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Here are older questions and answers processed by "Ask the Physicist!"

QUESTION:  
suppose there were a crazy architect who wanted to build a conical monument or perhaps working structure on the tip instead of at the wider base, and without any outside support beams. could the building be supported by a massive internal gyroscope?

ANSWER: 
Yes.

QUESTION:  
Am I right that planets tend to be generally spherical? (Not perfect spheres, of course, but for the most part sphere-like). Why is this? Your explanation of how/why fire manifests as sphere in space seems related, but wouldn't the properties of the matter which make up a planet have an effect on the shape of the planet? To this end, is it possible to have a hotdog-shaped planet, or will rotational and orbital forces (and others?) always collect a planet's matter into a sphere?

ANSWER: 
The main reason is that astronomical objects are usually formed by smaller pieces coming together. Initially, very small stuff (dust size) sticks together by colliding and since this is a random process, is just as likely to stick a little piece on any part of a larger piece with which it collides; therefore the initial "seeds" tend to be roughly spherical. Then, when a piece gets big enough to have significant gravity, it starts "sucking up" neighboring smaller pieces to grow but, because the gravitational force is spherically symmetric (i.e. it is equally strong in any direction the same distance from the object), it tends to maintain a basically  spherical shape as it grows. If it were hot dog shaped, gravity would pull harder on the ends than the sides and it would tend back toward spherical shape. I read a good analogy somewhere: Suppose you want to build a building 1000 stories high, essentially a nonspherical bump on our essentially spherical earth. You would likely fail because gravity would cause it to collapse under its own weight. The earth is actually slightly oblate, that is fatter at the equator than the poles, because it is rotating and the centrifugal force pulls it out at the equator.

QUESTION:  
If density plays a factor in the strength of an objects gravitational field, why is it not part of Newton's law of gravitation?

ANSWER: 
The universal law of gravitation is strictly valid only for point masses, not extended mass distributions. What you then do is to imagine two bodies each made up of an infinite number of infinetesmal point masses, find the force between each pair, and add them all up to get the net force (if you know calculus, this process is called integration). That is where the density comes into play since the (infinetesmal) mass at a point is proportional to the density there. Interestingly, if the density of each object is spherically symmetric (i.e. the density depends only on how far you are from its center) and if the shapes are spheres, you can actually treat each as a point mass with all the mass at the center and get the right answer.

QUESTION:  
Why do clouds float? Water vapor is heavier than air. And what determines their altitude?

ANSWER: 
Actually, clouds are not water vapor but either water droplets or ice crystals. If it were simply water vapor, it would mix with the air and diffuse about sort of uniformly. In fact, the amount of water vapor in the air is what determines humidity. Clouds stay aloft for the same reason that dust motes floating around, also heavier than air: air drafts push them around. For more information go to the weather network.

QUESTION:  
Is Einstein's theory of general relativity correct? It's taught in high schools (well, special relativity) and universities but there's a web site, http://www.relativitychallenge.com/index.htm, that claims there are mathematical errors in it. Also, are new theories (such as the string theory) based on relativity or do they assume that it's wrong?

ANSWER: 
What does correct mean? All observations regarding gravity are in accord with the general theory. But, there are some important predictions of the theory, black holes and gravity waves for example, for which we have indirect evidence but not direct evidence. Is it possible that someday some experiment may not be in accord with the theory? Of course! This theory cannot be the final word because nobody has been able to reconcile it with quantum mechanics, one of the other most important theories of nature. Special relativity is another issue and is generally considered certainly correct since it simply describes the nature of space and time. Regarding your website, I certainly will not critique it because I know that the world is full of persons with their own personal theories of the universe desperately seeking attention for their ideas. I will acknowledge that no theory is immune from mathematical errors which, even if present, do not necessarily negate the validity of the theory.

QUESTION:  
If you're driving a car at 100km/h on a flat, straight road, and the passenger is flying a remote controlled plane at 100km/h beside the car; what would happen if the plane is steered so that it flys inside the car window? Would it appear to hover, as it's speed, relative to the ground below is the same as the car, or smash into the windshield, as it's speed relative to the car has increased to 200km/h?

ANSWER: 
Before coming inside, the airplane is at rest relative to the car, so if it keeps flying it would hover when it entered. But, is that possible? How does the airplane fly? By moving through the air. Before entering the car, the airplane sees a 100 km/hr "wind" going opposite his direction of flight (assuming that the air outside the car is still); if the plane were at rest relative to the air, e.g. if there were a real 100 km/hr tailwind, the plane would drop to the ground! But that is exactly what the situation would be when the plane entered the car--it would suddenly be at rest relative to the air and drop to the floor. If it were a helicopter instead of an airplane, which flys by moving its wings (the rotor) through the air instead of moving the air over the wing, it would hover inside the car.

QUESTION:  
What are all of the types of particles in physics? The ones I know of are:

• electrons
• photons
• phonons

Could you give me the complete list with short descriptions?

ANSWER: 
What is a particle? How about a grain of sand? How about an atom or a nucleus? There are more than 150 particles known in elementary particle physics, but physicists no longer think of them as "elementary" because they can be thought of as being built from more elementary building blocks. One important example of those building blocks is the quarks. The whole issue is quite complicated, more than I can answer in a forum like this one. I recommend you do some reading. One good web site which does a good job at disentangling the whole mess is Wikepedia.com.

QUESTION:  
If an airplane's wing shape lets it fly. (curved allows more air to flow over it thus air pushes up on the flat part of the wing at least that's what they tell me...) How does an airplane fly upside down? Wouldn't the air pushing the flat part of the wing force it into the ground?

ANSWER: 
The standard textbook explanation of how airplanes fly is a considerable oversimplification. In addition to the Bernoulli effect to which you refer, the "angle of attack" is also important. I have included details in a previously answered question.

QUESTION:  
Is it theoretically possible to make a magnet-only powered motor capable of spinning forever?

ANSWER: 
I guess that if you could make something without friction it could spin forever. You wouldn't even need the magnet. But in the real world, perpetual motion machines are forbidden by the second law of thermodynamics.

QUESTION:  
What would happen if a car was traveling at the speed of light, and then turned on it's headlights? I read this question in a magazine but didn't understand the answer too well. Can you try to explain it please?

ANSWER: 
This is easy to answer: a car cannot travel at the speed of light.

QUESTION:  
A question I have to research...... A light source is 2m below the surface of the water in a calm pool. Find the radius of the circle through which the light travels from the water into the air. Take the refractive index of water as 4/3 and air as 1.

ANSWER: 
Since this sounds like homework, I won't work it out but I will tell you the idea. Light coming straight up from the source hits the surface perpendicularly (zero angle of incidence, relative to the normal to the surface) but light not straight up strikes at some angle of incidence other than zero. As you go farther and farther away from the straight up point, the angle gets bigger and bigger. Eventually the angle becomes greater than the critical angle and no light can escape.

QUESTION:  
I have a simple question concerning electorn orbit changes. How fast do electrons stay in an unstable orbit before dropping to their basic orbit?

ANSWER: 
There is no single answer to this question because it depends on what atom you look at and specifically on which orbits are involved in the transition. Typical lifetimes are on the order of nanoseconds (billionths of a second).

QUESTION:  
What is gravity - I am told it is a force that pulls objects together - but how and why?

ANSWER: 
This is a question about which whole volumes have been written. It is one of nature's four fundamental forces and it is, by far, the weakest force in nature. The reason why gravity is so weak is one of the great unsolved problems of physics. In simple, classical terms, gravity is a force which is caused and felt by objects which possess a property called gravitational mass which, as far as we can tell, is any material thing. You might find the statement that it is weak to be surprising since it is the force of which we are all most aware. But consider this: the weight of a pin is the graviational force which the whole earth exerts on it but that force is easily balanced by a small magnet (which uses the electromagnetic force, another of the four). If you want to probe more deeply you need the theory of general relativity. Here the idea is that the presence of mass actually causes the space around it to warp and this warp of space results in masses wanting to move toward each other. An often-used analogy is to imagine a bowling ball placed in the center of a trampoline which causes there to be a sag in the center; now place a marble on the trampoline and, of course, it rolls toward the bowling ball.

QUESTION:  
I had the following question on my physics test and could not figure it out. A child holds a sled weighing 77.0N at rest on a frictionless incline at 30.0 degrees. Find a) the magnitude of the force the child must exert on the rope, and b) the magnitude of the force of the incline exerts on the sled. Answer a) 38.5 N b) 66.7N

ANSWER: 
There are three forces on the sled, the force due to the child (F), the weight of the sled (W), and the force from the incline (N). Since the incline is frictionless, N has only a component perpendicular to the incline; F has only a component parallel to the plane. Hence N must be equal to the magnitude of the component of the weight perpendicular to the incline (77cos[30]=66.7) and F must be equal to the magnitude of the component of the weight parallel to the incline (77sin[30]=38.5).

QUESTION:  
This goes all the way back to high school (as well as college) physics. What is friction? It was always taught to me as simply something that exists between two surfaces and the friction between two surfaces (their relative coeficient of friction) must be empirically determined. That is how I was taught about friction. It seems to me with our deep understanding of physics down to sub-atomic and maybe string level, SOMEONE has had to come up with a better theory of friction than what I learned. It there an post-Newtonian theory of friction and is there a way to calculate the coeficient of friction between two surfaces?

ANSWER: 
I have previously answered a question similar to yours. Link here.

QUESTION:  
I am currently reading "The Elegant Universe" by Brian Greene. In his description of the "horizon problem" of cosmology, Greene describes how the uniform background radiation is too uniform according to the standard model of the big bank because light would not have time to travel between two currently distant regions of space no matter how close to the moment of the big bang we go. I don't understand this because it either suggests that a.) the two regions of space have traveled with a relative velocity of GREATER than the speed of light or b.) that there must have been an initial displacement between those two regions of space sufficiently large to account for light being unable to travel between the two regions. Neither of these seem consistent with other aspects of physics in the standard big bang theory. What am I missing here? Am I just not understanding Greene's explanation?

ANSWER: 
from L. A. Magnani:
The horizon problem is indeed a problem for STANDARD big bang cosmology (i.e., the version developed in the 1950's - 1980's.

The way out is to invoke a brief period of "inflation" during the early Universe when spacetime expands much more rapidly than the expansion rate we infer from galaxy redshifts today.

This inflationary explanation was proposed in the mid 1980's by Alan Guth and others and is supposed to be produced by a phase transition in the vaccum of some kind or other - the cause of the inflationary epoch is still a matter of debate.

The confusion for this person, I think,  is arising from mixing up the sound speed (which is what is necessary to establish thermal equilibrium between two regions) with the speed of light.  The inflation does not have to occur at greater than the speed of light.  It just has to occur at a velocity greater than the sound speed of the medium to effectively thermally decouple opposite sides.

From J.-P. Caillault:
The commonly accepted solution to the horizon problem is Inflation,  which was when the early universe must have expanded exponentially  (faster than the speed of light, but this doesn't violate relativity  since it's the universe itself which was expanding, not anything  moving within it).  Most cosmologists now accept Inflation as part of  the "standard big bang theory," but this NYU person is probably  thinking of the big bang paradigm that prevailed prior to the  introduction of the Inflationary idea (by Alan Guth in the late 1970s).

from L. A. Magnani:
I think JP is right. The thermal speed may not be relevant because the coupling is between photons scattering off plasma, rather than what goes on in a gas if the particles are doing the energy exchange.

But the expansion of spacetime can go on at faster than the speed of light - something that is recognized also in standard big bang cosmology.

QUESTION:  
Please explain insimple terms what E=MC2 stands for.

ANSWER: 
This means that mass (m), which measures the inertia of a quantity (and to which its weight is proportional) is just a form of energy. The amount of energy (E) is enormous because the factor c² is the square of the speed of light and c=3x10⁸ m/s=186,000 miles/second is a huge number. To give an example, suppose that you could completely change a pound of something into energy. The amount you would have would be about 4x10¹⁶ Watt-seconds which is about 10 billion kilowatt-hours; this amounts, approximately, to the total energy output of all nuclear reactors in the US in 4 days!

QUESTION:  
Two twins, Bill and Ben are 22.0 years old and they leave Earth for a distant planet 8 light years away. The twins depart at the same time on Earth, and travel in different space ships. Bill travels at 0.9c, while Ben travels at 0.5c. What is the difference between their ages when Ben arrives on the new planet?

ANSWER: 
This sounds suspiciously like a homework problem to me! But I thought it was particularly interesting so I answered it anyway! To see the solution, link here.

QUESTION:  
In an idealized case when no air resistance and engine-fuel factors are considered would the same plane travel the distances Vienna - Tokio and Tokio - Vienna for the same time? Why?

ANSWER: 
I'm not sure what you are getting at here. For starters, for no air resistance the plane could not fly! The most important issue in time differences in long distance flights is head/tail winds, but without air resistance, we would ignore these. Let's assume, rather than no air resistance, equal resistance for any direction (perfectly still air). Then, if there are identical airspeeds in any direction there would be identical groundspeeds, so the answer to your question would be that the times would be equal.

QUESTION:  
Relativistic theory says mass increases to infinity as speed of light is approached. Yet accelerators routinely accelerate particles to near light speed ( 99 percent in some cases) without the particles ever getting anywhere near infinite mass. Why? And if there is some mass increase, what is the largest ever recorded and at what "speed"?

ANSWER: 
You should look at masses relative to the rest mass. The mass of a particle traveling with a speed of .9999c is about 76.6 times its rest mass; this is about how fast an electron with kinetic energy 6 GeV at the CEBAF accelerator at Jefferson Lab travels.  If you were to make the energy 1000 times larger, the speed would only increase by about .01%. Records of largest mass are not kept. If you find the highest speeds recorded for a mass m₀, then the mass will be given by m=m₀[1-v²/c²]^-1/2.

QUESTION:  
If temperature is defined as the average kinetic energy of molecules in a mass, then why is there not a universal molar specific heat for all substances in all states?

ANSWER: 
In fact, the molar specific heat for most solids at temperatures near room temperature is nearly constant as you suggest. For a gas, however, if it can change volume it can therefore do work and so only part of the heat (energy) added increases the temperature and part comes out of the system as work.

QUESTION:  
Suppose you have a one inch perfectly square bar of length L resting on a flat perfectly rigid surface. You have a roller of weight W resting at some point on the bar. The roller is a cylinder so its contact with the bar is a line perpendicular to the length direction and parallel to the surface. What is the vertical force at each point along the bar due to the weight? (The point is the end of a line across the bottom of the bar that is perpendicular to the length and the question is about the force on that line.)
 
A practical application for this is the determination of the weight of a roller required to compress bonding tape to stick a bar to a sheet of metal. A particular pressure is required to cause the adhesive to adhere properly.

ANSWER: 
For the application you have in mind, your model (contact being a line) is too simple to yield a meaningful answer. The force which the cylinder exerts on the bar is W and that force is (ideally) distributed evenly across the line. However, pressure is defined as force/area and since the area of a line is zero, the pressure is infinite! That should give you no problem sticking the tape! To compute the pressure you need to let the line have some width w; then, L being the width of the rod (and length of your line), the area of contact will be wL and the (average) pressure would be W/(wL). This is still a simplification since the force is likely to vary across the distance w, but that is maybe more detail than you want (or that I could probably deduce!)

QUESTION:  
I would like to know what cold is. I would like to know what is happening on the atomic level that makes (we'll say) air, cold and pass on that coldness.
 
I know that heat is a form of radiation and that the molecules get excited and knock eachother around, but what do the molecules of cold do and how do they do it? Is it atomic spin, do they crowd other atoms and force them to slow down?

ANSWER: 
Cold is not a noun, it is an adjective. What you want to know is what is the difference between something cold and something hot; and you want to understand on a microscopic (atomic) level. Let's talk about the air in the room. As you probably know, all the molecules in the air move around and their velocities have a distribution, some fast, some slow, some moderate, etc. But you could, in principle, measure all the speeds and take the average. Now, the higher the average speed is, the hotter the gas is. That is what hot means--speedy atoms, on average. If you want to get more technical, you can talk about the average kinetic energy of the molecules in the room, kinetic energy being mv²/2 where m is the mass of the molecule and v is its speed. Now, temperature (that number we usually use to measure hot or cold) is merely a measure of the average kinetic energy of the molecules in the room.

QUESTION:  
why does "fire" behave the way it does in space?  why does it not "go up" like fire on earth, but instead look like a sphere or something?  also, he says that he's heard it's more "dangerous" [sic] [unpredictable?] in space and never goes out?  is any of that latter claim true?

ANSWER: 
This is a good question and you can find it discussed many places on the web. Two are Wonderquest and Scientific American. I will add my two cents' worth: How could a flame go up if there is no direction identifiable as up? If all directions are equivalent, then a physical phenomenon like a flame would of necessity be spherically symmetric like the space. Regarding the "never goes out" part, a flame is just a chemical reaction and if either the fuel or the oxygen runs out, the flame will stop. Regarding "dangerous", on earth the "updraft" of the flame allows oxygen to be "sucked in" at the point of combustion making for more efficient burning, so that would likely be a more dangerous situation. I believe that something burns more quickly in gravity for this reason.

QUESTION:  
While driving on an interstate highway the other day, I was idly day-dreaming about driving my vehicle up onto the ramps of a trailer that was being towed directly ahead of me. I was traveling at 70 MPH relative to the ground. The trailer ahead of me was moving at a speed slightly slower than me. As I approached, I thought - my wheels are turning at a rate that moves me along at 70MPH relative to the highway pavement, but if I start to drive up onto the ramps of the trailer ahead of me (which was traveling at - say- 68MPH relative to the pavement), once my turning wheels hit the ramps, I would be instantly accelerated to 138MPH - the sum of the trailer's speed relative to the ground plus my speed relative to the ground - clearly faster than I had been traveling an instant before I went onto the trailer.

Now - what if I was traveling at the speed of light, and the vehicle in front of me was traveling at just under the speed of light? Why wouldn't my speed suddenly exceed the speed of light as soon as I drove up onto the ramps?

ANSWER: 
Where did you get the idea that you would be accelerated to 138 mph? Your speed with respect to the road would remain 70 or close to it. Your front wheels would have to make a little adjustment because it would be like the road suddenly started moving backward at 2 mph so your wheels would have to start spinning as if you were going 72, but that would probably be no big deal (but your tires might give a short squeal like when you brake or accelerate quickly). Now, anything which you can understand using everyday examples like the one you give is not applicable to objects which are traveling near the speed of light; that is one of the important truths about the theory of special relativity, that our intuition is not a good measure of what is reasonable if we are in a regime (high speeds) where we have no experience.

QUESTION:  
Time moves slower for someone who is moving very fast than for  someone else at rest.' How can this be said if motion is relative? Example: Two people are floating out in space, and person A sees person B zip by him very fast. B of course sees A zip by him. If it is correct to say that A is moving and B is at rest, and correct to say B is moving and A is at rest, how can you decide who is moving slower through time, and thus ageing slower than the other?

ANSWER: 
To each observer the other's clock running slow. They do not appear to be running slow, they are running slow. This is very puzzling as you note in your question, but it is also very true. The trouble is that you have the standard intuitive feeling for time, that there is some ablsolute and correct clock with respect to which all others can be compared. In fact, time is such that there is no problem with A seeing B's clock being slow and vice versa. There is no way that they can sit down in a room together and look at the two clocks to find out who is right because they are not in the same reference frame. To do that, one or the other would have to accelerate and the theory of special relativity is not applicable to accelerating frames. You can understand time dilation without talking about acceleration by studying the "twin paradox" which I have discussed in answer to a previous question.

QUESTION:  
Can an object have positive acceleration and be slowing down?

ANSWER: 
Yes, of course. Acceleration, like velocity, is a vector quantity and so it has a sign in a particular coordinate system. (I will restrict myself to one dimensional examples for clarity.) Suppose that an object has a velocity v₁=-2 m/s and then, five seconds later, has a velocity v₂=-1 m/s; this object is moving in the negative direction (direction of decreasing coordinate) and is "slowing down". Now let's compute its average acceleration, the change in velocity over the elapsed time: (v₂-v₁)/t=(-1-(-2))/5=+0.2 m/s², a positive acceleration! The best known example of this is an object thrown straight up into the air: the object slows down on the way up and speeds up on the way down, but the acceleration is always the same.

QUESTION:  
What is the rate of speed at the point where the two blades of a scissor meet as they close?

ANSWER: 
That is determined entirely by how fast you "snip", how big the scissors are, and how far from the pivot point the mesh point is. For example, suppose the scissors are initially open 30 degrees (p/6 radians) and close in 1/10 of a second; the average angular velocity of one blade relative to the other would be w=p/6/(1/10)=5.24 radians/s. If the blades extended from 1 to 10 cm from the axis, then the relative speed of one blade with respect to the other would be calculated as v=Rw=5.24 to 52.4 cm/s where R is the distance from the pivot.

QUESTION:  
how can we prove that earth can be considered as an inertial frame of reference to a good approximation?

ANSWER: 
The definition of an inertial frame is one in which Newton's first law is true. That is, if an object has zero net force on it, it will move with constant velocity (i.e. move with constant speed in a straight line or be at rest). The degree to which this is true determines the degree to which it is an inertial frame. A rough measure would be to ask what is the maximum acceleration of the surface of the earth; to calculate this I will ignore accelerations due the motion of the earth around the sun and the motion of the sun around the center of the galaxy since these are demonstrably smaller than the acceleration due to the earth's rotation. Consider an object with mass 1 kg at the equator. It is sitting "at rest" on a scale which reads, of course, 9.8 N. But, does it really? The weight of the object is 9.8 N but the scale reads the normal force between the mass and the scale, and these cannot be exactly equal because the object is accelerating because it is moving in a circle of radius R_E=6.4x10⁶ m with a speed of v=2pR_E/T=2p(6.4x10⁶ m)/(1 day)=465 m/s; so the acceleration is a=v²/R_E=0.034 m/s². So the scale would read a "weight" of 9.77 N for an object whose weight was actually 9.8 N. If you can tolerate errors on the order of 0.3%, you may consider the earth to be an inertial frame of reference.

QUESTION:  
What would happen if the two slit experiment were done with electrically neutral particles like neutrinos or neutrons?

ANSWER: 
The interference has nothing to do with electrical charge, only with the wave-like properties of the interfering particles. In order to be able to observe interference, the slit spacing should not be large compared to the deBroglie wavelength of the particles. The wavelength is l=h/p where h is Planck's constant and p is the linear momentum of the particle. Once you know the wavelength and the slit spacing d, the analysis proceeds just as if you were doing the Young's double-slit problem for light, dsinq=nl. n=0,1,2... for maxima.

QUESTION:  
I am having a VERY difficult time with this question and I don't know why.  I have gotten 4 different answers!  I am just not sure which formula to use, or how to start anymore.  Please help.  The question:
Part 1:  Suppose you throw a 3 kg ball straight up at 40 m/s.  Using energy conservation, calculate how high the ball would go if there was no air resistance.
Part 2:  Suppose that the ball actually reached a maximum height of only 75 m.  How much energy was lost due to friction with the air on the way up?

ANSWER: 
Part 1:
E₁=mv²/2=2400 J
E₂=mgy=3x9.8xy=29.4y
but, E₁=E₂, so y=81.6 m.

Part 2:
E₃=mgy'=3x9.8x75=2205 J
therefore, DE=E₃-E₁=-195 J.
195 joules of energy was lost.

QUESTION:  
Since the earth is being continuously bombarded by cosmic rays, why can't we develop some method of harnessing the energy from these particles?

ANSWER: 
Many of these are either trapped in the Van Allen radiation belts by the magnetic field of the earth or lose much of their energy interacting with the atmosphere. Although I am not an expert, I believe that the total energy content would not be large and efforts would be much more productively directed at harnessing energy reaching us from the sun.

QUESTION:  
Why does an object gain mass the faster it travels? Where does this mass come from? Do scientists believe there is any way to get around this and somehow travel at or past the speed of light?

ANSWER: 
Mass is inertia, that is resistance to acceleration. When we say that the mass increases, this simply means that it gets harder and harder to accelerate a particular object as it speeds up. So, think of mass as inertia, not "stuff" and then you won't have to worry about where that "stuff" came from. Another way to think about the problem is to ask how much energy it takes to accelerate something up to some particular speed; it would take an infinite amount of energy to accelerate anything all the way up to the speed of light. Special relativity, on which all this is based, is very well verified by many experiments, so no scientists believe that there is any way to accelerate something beyond or even to the speed of light. There is some discussion of tachyons which are particles traveling faster than the speed of light, and they would behave in predictable ways. The problem is, that they must have always been there since you can't get there from here! Nobody has ever observed a tachyon and they (in my opinion) likely do not exist.

QUESTION:  

What will happen if the centripetal, gravitational force of Earth exerted on the moon becomes stronger ?

ANSWER: 
Suppose that the moon is in a roughly circular orbit with the current gravitational force. If the force were to suddenly increase, the orbit would become elliptical and the moon would come much closer to the earth. This is shown to the right where the the moon's current circular orbit is shown and then if the force increased at the point where the ellipse is tangent to the circle, the new orbit would be the elliptical (egg-shaped) orbit. The earth is not drawn to scale here.

QUESTION:  
In electrostatics we learn that the answers we get when computing voltages are independent of the definition of ground potential. What I mean by this is that the equations apparently "don’t care" if the ground we define to be Zero Volts is actually at Zero, or -pi volts, or + one gadzillion megavolts. Only voltage differences matter. So, is there a mathematical property embedded or encapsulated within the equations of electrostatics which ensures the physics will be invariant upon changes in the definition of the zero voltage? If so, what is this property called? I ask this because I am familiar with the idea that the equations of physics (for instance, Maxwell's equations) "don't care" what the velocity of the laboratory is in which those equations are derived, and in a certain sense this gives rise to special relativity. Thus my curiosity about this "don't care" condition involving voltages, and what the more fundamental principles involved might be.

ANSWER: 
The two examples you allude to are different kinds of "relative". Special relativity, which ensures that Maxwell's equations are the same in any reference frame, has one frame moving relative to another. Voltages are defined by considering one point in space relative to another. Voltage has the property you refer to (only the difference counts) because of the way it is defined. Voltage is related to energy (and work) and energy also has this property that the total energy is not relevant (because potential energy may be arbitrarily zeroed), only the change in energy. Consider an electric charge q and it takes an amount of work W_ab to move it from point a to point b. Then the potential energy difference is U_b-U_a=-W_ab (which is a definition); because this is the definition, you see that what U itself is is not well defined (e.g. if I add an arbitrary constant, say 5,000 J to both U_b and U_a, the equation is still true). Finally, the electric potential V is defined to be U/q, so V_b-V_a is just a measure of the work necessary to move a one Coulomb charge from one point in space to another but V_b and V_a themselves have no meaning.

QUESTION:  
I am a high school junior and I got stuck with this question while doing a prep test. And this is the one -A braking system for a roller coaster is designed to stop it over a distance of 15 m when the coaster enters the stopping area with a speed of 40 km/h. What acceleration must the braking system provide?

ANSWER: 
First, convert km/hr to m/s: 40 (km/hr) x (1000 m/ 1 km) x (1 hr/ 3600 s) = 11.11 m/s. Now, write the equations of motion for constant acceleration:
x=x₀+v₀t+at²/2
v=v₀+at
Now, taking the origin to be where the braking begins, x₀=0 and v₀=11.11 m/s. Now, let x=15 m and v=0 m/s:
15=11.11t+at²/2
0=11.11+at
Solving these two equations yields a=-4.11 m/s² and t=2.7 s.

QUESTION:  
The faster you move through space, the slower you move through time. I heard someone say on a television program, that this astronaut, out of all the astronauts in the world has been in space the longest. They said that because he has spent so much time circling the earth at such high speeds, he has traveled into the future a tiny little bit. My question is this: If we are always moving trough space because of the earth's many movements, isn't what they said false? Moving with the earth does count when concidering your actual speed through space, doesn't it?

ANSWER: 
What matters here is relative speed (relativity refers to how things are in one system relative to another). So, he ages less rapidly than you because he is moving relative to you.

QUESTION:  
My 7th grade Honors Math teacher want my class and I to find out what is the space shuttle acceleration launch speed? My math teacher said that it woud be less then 7 mph.

ANSWER: 
Well, there is a little problem here: "acceleration launch speed" doesn't mean anything in physics. The acceleration is one thing and the speed is another. Speed (velocity) tells how fast the height is changing and acceleration tells how fast the speed is changing. Maybe your teacher means "what is the speed of the shuttle at the instant when launch begins?" If that is so, then the answer is zero. The average acceleration during launch is about 33 m/s/s which is about 74 mi/hr/s which means that, on average, the speed increases by 74 mi/hr each second over the 8.5 minutes it takes to reach orbital speed. Of course, the acceleration is smaller at the start of the launch. At the end of the first second, for example, suppose that the whole thing has lifted one foot up; the average acceleration would be about 1.36 mi/hr/s and the speed would be 1.36 mi/hr.

QUESTION:  
Many years ago I worked for eight months in a medical radiation laboratory that serviced medical linear accelerators. The output from the "linac" was 4Mev and with this being the case I used the equation E=hf to determine that the photons being emitted must lie in the gamma radiation section of the electromagnetic spectrum.. I was however informed that it was x-rays the "linac" was emitting and was also told gama radiation and x-rays are the same anyway.  I have not dealt with these subjects for many many years so can you tell me..

1. Was I right to use the equation E=hf to determine the frequency of these photons and does it work out the gamma radiation is the correct output?
2. Are gamma and x-rays the same thing?

ANSWER: 

1. You would have been right if each proton (I presume it was a proton linac with the protons having 4 MeV kinetic energy) had stopped and all its kinetic energy were carried off by a single photon. In fact, the proton beam is smashed into a piece of metal where it interacts many time with atoms, giving each atom a little of its kinetic energy. Then each atom deexcites producing an x-ray.
2. They are not absolutely defined, so they can overlap a bit, i.e. a low energy gamma ray and a high energy x-ray might have the same energy. However, physicists often make the identification by where the photon comes from: gamma rays come from nuclei and x-rays come from atoms.

QUESTION:  
Why do air bags in cars reduce the chaces of injury in accidents?

ANSWER: 
It is all Newton's second law. Your momentum is proportional to your speed. To stop you, that is to take away your momentum, a force must be exerted. The more quickly you change your momentum, the greater the force which is required. Imagine jumping out of four-story building. When you hit the ground your momentum disappears in an instant and, for that to happen, you are subject to an enormous upward force by the ground; it is this force which hurts or kills you. However, if there is a big soft pillow that you land on, the effect is that it takes longer to stop you and so you will experience a much smaller force over the stopping time; therefore you are much less likely to be injured. I think that you can make the translation of this example to the airbag.

QUESTION:  
Was looking at a program on discovery channel that depicted a spacecraft propelled by use of a solar sail, the interesting piece was that it was propelled by a powerfull laser on a space station. The question is If a laser powfull enough is fired in a direction and is powerfull enough to propel the space craft why would'nt it (the laser that is) be pushed in the opposite direction to the way in which the light is travelling.

ANSWER: 
It would, but if you think of the space station as being attached to the earth, the whole earth/space station system would recoil but with negligible velocity because the net mass is so huge.

QUESTION:  
Relating to free-falling objects, if a object is thrown upwards at a velocity (v), when that object reaches it maximun height, the velocity of the object = 0.  My question is,  if you could instantaneously observe the object while at max height (duration when V=0) then, wouldn't the acceleration of that object be 0?  I understand that g is a constant and never changes, but wouldn't the acceleration of that object change?

ANSWER: 
Acceleration has nothing to do with velocity. Rather it measures the rate of change of velocity. The acceleration is proportional to the force on an object and if the force is the object's weight only, it will have always a constant acceleration which is pointing down (acceleration is a vector). Acceleration essentially tells you what the velocity will be a short time later, so if v=0 now, v will be a small velocity downward a short time later. If the acceleration were zero, the velocity would not change and the object would stay at rest forever.

QUESTION:  
If you skimmed a one molecule thick layer of water off the surface of the earth's oceans how much water would you have?

ANSWER: 
The surface area of the earth is about 200 million square miles and about 70% is water, so 140 million square miles; that is about 3.6x10¹⁴ m². The diameter of a water molecule is about 3 angstroms=3x10^-10 m. So the volume is 11x10⁴ m³ which is about 30 million gallons. It would fit in a cube of about 50 yards on a side.

QUESTION:  
The textbooks of  physics state that 1 coulomb is a charge equal to 6.242x10¹⁸ electronic charges, and that the charge of one electron is 1.602x10^–19 C.  My question is:  How did the number 6.242x10¹⁸ come into existence? What is its history?  Did this number originate from a measured quantity, that is, experimentally, or is it dirived mathematically?

ANSWER: 
What you are actually asking here is: "How is a Coulomb defined and how can the charge, in Coulombs, of an electron be measured?" (not to put words in your mouth, or anything!) It is somewhat circuitous since the thing which is defined is the unit of current, the Ampere (A), and the Coulomb (C) is defined in terms of the Ampere. If you have two very long parallel wires each carrying equal current I and separated by 1 m, the force per unit length (N/m, newtons per meter) is 2 x 10^-7 N/m when I=1 A; that is an operational definition of the Ampere. Now, a Coulomb is the amount of charge which passes through a wire carring 1 A of current in one second (s), so 1 A=1 C/s. That defines 1 C. Now, as you know, electric charges exert forces on each other. It may be determined that the force F (in N) felt by a particle with charge q₁ (in C) due to a charge q₂ (in C) which is a distance r (in m) away is F=9x10⁹(q₁q₂/r²); this is called Coulomb's law. Now that you know the force law, you can find the charge on an electron by measuring the force between two electrons separated by a known distance. This charge turns out to be 1.6x10^-19 C. If that is the number of coulombs per electron, then the number of electrons per coulomb is simply the reciprocal, 1/1.6x10^-19=6.24x10¹⁸.

QUESTION:  
What would be the final speed of an electron as it passes though a field generated by 1V potential difference and expressed in km/s.  We would assume the same conditions as those in which an electron would gain an energy of 1 eV. Is it possible to determine this speed experimentally?

ANSWER: 
Technically, one should use relativity to answer this question but 1 V inparts, as we shall see, a velocity which is much smaller than the speed of light, so I will use classical physics. You are right, the kinetic energy of the electron will be 1 eV and since 1eV=1.6x10^-19 J and the mass of an electron is 9.1x10^-31 kg, we can write that 1.6x10^-19=9.1x10^-31v²/2. Solving, v=5.93x10⁵ m/s=593 km/s (which is much smaller than the speed of light, 3x10⁸ m/s). And, yes, of course, it is possible to measure this experimentally.

QUESTION:  
What is the difference between Linear velocity and Angular velocity?

ANSWER: 
Linear velocity measures the rate of change by virtue of translation (moving in a line). For example, when we speak of a car going with a velocity 60 miles/hour it is going that fast down the road. Angular velocity measures the rate of change by virtue of rotation. For example, the earth is rotating on its axis with an angular velocity of 1 revolution/24 hours. The wheels of the car have both linear and angular velicity.

QUESTION:  
If I set up a laser that sends a beam out to a mirror and then the beam is reflected back upon itself, is it possible to adjust the the distance between the laser source and the mirror so that one could see interference effects?

ANSWER: 
Yes. You can set up a standing wave. But you could not "see" it because the nodes would only be half the wavelength of the light apart. This is a technique which is used to create a diffraction grating out of light.

QUESTION:  
Why is parking a car in a measured space easier while reversing than when moving forwad?

ANSWER: 
I don't know if this is really physics; more common sense. It is because you steer with your front wheels. If you steer your front end into a parking space, the rear end is left outside and there is no way to get it in. If you steer so that your rear end goes in first (you have to go in reverse to do this) then your front end is left outside but now you can steer it in.

QUESTION:  
Can a person get shocked from the electrical charge that comes up from the ground during a lightning strike or is it from the charge coming from the cloud?

ANSWER: 
Usually the bottom of a cloud is negatively charged, so when lightening occurs it will result in a large electric current of electrons flowing to the ground. This is what will kill you (I find "shock" too mild a word!) Also, you will get burned by the extremely hot plasma which is the path through which the electrons flow. There is a lot more detail at http://science.howstuffworks.com/lightning.htm

QUESTION:  
What causes light bulbs to glow?  Is it the gas inside?  Do different kinds of bulbs contain different gases? Like neon gas in neon light bulbs.

ANSWER: 
Usually when we refer to "light bulbs" we are talking about "incandescent" lights. Here electric current is passed through a very thin filament (wire) and it becomes white hot; that is the source of the light. The bulb is filled with an inert gas so that the wire will not burn as it would in air. There is a disadvantage to this kind of light, however--only a small fraction of the energy it uses is converted to light, only about 10%; most of the rest of the energy becomes heat. "Flourescent" lights are much more efficient. These devices have a mercury vapor inside them which is caused by a very high voltage across the ends of the tube to emit radiation; unfortunately, most of this radiation is in the ultraviolet region which is not visible. To remedy this, the tube is coated with a material called a phosphor. When ultraviolet radiation strikes the phosphor, it is absorbed and reemitted as visible light. (You may have seen a "black light" which makes some clothing, posters, etc. glow; it is an ultraviolet light and the the glowing things are phosphors.) If you fill the tube with other gasses it will often glow with visible colors without a phosphor, e.g. neon will glow orange.

QUESTION:  
If I hold a bicycle wheel (with an axle) that the wheel is free to spin about, and I hold the two ends of the axle in each hand, how would I would I find the minimum rpm (rev/min) that would allow me to hold it in one hand & it not fall to the ground? There has to be a minimum value for this horizontial gyroscope's angular velocity.

ANSWER: 
This is a very complicated question. In fact the top (I will refer to your wheel as a top) begins to drop the instant you let go of it regardless of how fast it is spinning and then "nutates" as it precesses. However, there is a simple formula which tells you the minimum angular velocity of the wheel (which is only valid for the angle q  with the vertical unequal to 90^o): S_min=[4mgI_s cos q ]^1/2/I where I_s is the moment of inertia of the top about its symmetry axis and I is the moment of inertia about an axis passing through the pivot point and perpendicular to the symmetry axis. For example, a top straight up spins in a vertical direction until the the angular speed drops below S_min= [4mgI_s]^1/2/I and then falls. You should get a book on intermediate mechanics (e.g. Marion and Thornton or Fowles and Cassiday) to study this very beautiful problem.

QUESTION:  
Why is the difference between the deviation produced by a prism onto red light and blue light called angular dispersion, and that of yellow light called mean deviation?

ANSWER: 
I will venture a guess. Red and blue light are approximately the longest and shortest wavelengths of the visible spectrum, and the angle between them is therefore a measure of the total dispersion of the system over the visible spectrum. Yellow light is in the middle of the spectrum and so its deviation is about halfway between red and blue, so this is the approximate mean (average).

QUESTION:  
I read on your website that electrons flow on the surface of a wire/conductor for AC currents, known as the "skin effect". I was wondering why this happens for AC currents and not for DC currents?

ANSWER: 
The thing which pushes the electrons out to the surface is the magnetic field. There is always a magnetic field for any current, but its effect on DC currents is small. However, if the current changes with time, then so does the magnetic field. It is beyond the scope of this site to work out the details, but new phenomena appear with time varying magnetic fields which result in much less negligible effects of the magnetic fields on the electrons; this does not become important until the frequencies are radio frequencies (MHz or more).

QUESTION:  
Why are objects as seen using mirrors closer than they appear to be?

ANSWER: 
The blunt answer is that they generally are not. If you stand in front of a mirror, your image is precisely as far behind the mirror as you are in front of it. You are probably referring to the sideview mirrors in cars which have a warning imprinted on them about objects being closed than they appear. The reason is that the mirror is convex rather than being flat like your bathroom mirror; convex means that the mirror has a curvature such that it is a portion of the outside of a sphere. (A concave mirror has a curvature such that it is a portion of the inside of a sphere.) The reason for this is that you will get a wider view of what is behind and beside you. I cannot give you a tutorial on optics here, but you can read about it in any elemtary physics text or many web sites, for example here.

QUESTION:  
Is there any instance (hypothetical or not) that only one of the four fundamental forces is at work or acting?

ANSWER: 
Since most particles in nature have mass, gravity is always at work there (even if negligible). Furthermore, if you are in a region of space which contains mass, even a massless particle (nowadays only photons are thought to be massless). But there is a hypothetical situation. Suppose that you have an electromagnetic wave propogating through totally empty space. Then there will be electric and magnetic fields so only the electromagnetic force exists. You could split hairs, of course, and say that it is a field, not a force, which is in the space through which the wave travels. 

QUESTION:  
Ok, i know what E=MC² is, but do you have a DETAILED description explaining it ? Do you have any examples of it that i can teach to a senior (College) class ?

ANSWER: 
It basically says that mass is a type of energy. You need to know, of course, what energy is. In a nutshell, energy is what changes about something if you do work on it, that is if you push on it over some distance. For example, if you push hard on a baseball at rest over a couple of feet (i.e. pitch) you do work and impart to the baseball kinetic energy which it did not have before. If you take a baseball on the floor and lift it up to a table top, the kinetic energy has not changed but work has been done lifting it; here you have imparted gravitational potential energy to the baseball. 

With that said, let us give an example of an experiment which could be done to prove that mass and energy are interchangeable. Suppose that we take an atomic nucleus, for example the nucleus of the most common isotope of carbon which consists of six protons and six neutrons, and rip it all apart into its 12 constituent pieces. Will this take work? Of course, because otherwise this nucleus would not exist since there would be nothing holding it together. Before we rip it apart we should measure its mass; I will call that M_C. After we have finished, we have done an amount of work W and have six protons, each of mass M_p and six neutrons, each of mass M_n. Does M_C=6M_p+6M_n? Someone who has studied chemistry is very likely to answer affirmatively to this question but the answer is no and it is not a hypothesis, it can easily be done. In fact the mass of the sum of the parts is larger than the mass of the nucleus and E=Mc² gives the result: W=(6M_p+6M_n-M_C)c². The mass gained is not some trivially small amount--it is on the order of 1%. Nuclear energy, of course, is where the energy from nuclear power plants and nuclear bombs comes from.

QUESTION:  
If spring scales (bathroom scales) measure weight (force), and Dr.'s scales measure mass, why do I "weigh" the same on both the spring scale and the balance in the Dr.'s office?

ANSWER: 
Both scales measure weight, they just do it in different ways. The spring scale measures the force necessary to compress (or stretch) a spring by a certain amount; knowing the properties of the spring, the scale can be calibrated. The doctor's scale is essentially a balance where your weight is compared with a known weight; the idea of torque is also used where perhaps 1/10 your weight is needed to balance your weight. Weight is a force, and mass is, conceptually, a very different thing: mass measures the resistance (inertia) which something has to acceleration when you push on it. Because of one of the most fortuitous "accidents" of nature, it just so happens that weight is exactly proportional to mass, so measuring weight turns out to be equivalent to measuring mass. The "accident" is that inertial mass is precisely the same as gravitational mass (which is a property of matter which measures how strongly its gravitational attraction to other bodies is). We now understand that this is not an accident; the theory of general relativity fully explains this equivalence. 

QUESTION:  
I teach AP physics in a high school in michigan, and can't seem to reconcile these two facts: The electric field due to an infinite conducting sheet with surface charge density sigma is E=sigma/Epsilon_0.  If I introduce an oppositely charged infinite conducting sheet facing the original, by superposition, I get that the field between them should be double in strength, i.e. E= 2*sigma/epsilon_0. However, gauss's law, using a cylinder with one flat face between the sheets and one face within one of the conducting sheets still gives me E=sigma/epsilon_0. Where is the flaw in my logic? When I look at the field lines, I see that the oppositely charged infinite sheet doesn't introduce more, since every positive charges field line on the positive sheet must end on a negative charge, either at infinity or on the negative sheet, but that doesn't explain to me why superposition doesn't seem to work here.?

ANSWER: 
The problem you are having is rather straightforward. You are correct in saying that with two sheets the field is twice as large between the plates; however, the field outside the plates, also by your superposition argument, is zero. Thus, when Gauss's law is applied there is no flux leaving the surface outside, which gives twice the field inside: e₀E₁*(2*A)=s A with one plate and e₀E₂*A=s A with two, so E₂=2*E₁

QUESTION:  
Since the orbital period of a satellite in near-earth orbit is much less than 24 hours, why does the earth itself rotate only at that rate? If the earth had formed from a collection of infalling particles, wouldn't they have been rotating at the average orbital period based on their distance from the centre of mass?

ANSWER: 
The orbital velocity has nothing to do with the earth's rotation. Suppose that when the earth formed it did so from a large number of rocks all at rest. Each would fall toward the center of mass and the resultant earth would have no rotation; the near-earth orbit would still be the same, though, because it depends only on the mass and radius of the earth. The real key to understanding how the earth rotates is to understand that how it ends up depends on how it starts and the operative concept is angular momentum. Angular momentum of the earth is the same as it was before the earth was formed; as the distribution of mass changes the angular momentum stays the same but the angular velocity changes. If the present day earth were suddenly to shrink to half its current radius, the length of a day would shorten by a factor of four, 1 day = 6 hours.

QUESTION:  
Is the amount of matter in the universe constant? A related question is can new matter be created?

ANSWER: 
Matter and energy are interchangeable, so matter can be created by adding energy to a system. The best known example is called pair production: a photon (quantum of light) may spontaneously create an electron/positron pair (a positron is the antiparticle of the electron). Another example is that the mass of the nucleus of an atom is less than the mass of all its neutrons and protons, so when that nucleus was made (probably in some star) a little bit of matter disappeared from the universe. Obviously, the amount of matter in the universe is not constant, but the amount of energy, we believe, is.

QUESTION:  
While helping my daughter in grade 5 with a wind power project I was wondering how to measure in a simple way the wind speed of the fan. We thought to try the approach where you suspend a ping pong ball from a thread. A table exists which relates angle of swing to wind speed. However I was wondering about the physics of it. 

If you have a ping pong ball suspended from a 30 cm thread and the ping pong ball weights 0.0027 KG then if a wind blows the string at an angle of 30 degrees from the vertical, then what would be the wind speed. What formula would you use if you ignore the aerodynamic effects of the wind going around the ball etc. I am helping Raeann with her wind power project. So we have a room fan that we use to drive a wind turbine (propeller hooked to a motor). It would be nice to measure the wind speed of the fan. It is expensive to buy a real anemometer so people on the net have published a table that relates ping pong ball angle to wind speed. However I was interested if you could calculate this. So the force downwards is mg for the ping pong ball. The tension onthe thread would have a downward force and a sideward force component. The sideways force would have to be matched by the pressure of the wind. Wind pressure would include the density of air and the cross section area of the ping pong ball I would imagine. Also there is the potential energy of the ball lifting up so many meters would be matched by the kinetic energy of the ball. So any thoughts. [Questioner also included data which came from http://marsville.enoreo.on.ca/mission/challenges/anemometer.htm .

Angle kph 
90 0.00 
85 9.30 
80 13.20 
75 16.30
70 19.00 
65 21.60 
60 24.00 
55 26.40 
50 29.00 
45 31.50 
40 34.40 
35 37.60 
30 41.50 
25 46.20 
20 52.30 .]

ANSWER: 
If you plot your data, angle as a function of wind speed, it will not be particularly enlightening. Before plotting anything you should think about the physics. This is the simple pendulum problem except with a horizontal force which keeps the ball at a particular angle. I will not do the details which you can get in any elementary physics text; I will give the results. Let us call the (horizontal) force of the wind on the ball F, the (vertical) weight of the ball W, and the tension (along the string) in the string T, and the angle the string makes with the horizontal q. Then, solving this problem we find that T=W/sinq  and F=Tcosq =Wcosq /sinq . To understand the physics, therefore, you should plot F as a function of cosq /sinq .  I have done this in the plot on the right. The black crosses are the data, the red line is a fit. In essence, what you find by fitting the data is that this is almost a perfect parabola, that is the force is proportional to the wind speed squared. 

If you want to now calculate the force of the wind on the ball, it is approximately F=W 0.001 v² where v is the speed of the wind in km/hr. Once you know the force, you can deduce the angle q =arctan[W/F]=arctan[1000/v²].  For example, if v=24,  q  = arctan[1.74]=60.1 degrees, in pretty good agreement with the data above. It is interesting that the length of the string is irrelevant; also, you do not need to know the weight of the ball as long as you have the quoted data. Probably more useful to you would be the inverse of this equation, v=[1000/tan q ]^1/2 ; for example, if the angle is 30 degrees, v=41.6 km/hr.

For common wind speeds on things about the size of ping pong balls, wind resistance is roughly proportional to speed squared. This is not always the case and it can also be proportional to the wind speed or to some combination of linear and quadratic.

So now you understand things. Perhaps the simplest thing to do is just take the given data as the "calibration" of your instrument and then, having measured the angle, interpolate.

QUESTION:  
Someone in an internet forum claims that Einstein's Theory of General Relativity shows that a geocentric model of the Universe is entirely equivalent as a heliocentric one. Is he right?

ANSWER: 
First, it is the solar system which we should talk about, not the universe. Geocentric has a specific meaning, namely that the earth sits still and the sun goes around us. But, as we all know, this is not a possible explanation using the laws of classical physics. What this person was probably referring to is that the principle of general relativity states that the laws of physics are the same in all frames of reference. That is, you may equally well understand the motion of the solar system from the perspective of a coordinate system tied to the earth as tied to the sun. This does not mean that geocentric and heliocentric are equivalent but rather that the question of who is at the center is meaningless.

QUESTION:  
Have scientists been able to accelerate a particle past the speed of light? Or at least up to the speed of light?

ANSWER: 
A "massless particle" necessarily must travel with the speed of light (like a photon, the particle associated with light itself). But, if a particle has any mass, it may become arbitrarily close to and below the speed of light, but never equal to or greater. The easiest way to understand this is to understand that the mass of a particle increases as its speed increases in such a way that the mass approaches infinity when speed approaches that of light. It therefore would require an infinite amount of energy to accelerate a particle to the speed of light and, of course, there is not an infinite amount of energy in the entire universe.

QUESTION:  
I am a sophmore in high school and i have a question that i thought of while in chemistry. Is it possible to trap light(laser beam would probable work best) using mirrors that would continually bounce the light off each other without letting the light escape? If this is possible will the light still be there even after the original light source was shut off?

ANSWER: 
Yes, that is possible but you need to devise a mirror which is perfectly reflective and that is not such a trivial thing.  Think about a one-dimensional trap, two plane mirrors one meter apart. Suppose that they are 99% efficient at reflecting the light (much better than your bathroom mirror).  And, you have trapped a beam of light in there (easiest to think of it as a very short pulse moving back and forth.  Each time it reflects it will loose 1% of its intensity.  Now, the speed of light is 3x10⁸ m/s, so the time between when the pulse leaves one mirror until it hits the other is 0.33x10^-8 s, that is it has 300,000,000 collisions per second. If it loses 1% each collision, there will not be much left after a second.

QUESTION:  
What causes say, wood or metal, to bend and break? If I were to put a board on bricks and hit it hard/fast enough it would break because it causes shear (I believe) but what would cause the board to break, say I was in space and I hit it extremely hard? It would definetely still break but nothing is pushing on the outsides of the board so why wouldn't the board just go forward rather than bend and break?

ANSWER: 
Suppose you have a board of length 2L and you exert a force F in the center.  Then there will be a torque FL about one end.  You should think of this torque which breaks the board.  If the ends of the board are held fixed, there will be four forces on the board, a force N up on each end of the board, the applied force F, and the weight W as shown in the figure.  So, you can see, the torque about one end is (F+W)L-2NL=(F+W-2N)L.  Now, if you are in empth space, the forces N and W go away, but there is still a torque about the end due to F.  So pushing on the object will do two things: accelerate it (because of the unbalanced force) and deform it (due to the unbalanced torque).

QUESTION:  
A friend and I were discussing ballistics at a 1000 yard target shooting match and need some expertise on a question. If two bullets leaving the same caliber rifle with the same ballistic coeffiecents are fired with the only difference being the weight of the bullet (for example, 300 gr versus 150 gr), which bullet will incur the most wind deflection?

ANSWER: 
I know little about ballistics. As best as I can tell (with a cursory internet search), a ballistic coefficient tells what the air drag on a bullet is for a particular velocity. So, imagine that you have two bullets which have the same speed and therefore experience the same force F due to air friction. Newton's second law tells us that a=F/m, so the one with less mass has a greater acceleration and so it will lose its velocity more quickly. For the same reason (a=F/m), the lighter bullet is likely to have a larger muzzle velocity (the speed it exits from the rifle) if the force propelling the two bullets is the same. The air friction force F depends on the speed v, probably approximately like F=cv² where c is a constant (probably related to your ballistic coefficient). Therefore, the lighter bullet probably experiences a bigger F than the heavier one. Looks to me like the heavier bullet wins on both fronts.

QUESTION:  
My husband and I may get divorced over this question!  We both have our positions, so maybe you can help us out.  It's extremely cold here in Calgary, about -20 celcius, and this came up on the way home after starting up a very cold car.  When starting the car, after the temperature gage starts to indicate that the engine is warming up, my husband cranks the heat full blast.  It's my position that if he were to keep it at a low setting, the air coming out of the vent would be warmer, just not as much of it.  If we select the high setting, the temperature coming out of the vent will be cooler.  I think this is because it is forced air, and cold air is being added to warm air from the engine that is not so warm yet, thereby diluting it.  Once the engine has warmed up enough, the effect of the forced air created by cranking the heat is irrelevant because the engine is very hot (meaning that the temperature of the air coming out of the vent is the same at any setting, once the engine is hot).  He says that the setting of the fan does not change the temperature coming out of the vents at the same engine temperature. Which one of us is right????

ANSWER: 
Well, it depends on what you want. If you want the air to be as warm as possible coming in, you are likely right. On the other hand, what you probably really want is to maximize the rate at which your car is heating up and, in that case, your husband is likely right. I say "likely" for the following reasons. Heat will be transferred from the heating coils to the air passing over them at some rate and that rate may or may not depend on the rate at which air is flowing over them.  One possible scenario is that the rate is about the same regardless of whether the fan is high or low, i.e. maybe the same amount of heat per second is achieved with either fast or slow air flow; in this scenario, the air from the slower fan will be warmer than from the faster fan but each will warm the car up in the same amount of time because each carries the same number of calories or BTU or whatever per second. It is my guess that your husband is right if you want to heat the car up as soon as possible since I would guess that fast air blowing across the heater coils would take the heat away faster from the coils. 

But, as is often the case in science, there is nothing to take the place of a measurement and that might be what you have to do to get a definitive answer. Let us make up what an experiment might measure so you can see how you could definitively do a measurement. The first thing you need to know is that the energy contained in a gas is proportional to its absolute temperature, i.e. E=a(T+273) where a is some constant, E is the energy, and T is the celcius temperature; the 273 is to convert T to absolute temperature (-273 C is absolute zero). Suppose that the temperature of your air is 15 and your husband's is 5.  Then, the same volume of air contains energy in the ratio E_wife/E_husband=288/278=1.036 (you are winning so far!)  But, the volumes of air are not the same--your husband's method moves, let's say, twice as much air, so E_wife/E_husband=1.036/2=0.518, your method now losing out by nearly a factor of two. This is not definitive since it depends on the relative temperatures and air flow volumes. I expect, as I said above, that the way to warm up the car the fastest is your husband's.

QUESTION:  
Hey, do different frequencies of light have different amounts of heat energy attributed to them? In otherwords, is UV light hotter/cooler than visible light?

ANSWER: 
Any frequency of light may carry any amount of energy--that is what the intensity of the light is. However, we know that light is made up of many photons, each carrying the minimum energy that such a frequency can carry.  The energy E of a photon is determined by by the frequency f by the relation E=hf where h is Planck's constant (an extremely tiny number).  Therefore, one photon of UV carries more energy than one photon of visible light because its frequency is higher.  So, UV light of the same intensity as light in the visible range has fewer photons.

QUESTION:  
I was told to ask this question to a phyicist, so here goes. Where did air come from?

ANSWER: 
Well, how far back do we want to go?  All heavy elements (essentially heavier that hydrogen) were produced in stars and then, when the star was "all burnt up", it exploded and sent all the heavy elements flying into space and then they eventually come together again to form planets, etc.  (Scientists like to say that we are all made of "star dust".  Then, depending on the chemistry of the planet, its temperature, and other factors, some of the planet will become an atmosphere, i.e. gases will escape from the surface somehow  In some cases (like the moon) the gravity is not strong enough to hold the atmosphere and it eventually "leaks" off into space.  In the case of the earth, there is virtually no hydrogen or helium in the air because it has all leaked off.  The detailed composition of the atmosphere depends on chemistry and biology.  For example, it is thought that originally the earth had much more carbon dioxide in its air but that evolution of green plants resulted in there being much more oxygen now.

QUESTION:  
Hi.  I was just wondering if you could give me an explanation on why cars cannont fly? I realize that the gravitional pull has an effect on it, but I want to know more specifically all the reasons.

ANSWER: 
Anything can fly.  You simply need to exert an upward force equal or bigger than the weight of the object.  An airplane has wings and the air is made to flow over the wings such that the air pressure on the bottom is greater than the top so there is a force up which, if big enough, can lift it off the ground.  A car could fly if you gave it some upward force; for example, lift it up with a crane!  Or fit it with wings and an engine to keep it moving forward.

QUESTION:  
I am trying to get an estimated maximum wind speed that it would take to blow over a 500 lb security tower that stands 10 feet tall. Can you help me find ways to determine this?

ANSWER: 
You have not given enough information.  The force which the wind exerts depends on the geometry of the tower.  Also, is the tower anchored to the ground in any way?  Look here where I will put a very rough calculation.  The answer, about 60 mi/hr, is about what you would expect, and it is likely that any other calculation would not be a much better predictor.  

QUESTION:  
being that energy is conserved, what becomes of a sound wave in a vacuum (i.e. space)?  where does the energy go that would otherwise go to produce the sound?

ANSWER: 
Imagine that you have, as an example, a vibrating reed.  It has, as you imply energy.  As it vibrates, it loses energy in several ways: 

• As you note, the sound carries away energy.
• As it moves through the air, it experiences air friction which takes energy away; this ends up as heat in the air and in the reed itself.
• There is "internal" friction because the reed is not perfectly elastic; for example, if you have something like a piece of thin metal and repeatedly bend and unbend it, it will get hot because of internal friction.

Those three will be the main modes of energy loss.  Now, if you take away the air, the first two modes of energy dissipation are no longer available and so the reed will simply lose its energy more slowly, i.e. the reed will vibrate much longer before it stops.

QUESTION:  
Hi,  my friend and I were discussing rolling objects down a ramp. I said that if one object is a cylinder and the other is a sphere, with both the same radius and mass, that they both would have the same speed at the bottom of the ramp.  But my friend said that no she thinks the sphere would be going faster.  We are very interested to find out which is right?

ANSWER: 
The rolling object with the smallest moment of inertia will win the race (and hence be going faster at the bottom of the ramp).  A solid uniform cylinder has a moment of inertial I=mR²/2 and the solid uniform sphere has I=2mR²/5.  So the sphere is the winner since 2/5<1/2; but it is a pretty close race.  You can try this experimentally but since it is so close, the results will often not be definitive because of other factors (rolling friction, nonuniformities, air friction, bumpy ramp, etc.).  If you want to try it experimentally, try a race with a cylinder and a hoop (hollow cylinder) which has a moment of inertial I=mR².  Here the solid cylinder should be the clear winner since 1/2<1 by a pretty good factor. 

QUESTION:  
how do waves "rob" energy from one another very rarely to form massive "killer" waves that rise somewhere around 100 feet in the middle of the ocean?

ANSWER: 
I am not really sure here.  Usually "killer waves" refer to tsunamis (tidal waves) which are caused by earthquakes, volcanoes, or other geological catastrophes.  However, water waves, like any others, are subject to the superposition principle which states that if two or more waves come to the same place the net disturbance will be the sum of all the individual disturbances.  Simplistically, think of two waves, each 40 ft high and one comes from the southeast and one comes from the northeast.  If they collide someplace where they are in phase (both are up at the same time) then an 80 ft high wave will appear there.  However, if they collide someplace where they are out of phase (one is up and one is down), that point will be calm.  It is also what happens with a lens which focuses waves: it gets very bright where the light comes to a focus because many waves are adding up.  But it is not a case of "robbing" energy; it is more a case of combining their forces.

QUESTION:  
I just got my last test back in college physics and I got this question wrong,  and I want to find out what was the right way to do it.  

A pitcher accelerates a .14 kg. ball from rest to 42.5 m/s in .06 seconds.
a.) How much work does the pitcher do on the ball?
b.) What is the pitcher's power output during the pitch?
c.) Suppose the ball reaches 42.5 m/s in less than .06 seconds, Is the power produced by the pitcher in this case more than, less than, or the same as the power found in part b. Explain.

ANSWER: 
a.) The work done is equal to the kinetic energy change.  Since the ball started at rest, W=mv²/2=126.4 J.  
b.) The average power is the work divided by the time it takes to deliver that energy.  P=W/t=2,107 W.
c.) If the same amount of energy is delivered in less time, the power will be greater.

QUESTION:  
If a puck slides across ice, and slows from 45m/s to 44 m/s in 25 m. , why does after another 25 m. does it slow to less than 43 m/s?

ANSWER: 
The force on the puck is approximately constant and so its acceleration is constant.  Suppose that it takes a time t₁ to go that first 25 m.  Then it will take it t₁ until the speed decreases to 43 m/s.  But, it is, on average, going more slowly during the second t₁ and so it will go less far than 25 m.

QUESTION:  
Reflected light wave will have a phase change of 180 degrees at denser medium, say when it travels from air to glass. The speed of light in glass is smaller than that in air and we define glass as a denser medium. For sound wave, its speed in air is smaller than that in glass. Should we define air is a 'denser' medium for sound?

ANSWER: 
For any kind of wave, reflection at a boundary will have a phase change if the speed in the medium from which the wave is reflected is smaller than the speed in the medium in which waves are traveling.  

QUESTION:  
At the most fundamental level, exactly where does the energy from fusion and fission come from? I know e=mc^2 describes how much energy, but not the process itself. I know about the curve of nuclear binding energy. E.g, when four hydrogen nuclei fuse, the resultant helium atom has less mass and the excess is released as energy. But where exactly does the energy come from? Is it correct to say the strong nuclear force ultimately provides this? Or is simply an intrinsic process we accept ("it just happens")? At the lowest level, is there a describable mechanism by which matter stores energy, or by which the mass->energy conversion releases energy?

ANSWER: 
It does indeed come from E=mc².  And yes, it comes from the strong interaction.  The example you state (4H going to 1He) is not a good one because it is incorrect because two of the protons have to turn into neutrons + electrons which complicates things (but happens ultimately).  Better to fuse two deuterons (nuclei of "heavy hydrogen" which consists of a bound neutron and proton) into an alpha particle (a He nucleus).  As you correctly state, energy is released because the mass of an alpha particle is smaller than the mass of two deuterons.  It comes from the process of their becoming bound together so, as you suggest, the strong force is responsible.  It is perhaps easier to understand to think of the reverse process: in order to pull apart an alpha particle into two deuterons, you must supply work, right?  Where does the energy that you put in go?  It goes into mass.

QUESTION:  
If two trains,one loaded with lead, the other empty, are travelling at 60 miles per hour on identical flat tracks and at the same time their engines were put in neutral which one would travel further and why?

ANSWER: 
It all depends on the friction which each train experiences.  Normally we think of friction between surfaces sliding on each other as increasing as those surfaces are pressed to gether harder.  The wheels are not slipping and furthermore being steel are not very deformable, so their contribution to the friction is rather small and probably similar for the two trains.  However, there are bearings which have some friction and the friction will surely get larger as you increase the force (coming from the train's weight) on them.  So, the heavier train will have more friction and therefore go less far.

QUESTION:  
I learned that the interior of canons when smooth provided less accuracy.  When we learned to machine a spiral on the interior it increased the accuracy much like a football  through is more accurate if you put a spin on the ball when releasing it.  Why does setting a spin on a projectile increase the accuracy of that projectiles aim?

ANSWER: 
You are right--the rifling (which is what the machined spirals are called) imparts spin to the projectile.  Why should that help accuracy?  Well, if something is spinning it will continue pointing in the same direction forever unless there is some external torque on it (this is how a gyroscope works); this is called conservation of momentum.  It is well known that such a projectile is more accurate.  But the reason is not just that it is spinning and not "tumbling".  It has to do with the interaction with the air; a tumbling projectile will tend to be deflected by the air it is moving through more during its trajectory than one which is not tumbling.  If there were no air, any projectile, no matter how it spun or tumbled, would be equally accurate since the center of mass would move as if it were a simple point.

QUESTION:  
why is Ke=1/2mv^2; especially if it takes onlytwice as much rocket fuel to accelerate it to twice the speed?

ANSWER: 
I do not know where you got the idea that twice the fuel results in twice the speed. That is incorrect. But you are correct in your implication that twice the fuel will not result in twice the kinetic energy. The problem is that when you burn fuel, a certain amount of energy is released; but, you also "throw out" the burnt fuel. In order to conserve the momentum of the system, you cannot give all of the released energy to the rocket--the spent fuel gets some of it.  So looking at the relation between energy released to the energy gained by the rocket is not a useful thing to do.  To answer your question, though, the reason we define kinetic energy as mv²/2 is because if you do work W on a particle, its kinetic energy increases by exactly W.

QUESTION:  
In rotational motion of a rigid object why are torque, angular momentum, angular velocity and angular acceleration as vector quantities defined along the axis