusoidal functions of time, i(t)=Isin(ωt) and v(t)=Vsin(ωt+φ), so p(t)=IVsin(ωt)sin(ωt+φ). The graph above shows three choices for the phase φ between i and v. For φ=π/2 the time average of the power is zero, no energy flow; for φ=π and φ=0 the time average of the power is negative and positive, respectively. The motor in a mechanical meter turns in opposite directions for different signs of the average power; in a digital meter the average power is determined by an electronic circuit.

FOLLOWUP QUESTION:
Thank you for your reply to my question about the power direction with energy generated by solar panels. I now understand that phase angles are crucial. The inverter in the loft takes DC from the panels and converts it into AC. To feed energy back into the grid does the inverter have to deliberately adjust the phase or does this occur naturally when there is an excess of energy?

ANSWER:
All that matters is what the phase is at the meter. If energy is flowing into your house the phase will be one way, if flowing out it will be the other.


QUESTION:
Why don't liquid pipelines that run downhill rupture from the weight of the liquid in them? For instance, a 14 mile long section of 10" ID pipe carrying crude oil that runs at a 22.5 degree angle has about 301,592.89 gallons of crude in it. That Crude weighs 91,328,360.39 pounds. I calculate that the static weight at the bottom of that run should be about 22,832,090.10 pounds of oil. That exceeds the tensile strength of the pipe wall by a factor of 50 to 100. At first I thought it was because a closed pipe would have sort of a vacuum at the top, but then I realized that would make the pipe crush from atmospheric pressure. I'm missing something simple I am sure, but darned if I can figure out what it is...

ANSWER:
There is something seriously wrong with your numbers. They imply that the weight of one gallon of crude is about 9x107/3x105=300 lb, and 14 miles at 22.5° would take you to 14sin22.5°=5.4 miles, higher than Mount Everest! Also, since we are working with a fluid, pressure would be a more appropriate quantity to look at than force. I will start from scratch with new numbers: the density of crude oil is about ρ=900 kg/m3 and I will take a distance of about y=1000 m between the top and the bottom, about the height of a small mountain; you need only the drop, as we shall see below. Like you, I will assume that the oil in the pipe is static which simplifies things. A good approximate way to solve this kind of problem is to use Bernoulli's equation, P+ρgy+½ρv2=constant; P is the pressure, g=9.8 m/s2 is the acceleration due to gravity, and v (=0 for us) is the speed. At the top, Ptop=PA and ytop=1000 m and at the bottom Pbottom=P+PA and ybottom=0; here, PA is the atmospheric pressure. Therefore, PA+900x9.8x1000=P+PA+0. So the gauge pressure is P
≈107 N/m2≈100 atm=1450 PSI. The brief research I have done indicates that this pressure is at the extreme upper limit of specifications for pipelines. To make the oil move, you need to add a lot more pressure. My use of Bernoulli's equation is a very crude approximation because it assumes a fluid with no viscosity and no frictional forces with the walls, obviously not a very good approximation.


QUESTION:
Suppose I have a 10 tons weight hanging 5 meters up in the air. I want to get electricity by lowering the weight against a dynamo (for example). How much energy do I get? A 100 W light bulb needs 100 W of power when it's ON. So, if it stays on for 10 hours it will consume 1 KW, am I right?...

Ok, so my question is... How many 100 W light bulbs can I have ON at the same time with the energy coming from that falling weight? -- while the weight is falling, obviously.

  1. if the weight falls for 1 hour

  2. if the weight falls for 2 hours.

What's the formula? Somebody asked the same question on some forum on the web. His weight was 200 tons falling 100 meters for 1 hour, and someone said that the solution is:
dU=Fdy = 200,000kg * 9.81m/s2 * 100m
= 196.2MJ = 196.2MW/3600 = 54,500KW/h
Is the formula right? If yes, how do I apply it? Because I get extremely small numbers if I change his 200,000 with my 10,000, and his 100 meters with my 5 meters. Plus, I don't know what KW/h means. All I'm interested is knowing how many Watts are available at any given moment while the weight is falling.

ANSWER:
The first thing we need to get straight is what a watt is. The unit of energy in SI units is the Joule (J); 1 J is 1 N·m where a Newton (N) is the unit of force and the meter (m) is the unit length. A Joule is the kinetic energy which a 2 kg mass moving with a speed of 1 m/s has; or, it is the work you need to do to lift a 1 kg mass to a height of 1/9.81 m. A Watt (W) is the rate at which energy is delivered or consumed, 1 W=1 J/s. Therefore, your 100 W bulb consumes 100 J of energy every second. Incidentally, if you look at your electricity bill, you will be billed for how many kW
·hr you have consumed; a kW·hr is a unit of energy, 1 kW·hr=1000x3600 J=3,600,000 J.

The example stated is correct but the units are not. It is fine up to the point where the potential energy of the mass is 196.2 MJ (mega=M=106). Now, if you let this mass drop over 3600 s, it is losing its energy at the rate of (196.2x106 J)/(3600 s)=5.45x104 J/s=54.5 kW (not kW/hr). For your case, your mass has a potential energy of 104x9.81x5=4.9x105 J. If you deliver this energy over an hour, the power is 4.9x105/3600=136 W; You could power one light bulb over this hour and have some energy left over at the end (about ¼ of what you started with). Clearly, the power delivered over two hours would only be half as much, not enough to power even one 100 W bulb.


QUESTION:
If there's less gravity on the moon, then why do astronauts move slower? Why don't they have more spring if gravity's pull is weaker? I'm thinking that this should be a matter of resistance, but obviously there's a factor I'm not accounting for.

ANSWER:
Sure, with less gravity (about 1/6 of earth) an astronaut can jump much higher, but it will take longer to get to the top and back down than on earth; that would look like slow motion, right? Or, just think about taking a step. Your center of gravity is forward of your trailing foot and so you rotate about that foot. The rate of rotational acceleration is only 1/6 that on earth, again like slow motion.


QUESTION:
Engineers in the Bay of Fundy are trying to harness tidal power to generate electricity. It's claimed that they can generate enough electricity to power the entire Atlantic Provinces of Canada. This got me to thinking, if that much power can be harnessed, where has that energy been going? I'm assuming it goes to heat and warms the water. If that's the case, would harnessing the power therefore cool the water and potentially harm aquatic ecosystems?

ANSWER:
My research shows that all the power projects on the Bay of Fundy will generate about 20 MW. These will be powered by underwater turbines. I did a very rough estimate of the total power available by the falling water: The average rise in sea level is 15 m, area of the bay is 13,000 km2, density of water is 1000 kg/m3. I find that the total volume to fall is about 2x1011 m3, the mass is 2x1014 kg, and the potential energy of this mass is about 3x1016 J. If you deliver that much energy over the course of a day, the average power is about 350 GW. So, the power plants will only reduce the energy of the tidal flow by less than 0.01%, a truly negligible amount.


QUESTION:
i was studying something on the internet where i need to know one question i.e If an object Travelling at about 2500 km per hour or may be higher collides with other object in the ocean around 90 meters below the ocean level is it possible that the debris of that object will go around 2 km approx ahead in the water itself?

ANSWER:
Extremely unlikely. Let me show you a very rough calculation which will demonstrate this for an extreme case. If one object collides elastically with another mass whose mass is very small compared to the incident mass, the collided-with mass will recoil with a speed twice the incident speed, in your case that would be 2x2500 km/hr=5000 km/hr
≈1400 m/s. The drag force on an object with speed v in water may be approximated as FdragCρAv2; here I will choose C≈1 (order of magnitude for most shapes) is the drag coefficient which depends only on the shape, ρ≈1000 kg/m3 is the density of water, and A≈1 cm2≈10-4 m2 is the cross sectional area of the object. I want this object to go as far as possible, so I have chosen A to be relatively small; an object this small will have a relatively small mass, certainly no larger than m≈100 gm=0.1 kg. Knowing all this, one can calculate the velocity v and position x as functions of time t, v=v0/(1+kt) and x=(v0/k)ln(1+kt) where kCρAv0/m≈7000  s-1 and v0=1400 m/s is the starting velocity. I find that at t=½ s, v≈0.4 m/s and x≈1.6 m; the object will have lost nearly all its speed after having traveled only about a meter and a half. I can think of no earthly way that any debris could propogate 2 km!


QUESTION:
Would my weight be the same on the surface of earth and one mile underground? How about one mile in the atmosphere?

ANSWER:
Above the surface of the earth the gravitational force falls off like 1/r2 where r is the distance from the center of the earth. If R=6.4x106 m is the radius of the earth, W is your weight at the surface, and W+ is your weight 1 mile=1.6x103 m above the surface, then W+/W=R2/r2=0.9995; your weight would be about 0.05% smaller. If you assume that the mass of the earth is uniformly distributed throughout its entire volume, the gravitational force falls off like r as you go toward the center. Then W-/W=r/R=0.99975; your weight would be about 0.025% smaller. Given other factors like local variations in the density of the surrounding earth, these would be unmeasurably small; one mile (about 1600 m) is, after all, extremely tiny realtive to the size of the earth. I should also note that approximating the earth's density as uniform is a very poor approximation; see an earlier answer. If you had asked your weight 100 miles below the surface the answer would be that your weight is nearly the same as at the surface.


QUESTION:
Helium. Where do we get it from if it is lighter than air and doesn't react with any other elements in the normal human tolerant environment?

ANSWER:
Good question. Even though it is the second most abundant element in the known universe, there is virtually none in the atmosphere (because it is so light that its average speed is greater than escape velocity and it shoots off into space) and is not tied up in rocks, water, or other chemicals (because it is inert) like hydrogen is, for example. This element was not even discovered until 1868 as a spectral line in the sun (where untold zillions of tons are being produced every second from nuclear fusion) and not found on earth until 1895 when trace amounts were found coming from uranium ore; the source was as a nuclear decay product in
α-decay. The first large amounts were discovered in 1903 as a byproduct mixed with the methane in natural gas wells; today large scale amounts come only from helium trapped underground.


QUESTION:
I am curious about a topic. In golf, if I hit a ball very hard and then I hit one very softly, is the one hit very softly more likely to move or sway in its straight path?

ANSWER:
You refer to "its straight path". No golf ball goes in a straight path, so I presume you mean that it does not curve left or right; such a ball, if not curving, would have a projected path on the ground (like the path of its shadow) which is straight. For a right-handed golfer, a ball which curves right is called a slice and one which curves to the left is called a hook; these have opposite spins. Neglecting the possibility of wind, the reason that a ball curves is because it has spin. But now it gets complicated because:

  1. the hard-hit ball is in the air much longer than the softly-hit ball;

  2. the lateral force causing the curve depends on both the rate of spin and the speed of the ball, so the hard-hit ball will experience more lateral force than the softly-hit one if they have the same spin;

  3. even if the slow ball has a bigger lateral force, the fast ball is likely to be deflected a greater distance because of its longer flight time;

  4. a lateral wind will exert the same force on both, but the fast ball will be deflected farther because of the longer time.

So, you see, there is no simple answer. To avoid curving, learn to hit the ball without imparting significant spin!


QUESTION:
We had a phenomenon happen recently about 8:30 PM that is inexplicable to us, but there must be some explanation. My wife and I were in separate rooms when we both heard an extremely loud noise from the living room! The noise sounded like a large glass that just hit a hard tile floor, but loudness was magnified. As it turned out we came into the living room to find a glass platter that we had sitting on the coffee table for about a year just shattered. –It broke completely by itself as there was no one in the room. Do you know how this may have shattered/blew apart all by itself?We used the platter to put 3 little oil lamps on. Inside our house the next morning at 6 AM we heard thunder outside so thought it might have had something to do with the barometric pressure.Very low barometric pressure and the type of glass it was made up combined just right to explode it like that? The temperature was a constant 68 degrees as it was for the months that was on the table. If you have any idea about this, we would appreciate it.

ANSWER:
Glass, as you know, is manufactured at very high temperatures. It has a quite large coefficient of theremal expansion (a large change in size for a small change in temperature) and is a poor conductor of heat. This means that as it cools it does not all cool at the same time. This can result in very large stresses being "frozen in" at some locations. What causes it to spontaneously break is usually difficult to determine; most likely it had recently been bumped or your oil lamps might have caused hot spots on the glass. Such things could have caused a tiny fracture to begin and the final shattering could easily come at some unpredictable later time. Unusual but not unexpected.


QUESTION:
On a skate board going down a .5 mile hill at 45 degrees slopes if I weigh 187 lbs how many mph would I be going by the bottom of the slope.

FOLLOWUP QUESTION:
This isn't homework I'm a 35 year old heavy equipment operator and my son had a accident on skate board and we are curious how fast he was going when he wiped out. I just wasn't sure how accurate I was when I said about 30-35mph. Please if you don't know just tell me so I can find someone who does—we got bets on it now amongst the family.

ANSWER:
Wow, 45
º is pretty darn steep! A half mile would correspond to his having dropped by about 0.35 miles≈560 m. If there were no friction at all his speed would have been v=√(2gh)=√(2x9.8x560)=105 m/s=235 mph! Back to the drawing board! There is some friction due to the wheels and bearings and I estimate that this is probably not more than about 15 lb; this would only slow him down to about 99 m/s=220 mph. Back to the drawing board! Finally, since the speed is going to get pretty big, we need to take air drag into consideration because the drag force is proportional to the square of the speed. A rough estimate would be that the force is about Fdrag≈¼Av2 where A is the area his body presents to the onrushing wind. When Fdrag is equal the net force down the incline (component of weight minus friction, which I estimate to be about 117 lb=520 N), he will stop accelerating. Taking his area to be about 2 m2, you can then solve ¼Av2=520 to get v=32 m/s=70 mph. This is all very rough but should give you an order-of-magnitude estimate. (I still find it hard to believe that he went down a half mile, 45º slope without braking at all!)


QUESTION:
I am curious about generating power in space. Why do they always use solar instead of the windmill type of generation? A coil/magnet rotating. It seems to me, once the rotation is started, it would continue forever? Thus if you used a rocket to start the rotating part of the generator, and it kept spinning, could you use the magnetic field to protect say, an astronaut inside the generator? If it was big enough. Would you get perpetual energy if you used the electricity created in say, a microwave rocket engine or electromagnet. Or does the magnetic force alone cause the spin to lose momentum?

ANSWER:
So, you start something rotating in a vacuum and it never stops because there is no air drag. You could even imagine making extremely low-friction bearings so you could mount this on the side of your spacecraft and it would at least spin for a very long time before slowing down. But, the minute you hook it up to a generator you are asking it for energy so it immediately begins to slow down, giving its kinetic energy to you to power a light bulb, maybe. There is no free lunch in this universe, and if you want energy you need something to give it to you and the sun is the most convenient source in our neighborhood.


QUESTION:
If the planet earth was perfectly smooth and spherical will the water cease to flow?

ANSWER:
Not if everything else stayed the same. If the earth were completely isolated, not rotating, and without atmosphere, water would flow until it formed a uniform layer over the earth; eventually any currents would damp out due to the viscosity of the water. The fact that the earth is rotating and heated by the sun and has an atmosphere would mean that the water would try to distribute itself mostly uniformly but with an equatorial bulge; however heating and cooling of the atmosphere would cause weather patterns and the resulting winds would move the water around just like what happens today. Also, the moon causes tides which are, by definition, motions of the water. You probably could think of many more reasons the water would not become totally static.


QUESTION:
We're trying to design a vessel for working in the vacuum of space. We have a vacuum chamber that can pull a 0.01 atm partial vacuum, so the question is : How does the force difference compare on the walls of a vessel, with 14 psi inside to outside chamber or space, i.e. force comparison between 0.01 atm in the chamber and the 10-14 in space? My guess is that we are capturing 99% of the effective force differential using the chamber, so not much more to expect from the vacuum of space.

ANSWER:
Ok, the 14 psi inside your chamber is about 0.953 atm and the pressure outside is 0.01 atm making the net pressure difference 0.943 atm. The pressure outside in space is, for all intents and purposes, zero, so the net pressure difference would be 0.953 atm. So, the percent difference is 100x(0.953-0.943)/0.953=1.05%, about what you guessed. In other words, the force on any part of the walls of your chamber is about 1% smaller than it would be in space.


QUESTION:
Not sure if this is physics or not but how can you record silent sound ? I found the patent for it on google it's 5159703 and I wanna know how you can record it because a regular microphone doesn't pick it up.

ANSWER:
The idea here is essentially the same as AM radio where the high-frequency radio wave is modulated by the audible message. For this invention the radio wave is replaced with sound of a frequency larger than is audible but modulated by an audible signal. You could certainly make a detector (call it a microphone if you like) to detect these high-frequency sound waves; ultrasound imaging in medicine does just that. Then you would need some electronics to extract the audible signal from the carrier, just like you need a radio receiver to extract the audible signal from the AM radio carrier.


QUESTION:
Imagine if you wrapped a rope tightly around the earth. How much longer would you have to make the rope if you wanted it to be exactly one foot above the surface all the way around?

ANSWER:
I hope you don't think that the rope would spontaneously rise up if it were longer than the circumference of the earth; you would have a slightly slack rope laying on the ground. You are specifying the difference in radii between one circle with a circumference C and another of circumference C+
δ; that is not really physics. But, it is easy enough to do. If C is the circumference of the earth, then C=2πR where R is the radius of the earth and C+δ=2πR' where R' is the radius of the circle your rope would make if δ=1 ft. Then δ=2π(R'-R)=2π=6.28 ft. Note that δ depends only on how high the rope is above ground, not how big the earth is: if the earth were 1 ft in radius and you increased the length of the rope by 6.28 ft, the rope would be 1 ft above the surface!


QUESTION:
What will happen if we fill water in the tyres of our cars instead of air?Does it have any effect?.

ANSWER:
Three important issues I can think of. First, it would add a lot of weight to the vehicle which would hurt your gas economy. Second, the moment of inertial of a wheel would be larger requiring a larger torque having to be exerted for either acceleration or braking. Third, air is compressible and water is not and so the wheel would not have a cushioning effect on the ride.


QUESTION:
I just saw a music video in which a group of performers appear to be in an aeroplane cabin in free-fall for 2 minutes and 40 seconds. The choreography is spectacular, and it appears to have been done in ONE take! How far would the plane have had to descend to maintain zero gravity conditions for 160 seconds?

ANSWER:
This video was shot in Russia in a reduced-gravity jet provided by S7 Airlines. Weightlessness is not achieved by falling but by following the parabolic path which a projectile would follow. Imagine that someone shot you from a cannon with a speed of 500 mph (the typical speed of a commercial jet). If there were no air drag, you would follow a parabolic path. The plane which contains you now follows that exact path and that is how you appear to be weightless. An alternative way would be for the plane to simply go straight down with an acceleration of 9.8 m/s2, but I think you can see that this would not be a very safe situation. Anyhow, back to you question, I could not find reference to any such parabolic flight lasting longer than 30 s, so the video must have been shot in more than one take. Because this is such an unfamiliar environment, I cannot believe that, even with a lot of practice, it could be done in a single take without errors. And, if the plane were simply falling for 160 s, it would have to have started at an altitude of about 80 mi (far higher than a plane can actually fly) and would end with a speed of about 3600 mph (far faster than the plane could fly without disintegrating).


        

QUESTION:
Have scientists done experiment on what is the value of gravity below the earth surface as depth increases? if done pl. provide chart g vs depth.

ANSWER:
The deepest hole ever drilled is only about 12 km deep. I could not find any reference to attempts to measure g at various depths down this hole. Since the radius is about 6.4x103 km, you would only expect about a 0.2% variation over that distance. There are models of the density of the earth, though, which have been determined by observing waves transmitted through the earth during earthquakes or nuclear bomb tests; these are believed to be a pretty good representation of the radial density and can be used to calculate g. The two figures above show the deduced density distribution and the calculated g.

Usually in introductory physics classes we talk about the earth as having constant density, but as you can see, that is far from true—the core is much more dense than the mantles and crust. If it were true, g would decrease linearly to zero inside the earth. Instead, it increases slightly first to around 10 m/s2 and remains nearly constant until you are at a depth of around 2000 km. There is little likelihood that g will ever actually be measured deep inside the earth because the temperature increases greatly as you go deeper, already to near 200ºC at 12 km. However, if you have detailed information on density distribution, there is really no need to measure g.


QUESTION:
Many Science Fiction ships have for protection a shield that stops projectiles and saves the ship from a lethal impact. Such an example would be the energy shields possessed by the faction known as Covenant from Halo. So given the laws of Newton and the third law about there always being an equal force countering the force that was exerted first, wouldn't this just mean that whenever the energy shield takes a hit by a projectile, the force would ''travel'' from the shield to whatever generator generates the shield. Like the UNSC Frigates shoot a 600 ton slug at 30km/s. They're 30ft long and around 7ft wide. So they have a lot of force and momentum behind them. So wouldn't an impact like this just cause the shield generator to be violently thrown off its attachments and ''fly off'' through the compartments of the ship destroying a lot of the ship?

ANSWER:
"So they have a lot of force and momentum behind them." Yes, these projectiles have a lot of momentum, but saying that "…there is a lot of forcebehind them…" has no meaning. The momentum a slug has is p=mv=(6x105 kg)(3x104 m/s)=1.8x1010 kg m/s. When this hits something, it will certainly exert a force, but the magnitude of that force will depend on how long it took to stop. I have no idea how big it is, but suppose it has a radius of 10 km from the ship; I will think of it as very flexible and suppose that it stretches inward just stopping before it hits the ship. I also will assume that the ship is much more massive than the slug; (elsewise how could a comparably-sized ship carry a bunch of them and fire them without huge recoil?) If it stops in 10 km=104 m with uniform acceleration, I can apply simple kinematics, -3x104=at and 104=3x104+½at2, and find that t=1.5 s, the time for the slug to stop. The average force felt by the slug is (Newton's second law) the rate of change of the momentum, F=1.8x1010/1.5=1.2x1010 N. You are certainly right, this very large force will be felt by the ship because of Newton's third law. But suppose that the ship is 100,000 times more massive than the slug, 6x1010 kg; in that case, the final velocity of the ship after being hit will be found from F=mv/t=6x1010
v/1.5=1.2x1010 N, so v=0.3 m/s, not so bad! If the shield were very rigid, it would be catastrophe for the ship. I have never played these games but I expect the shield is shown as stopping the slug almost instantly.

A little should be said about the other end, launching the slug in the first place. In this case, unless the cannon has a 10 km barrel, the recoil force on the ship will be huge. You would be interested in similar Q&As along the same line as yours.


QUESTION:
I am writing a blog and had my friends to ask of what they would want to talk about.. I get this one. I have no clue with physics, so, I am asking. Explain why a photon particle- which is a very small bundle of energy and travels at the speed of light- seems to defy the laws of physics by never losing speed or velocity?

ANSWER:
There is no law of physics which says an object naturally loses velocity. To change the velocity of something you have to apply a force to it, it must interact with something. If you had a bowling ball which had no forces on it it would continue going with a constant speed in a straight line forever. This is just Newton's first law. However, Newtonian mechanics is not valid for a photon, but it behaves like any other particle when it experiences no interactions which would change it. There is one important difference
—regardless of how it interacts with something else, it never speeds up nor slows down; the speed of light in a vacuum is a constant of nature. If you look on my faq page you will find links to discussions regarding why the speed is constant and why it has the value it does. When you throw a ball up in the air, it slows down; you throw it down from a tall building, it speeds up. Photons don't do that but they do change their energies by changing to a longer, redder (shorter, bluer) wavelength when going up (down) in a gravitational field.


QUESTION:
Gasoline contains 40 megajoules of energy per kilogram and gasoline trucks have around a hundred tons of it. So how does a gasoline truck exploding not produce an explosion similar to a small nuke?

ANSWER:
Since it is always a little ambigous what is meant by a ton, I did my own calculation using the volume of a tanker truck of about 10,000 gallons and the density of gasoline of about 2.7 kg/gallon. I got the total energy content of about 1012 J. The energy of the Nagasaki bomb, a small bomb by today's standards, was about 1014 J, 100 times bigger. Two things to consider are:

  1. The bomb number represents total energy delivered whereas I would guess that likely less than half the energy content of the gasoline would actually be delivered.

  2. The time over which the energy is delivered is likely much longer for the gasoline explosion than the nuclear explosion. As an example, just to illustrate the importance, suppose the bomb exploded in 1 ms=10-3 s and the tank in 1 s. Then the power delivered by each is 108 GW for the bomb and 103 GW for the tank. As a result the destructive power of the bomb would be much bigger.


QUESTION:
If a man could travel with a near speed of light, what would happen to him if he'd run though an elephant. Would that man be demolished or could he survive that impact?

ANSWER:
Are you kidding? A man going 200 mph, far below the speed of light, would be instantly killed in this scenario. A 100 kg man going at 80% the speed of light would bring in about 5x1018 J of energy to the collision which is equivalent to about 10,000 Nagasaki atomic bombs. Not only would the man and elephant be obliterated, also anything within miles would be.


QUESTION:
Bodies of water bend with the curvature of the planet. How large would a body of water have to be in order to measure a difference of 1 inch from one end to the other.

ANSWER:
I often get questions like this. I have used this figure many times before. Here R=6.4x106 m is the radius of the earth, d=1 in=0.024 m is your 1 inch,
θ is the angle which subtends the arc length, call it s, you seek. From the triangle you can write cosθ=R/(R+d)=[1+(d/R)]-1≈1-(d/R)+… where I have done a binomial expansion of [1+(d/R)]-1 because (d/R) is extremely small. Now, because θ is also very small, I can represent cosθ by the expansion cosθ≈1-½θ2+… so (d/R)≈½θ2. Finally we can write that θ=s/R. If you now solve for s you will find s≈554 m.


QUESTION:
I'm a science geek and an IT person who just found out that there are sixteen types of water ice. I've been googling the phenomena, and can only find discussions of the physical make-up at the atomic level. Can you help me with some discussion of the various forms of ice at a macro level? Like, what does it look like, how does it act, etc. Everything I've found is in science speak, which I really can't envision myself.

 

ANSWER:
Refer to the figure above which came from the Wikepedia article on ice. You can get a clearer picture there. The thing to notice is that all the ices except for ice I and ice XI occur at extremely high pressures
—1000 atmospheres or higher. So, you cannot really "look" at them and say what they look like since they are formed in a containment vessel of some sort. Ice XI occurs at atmospheric pressure but only at very low temperatures. If you look at the Phases section of the article, you will find links to separate articles for all 16 forms of ice where you can get information about their properties. Although the terminology for the crystal structure is pretty "science speak" as you say, you will find usually pretty comprehensible pictures of these crystal structures. I think you would find these articles about as understandable as you will find.


QUESTION:
If atoms at room temperature move around at roughly the speed of a jet airplane, how fast do atoms that make up a jet airplane move when said airplane is moving (at room temperature)?

ANSWER:
I assume you are talking about molecules in a gas. It is much more complicated to talk about molecular speeds in solids. So let's talk about the air in the airplane cabin. The speeds are distributed from very low to very high, but the most probable speed would be around 1000 mph, about twice the speed of a commercial jet. But, that does not mean that the most probable speed of molecules in a jet flying by would be around 1500 mph because the molecules measured inside the airplane would be moving in all directions so the result of adding 500 mph to all the molecules going 1000 mph would yield anything from 500 mph to 1500 mph. Measured inside the airplane, the average velocity of all the molecules would be zero because for every molecule going in one direction with some speed v there is always another going in the opposite direction with speed v. The average velocity of the air in the airplane as measured by an observer on the ground would be 500 mph. It could be thought of as like a wind in which there is a net flow of air in the direction the wind is blowing.


QUESTION:
In what medium would sound travel the fastest?

ANSWER:
I have not done an exhaustive search, but the largest I found was beryllium with a speed of 12,890 m/s. Diamond is a close second with a speed of 12,000 m/s.


QUESTION:
if a cat fell from 100 feet how fast was the cat in mph falling when it hit the ground

ANSWER:
The terminal velocity of a cat is about 60 mph and that speed is achieved after falling about 50 ft. Therefore falling from 100 ft the speed would be about 60 mph. See earlier answers (1 and 2) for more details. Keep in mind that all cats are not the same size, weight, or fuzziness, so this can only be an approximate answer. It is interesting that about 10% of cats falling from 5 stories are killed but fewer from higher stories because, once reaching terminal velocity, they can relax, spread out (to slow down) and get ready to hit.


QUESTION:
When I was very young, I used a hand-held fish scale to try and measure my own weight by attaching the hook (normally placed in the gills of the fish just caught) to my belt and then pulled up on it. I'm interested in the physics behind my folly and, expanding it further, if the scale was attached to a light (not heavy) bar (that would support more than my weight) and the scale could measure a fish weighing more than me, and I was strong enough to lift more than my weight above my head, how close could I expect to get to seeing my weight on the scale (attached to the bar I'm pushing up, and a belt-device around my waist)?

ANSWER:
The way you always solve a statics problem like this is to first choose a body, then apply Newton's first law which states that the sum of all forces on the body must equal zero; I choose the scale as the body. What are the forces on the scale itself? Your hand pulls up with a force Fhand, your belt pulls down with a force Fbelt, and the earth pulls down on the scale (its weight) with a force Wscale.  These three have to add to zero which means that Fhand=Fbelt
+Wscale. Now, the scale is calibrated so that it reads zero when Fbelt=0, so the scale will read whatever force your hand exerts up. Note that when you do this analysis, the desired quantity, your weight, never appears; everything would be just the same if you weighed 1000 lb. Regarding your second question, it is really no different from the first question: simply replace 'belt' by 'bar' everywhere. In either case you would observe the scale reading your weight when you pulled up with a force equal to your own weight.

FOLLOWUP QUESTION:
Thank you! So it sounds like it wasn't a folly after all (except for the fact that the scale I used wouldn't support my weight at that age).

ANSWER:
Of course it was folly, total folly! Doing this experiment gives you absolutely no information about your weight. Only if you already knew your weight and were able to pull with a force that hard would the scale read your weight.


QUESTION:
Hi, I was wondering what are the chances of survival from falling from the ninth floor of a building, going over the science of that how does surface affect the fall, body weight and trajectory. What is the difference from falling from a third story window as opposed to a higher up one?

ANSWER:
Someone else also asked this question; apparently it refers to a recent actual incident of a student falling out a dorm room window about 85 ft
≈26 m high; the student survived without serious injury. The second person also wanted to know if I could estimate the force experienced on impact. First I will calculate the speed he would hit the ground if there were no air drag. The appropriate equations of motion are y(t)=26-½gt2. and v(t)=gt where y(t) is the height above the ground at time t, and g is acceleration due to gravity which I will take to be g≈10 m/s2. The time when the ground (y=0) is reached is found from the y equation, 0=26-5t2 or t=√(26/5)=2.3 s. Therefore v=10x2.3=23 m/s (about 51 mph). The terminal velocity of a falling human is approximately 55 m/s, more than double the speed here, so the effects of air drag are small and can be neglected for our purposes of estimating. (If there is air drag, terminal velocity is the speed which will eventually be reached when the drag becomes equal to the weight.)

Estimating the force this guy experienced when he hit the ground is a bit trickier, because what really matters is how quickly he stopped. Keep in mind that this is only a rough estimate because I do not know the exact nature of how the ground behaved when he hit it. The main principle is Newton's second law which may be stated as F=mΔvt where m is the mass, Δt is the time to stop, Δv=23 m/s is the change in speed over that time, and F is the average force experienced over Δt. You can see that the shorter the time, the greater the force; he will be hurt a lot more falling on concrete than on a pile of mattresses. I was told that his weight was 156 lb which is m=71 kg and he fell onto about 2" of pine straw; that was probably over relatively soft earth which would have compressed a couple of more inches. So let's say he stopped over a distance of about 4"≈0.1 m. We can estimate the stopping time from the stopping distance by assuming that the decceleration is constant; without going into details, this results in the approximate time Δt≈0.01 s. Putting all that into the equation above for F, F≈71x23/0.01=163,000 N≈37,000 lb. This is a very large force, but keep in mind that if he hits flat it is spread out over his whole body, so we should really think about pressure; estimating his total area to be about 2 m2, I find that this results in a pressure of about 82,000 N/m2=12 lb/in2. That is still a pretty big force but you could certainly endure a force of 12 lb exerted over one square inch of your body pretty easily.

Another possibility is that the victim employed some variation of the technique parachuters use when hitting the ground, going feet first and using bending of the knees to lengthen the time of collision. Supposing that he has about 0.8 m of leg and body bending to apply, his stopping distance is about eight times as large which would result in in an eight times smaller average force, about 5,000 lb.

Falling from a third story window (about 32 feet, say) would result in a speed of about 14 m/s (31 mph) so the force would be reduced by a factor of a little less than a half.

ADDED NOTE:
A rough estimate including air drag would have his speed at the ground be about 21 m/s rather than 23 m/s as above. Given the rough estimates in all these calculations, this 10% difference is indeed negligible.


QUESTION:
When in the early universe did life become possible? I'm assuming it would have had to have been at some point when the temperature had cooled down enough so that the protons and neutrons of basic elements of life like carbon and oxygen could bond and come together. Also, what do you believe is the purpose for intelligent life in the Universe?

ANSWER:
I usually do not answer questions about astronomy/astrophysics/cosmology as stated on the site. I can give you a little information here, though. The universe just after the big bang was almost exclusively hydrogen. No elements which could be used to form planets where life might develop or the material for life itself. The first stars started forming about 100 million years after the big bang, basically pure hydrogen stars. These had to be much larger than the sun (perhaps 300-1,000 times heavier) because of the lack of heavier elements and consequently their lifetimes were too short (a few million years) for life to evolve (it has taken about 5 billion years to reach our stage of evolution, about half the sun's lifetime). Inside these stars nuclear fusion caused heavier and heavier elements up to about iron to form; then when those stars used up all the fuel, they exploded (super novae) scattering the heavier elements to eventually be part of clouds of dust and hydrogen which subsequently formed new stars with the possibility of planets. (As you can see, it is not "cooling down" which is responsible for heavier elements which are created in stars which are super hot.) So, we are now at least several billion years into the age of the universe. More detail on early stars can be read in a Scientific American article. The "purpose" for anything is not within the purview of physics.


QUESTION:
What is the purpose of utilizing a percentage of body weight to determine how much weight to bench press/push/whatever? I know this seems like a fitness question and not a physics question, but what I am interested in is WHY weight would be used to determine how much one could (or should be able to) lift/push? For example: A gym teacher wants to grade his students on their strength. He decides to use abililty to push a weighted sled across the floor as the measure. He wants to make the task equally difficult for every student in order to make the grading fair. So, he decides that each student will push 2x his/her body weight for 5 minutes and the grade will be based on how FAR the student is able to push. So, Student A weighs 170 pounds and pushes 340 pounds (including the weight of the sled) for a total of 160 yards. Student B weighs 240 pounds and pushes 480 pounds (again, including the weight of the sled) for 80 yards. Student A pushed farther and gets a better grade, but Student B complains that he had to push much more weight so he should not get a worse grade. Does Student B have a legitimate complaint or does his heavier weight contribute somehow to his ability to push that doesn't have anything to do with his strength? As in, does his weight help push the sled in some way? Sorry, I don't know enough about physics to ask this question using proper physics terms like force, mass, etc. I hope you will still answer my question!

ANSWER:
I cannot comment on the rationale for correlating weight to strength. I can certainly comment on the physics of your particular example of sled pushing. I would first of all comment that this example is certainly not one solely of strength because, since it is a timed activity, endurance as much as strength is being tested; if one student, for example, were a heavy smoker, he would likely become exhausted more easily. As a physicist, I would equate "strength" with force. The specific example you give, though, seems to me to be more related to energy (work done by the student) or power (rate of energy delivered) than strength; purely in terms of strength, the heavier student exerts more force. The force F which each student must exert depends on the weight w he is pushing and the coefficient of friction #956; between the sled and the ground, F= μw. The work W done in pushing the sled a distance d is W=Fd= μwd. The power generated if W is delivered in a time t is P=W/t=μwd/t . Both students have the same μ and t , so WA/WB=PA/PB=dAwA/dBw
B=(160x340)/(80x480)=1.42. So student A did 42% more work, generated 42% more power, than student B. From a physics point of view, B demonstrated more strength, A demonstrated more power. I would judge that this is not a fair way to assign a grade. It would be interesting to see if A (B) could move B's (A's) sled 80 (160) yards.


QUESTION:
The demonstration wherein one pours water from a clear vessel and one shines a laser pointer (a red laser pointer in my case) through the water and it appears the laser beam bends with the water pouring out of the clear vessel; What causes the beam to bend with the water? Would this same type of effect work with other fluids than water, such as air or glass?

ANSWER:
It is caused by total internal reflection. If the angle which the light hits the surface between the water and the air is glancing enough, the light will be reflected back into the water rather than be refracted into the air. Total internal reflection can happen whenever light strikes the interface with a material of smaller index of refraction; the minimum angle for which it can occur depends on the relative indices of refraction.


QUESTION:
Why simple harmonic motion is called simple?

ANSWER:
Take a look at the figure above. The red curves are all pure sine waves, just having different frequencies. These are all called simple harmonic motion because they may be expressed as a single sine wave. Now, take all four of these and add them together. The result is the black curve. This curve is still harmonic (which means that it is periodic, it repeats itself after some time, called the period, has elapsed) but it is not "simple" because to describe it you must use four different sine waves.


QUESTION:
Hi ...here is a link to Felix Baumgartner's freefall jump from space - https://www.youtube.com/watch?v=vvbN-cWe0A0 135,890 feet - or, 41.42 km (25.74 mi) In the video you see speed at which he is supposedly travelling, 729 mph (1173km/hr), 46 seconds after he jumped. The footage is cut then seconds later speed strangely falls to 629 mph...anyway after 4 mins and 18 seconds of free falling he releases parachute. My questions are What speed would he be going at a 4 mins and 18 seconds into freefall? Also how do you explain the deacceleration when it was at 729 mph then down to 629 mph?

 ANSWER:
(You might be interested in an earlier answer.) There is a better video at https://www.youtube.com/watch?v=raiFrxbHxV0; this video shows data acquired by instruments on Baumgartner. Here some clips from that video:

The first three are the times also showing speeds; these are roughly the speeds you refer to in your question. The second three show speeds and altitudes. The third graph shows the whole history of altitude, speed, and mach speed. The speeds are all larger than indicated in your video. The speed at 4:20, 113 mph, answers your first question. The speed at 0:50 is about the maximum, 847 mph or mach1.25. The speed at 1:01 has dropped to 732 (about the same change as your video); I suspect this deceleration is due to two factors: there is getting to be much more air resulting in higher drag and, probably after he broke the record he oriented his body to increase drag and slow down. The official maximum speed after everything was calibrated was 843.6 mph.


QUESTION:
Will the drag coefficient be the same in air and water?

ANSWER:
There is no simple answer to this question. The drag coefficient CD is a constant characterized by the geometry of an object used to calculate the drag force FD if it is proportional to the square of the velocity v: FDCD ρAv 2 where A is the area the object presents to the fluid flow and ρ is the density of the fluid. Whether or not this equation is true depends on a quantity called the Reynolds number Re=Lρv/η where L is a length along the direction of flow and η is the viscosity of the fluid. It turns out that only if Re>1000 is the velocity dependence approximately quadratic. If Re<1 the drag force is approximately proportional to v. Anywhere between these extremes the drag force is a combination, FDCD ρAv 2+kv. CD ≈constant only for the case Re>1000; the drag coefficient would then be the same for identically shaped objects. It is interesting, though, to get a feeling for what the relative speeds in air and water corresponding to Re=1000 are. The necessary data at room

 

temperature are ρ air≈1 kg/m3, ρ water ≈1000 kg/m3, η air≈1.8x10-5 Pa·s, and η water≈1.0x10-3 Pa·s. Then vwater/vair≈(1.0x10-3/1000)/(1.8x10-5/1)=0.056 (which is true for any Re). Taking a sphere of diameter 0.1 m as a specific example for the critical Re=1000, CD=0.47, A=7.9x10-3 m2, L=0.1 m, vair=1000x1.8x10-5/(0.1x1)=0.18 m/s and vwater=1000x1.0x10-3/(0.1x1000)=0.01 m/s. Since the speeds are relatively low, you can conclude that for many cases of interest the quadratic drag equation holds for both water and air. Therefore, for many situations you can approximate that the drag coefficient in air and water are about the same. For a specific case you should check the Reynolds numbers to be sure that they are >1000. The bottom line is that if the drag force depends quadratically on velocity, the drag coefficient approximately depends only on geometry, not the properties of the fluid. Keep in mind that all calculations of fluid drag are only approximations.

ADDED COMMENT:
As I said above, for 1<Re<1000, FDav+bv2 where a and b depend on Re; e.g., a≈0 for Re>1000 and b≈0 for Re<1. So, for Re<1, a is just a constant and FDav≡½CD ρAv 2 so CD=2a/( ρAv )=2aL/(A ηRe )≡c/Re where c is a constant. If FD is proportional to v, CD is inversely proportional to Re; this is called Stokes' law. As we saw above, Re>1000 leads to CD=constant. Ferguson and Church have derived an analytical expression which very neatly reproduces data for the transition from Stokes' law (1/Re) to constant CD. Calculations for a golf ball are shown at the left (constant CD, the green line, is called turbulent in the legend). Note, as we have stated, that the transition occurs in the region 1<Re<1000. Note the sudden drop in the data around Re=500,000. I believe that this must be due to the dimples on the golf ball which reduce drag.