Ask the Physicist!

home
the physicist
groundrules
answers
old answers
donate

Old Questions and Answers

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

QUESTION:
If Hydrogen is the simplest molecule, was it also the first?

ANSWER:
I presume you mean simplest atom. It is believed that the very early universe was nearly pure hydrogen with a small amount of helium and a smaller yet amount of lithium.

QUESTION:
Free neutrons are unstable. But free nutrons are used in fission reactions, neutron scattering and other processes. How is that possible? Don't the neutrons get converted into protons on the courese of motion?

ANSWER:
The average lifetime of a neutron is about 15 minutes, so their use in the applications you mention is not appreciably affected.

QUESTION:
What is meant by "spin = 1/2" for elctrons? DOes it have anything to do with the spinning of electrons?What is the physical significance of the quantity "spin quantum number"?

ANSWER:
Elementary particles, like classical particles, may have angular momentum. A particle may have orbital angular momentum (like an electron orbiting around the nucleus in an atom or like the earth orbiting the sun) or it may have intrinsic angular momentum (like the earth spinning on its own axis or like the spin angular momentum of the elementary particle). When one goes to the microscopic level of elementary particles, angular momentum is quantized, that is only discrete amounts of angular momentum are allowed; for example, if the angular momentum quantum number of a particle is L, its angular momentum is [h/(2π)]√{L(L+1)} where h is Planck's constant. For a spin ½ particle, the intrinsic angular momentum quantum number is ½ and so the particles intrinsic angular momentum is h√3/(4π). Although it is sometimes described as spinning of the particle about its own axis, this is a classical picture which is useful only as a rough means of understanding what spin is. For example, it is impossible to do anything to change the spin of the particle.

QUESTION:
All the diagrams of electromagnetic waves that I have seen in textbooks show the electric and magnetic waves being 180 degrees out of phase. I always thought that the decay of one field caused a buildup of the other and that this would put them 90 degrees out of phase. Are the pictures wrong?

ANSWER:
I do not understand what you mean by phase. In the figure to the right the electric and magnetic fields are in phase; this is the diagram you normally see. The fields are in phase in a vacuum or a nonconducting medium. In a conducting medium they are not in phase, but I do not think that is what you are interested in. This phase relationship is what is predicted by solving Maxwell's equations. What is shown here is what is called a sinesoidal plane-polarized plane wave; the wave fronts are infinite planes, the electric fields are everywhere along one dimension and the magnetic fields are everywhere along one dimension perpendicular to the direction of the electric fields.

QUESTION:
if an object falls towards the earth is because it is atracted by the earht's gravity OR it is because it's following the path of the space curved by the earth's mass and density? Second, is it true that every object in space is affected by the gravity of every object, but in very very very small quantities?

ANSWER:
Our best understanding, based on general relativity, is that it is the latter—space-time is curved. But the consequences of general relativity can be understood as saying that objects with gravitational mass attract each other. Certainly, any object with mass will attract any other.

QUESTION:
I am wondering if my idea is valid, since I have never seen it used before. It seems to me that a rocket launched vertically wastes a great deal of fuel just overcoming inertia AND gravity; and it seems to me that a rocket launched on a horizontal track, like a roller-coaster, which curves upward to the vertical would overcome inertia immediately, and upon leaving the vertical end of the track , would already have attained great speed. Can you tell me the pros and cons of this launch method?

ANSWER:
In the absense of friction it makes no difference how you get from point A to point B because the forces are conservative. You make it sound like you just overcome inertia and then can move on to overcoming gravity. In fact, the rocket has the same inertia regardless of its motion, it is not something you can just get rid of. Using a horizontal track would increase the friction compared to air friction, so it would be less efficient overall. Since the rocket will go very fast, air friction becomes important and so going vertically originally gets you out of the atmosphere as quickly as possible. You can get a little boost by using the rotation of the earth; that is why launch sites are as far south as practicable, for example France launches from French Guiana in South America.

QUESTION:
I have been reading about the new LHC (Large Hadron Collider) that will begin running in Europe soon. I noticed that the LHC will use proton-proton collisions. My question is, why did they decide to use proton-proton collisions instead of proton-antiproton collisions? It seems to me that proton-antiproton collisions would be more advantageous since protons and anitprotons attract and are therefore easier to make collide and protons and antiprotons also produce a disintegration energy when they collide that would add to the attainable energy of the collider.

ANSWER:
The main reason is that it is difficult to get an intense antiproton beam; the antiprotons first have to be made and then bunched together and accelerated. When doing experiments that look for rare events, intensity of the beam is paramount to give one a chance to see the event. Also, your ideas regarding an advantage from the attraction or the "disintegration" is flawed because the kinetic energies (TeV) are so high that the weak coulomb attraction is a negligible component and the mass energy of a proton-antiproton pair (around 2 GeV) is also neglibible.

QUESTION:
My Physics teacher was talking about electrons moving further away from the core when the atom is heated, and then unleasing energy as they move back, when the atom gets colder again... My question is; would it be theoretically possible to utilise that energy to knock a proton out of the core, or make it change polarity and remove itself from the core?

ANSWER:
No, not possible, because the energies associated with atoms is thousands of times smaller than the energies associated with nuclei. Also, the polarity of an electric charge (proton, for example) cannot change.

QUESTION:
My understanding of the nuclear fusion reactions, that are to be the basis of proposed thermonuclear fusion reactors of the future, is that a significant neutron flux is created? How is the structural integrity of the walls of such toroidal reactors going to be maintained, if bombarded by the neutron flux for extended periods?

ANSWER:
You have just hit on one of the many reasons why controlled nuclear fusion has proven so difficult to realize. It still seems decades away from realization. I have heard that it is generally accepted that the containment vessels will have to be changed periodically. That is by far not the most difficult problem faced.

QUESTION:
Is it possible to manipulate magnetic fields? If so, how?

ANSWER:
Of course. If you have a magnet and move it around you are manipulating the magnetic field. If you have an electromagnet you can vary the current to vary (manipulate) the field.

QUESTION:
Yesterday my manager came into work with a cup of water that had frozen in his car overnight. There wasn't a straw, or anything else, in the cup. But the ice, instead of being flat, had what looked like a thin, inch-long shard of ice sticking diagonally out of it. Also, the rest of the surface was kind of wavy, like hardened lava. Why would a frozen cup of water make that strange formation?

ANSWER:
This question has been previously answered.

QUESTION:
It is a simple question, but one that has great meaning for me. I am PhD biologist retired and playing around in a new area. Three bodies in a fixed volume have a fixed total momentum, distributed in the first case evenly, (5, 5, 5), and in the second case unevenly, say, (9, 5, 1). Are the collision rates the same? The answer I would prefer to hear is that the unbalanced case has a lower collision rate, though my instincts from Resnick and Halliday studied long ago fear that the collision rate of the system is just a simple function of the total momentum. Which? Use energy distribution instead of momentum distribution if that makes things easier.

ANSWER:
An important concept here is mean free path (L) which is the average distance a particle travels before encountering a collision. The mean free path depends only on the density of the gas (number of particles per unit volume) and the size of the particles. Average time between collisions will therefore be L/v where v is the average velocity of the particles. (So collision rate would be v/L.) So, in your example, if the masses of the three particles are the same, the average velocities would be the same and the collision rates would be the same. So what you need to look at is not the relative momenta but rather the relative speeds if the masses are unequal.

QUESTION:
If the acceleration of an object toward Earth is independant of it's mass, where is my logic wrong in this hypothetical situation: Suppose there are two objects. One is a golf ball. The other is an object the same size as the golf ball but with significantly larger mass than the earth (say 1,000,000,000 times the gravity of the sun). If you were to time the golf ball falling to earth and the object falling to earth from the same height at the same position in space, it seems they would not fall at the same rate. The object of larger mass would pull the earth instead of the earth pulling it. Since our reference point is the earth, we would see the object "falling" to earth just like the golf ball. But because the gravitational force of the object is many times greater than the gravitational force of the earth, it would have a faster acceleration than "g". So what I'm getting at is that from my limited understanding of this stuff, it seems like mass is negligible only if the mass of the falling object is NOT significantly larger than the object it is falling "towards". But mass is not supposed to matter in a free fall situation. Where am I confusing myself?

ANSWER:
Both objects will have the same acceleration, g. The reason is that each particle experiences a force F proportional to its mass m and each also has an acceleration a=F/m so the acceleration does not depend on the mass. But, Newton's third law says that in each case the earth feels an equal and opposite force due to other object. But the acceleration of the earth toward the golf ball will be unmeasureably small because the force is small and the mass of the earth is big; so the earth will essentially sit still while the ball falls. But the other object has a huge mass and so it exerts a huge force on the earth; so the earth will accelerate "up" with an acceleration much larger than the object accelerates "down", and comes up to meet it. In each case, the object has the same acceleration but the earth has different accelerations. It will therefore take a much longer time for the golf ball to hit the ground than the heavy object even though their accelerations are the same.

QUESTION:
The first question is about pair production. Could you explain it in a very simple (and yet on track) explanation for about the age of 13? The second question is about the law of conservation of mass/matter. While the universe is expanding, does this law apply? Why or why not?

ANSWER:
In future, please abide by the groundrules which stipulate single questions. Second question first: There is no such thing as conservation of mass/matter; in chemistry, it was one of the keystones: combine 16 grams of oxygen with 2 grams of hydrogen and get 18 grams of water. However it turns out that this is not quite true because of E=mc²; some energy is released when you burn hydrogen and this consumes a little mass. However, the chemistry rule is very close to true for chemistry because the energy released is tiny compared to the energy of all the mass. But it is not true for nuclear fusion which is what fuels stars like the sun and these stars get measurably lighter as they age. What is true is conservation of energy for a system (including mass energy).

Your first question answer: Again we are dealing with E=mc²; if we consider a photon (which is a little bundle of light), it has energy. The shorter its wavelength, the more energy it has. For very energetic photons, called gamma-rays, their energy might exceed the mc² energy of an electron plus a positron (the antiparticle of the electron, having the same mass but opposite charge as the electron). If this is the case, then it would not violate energy conservation if the photon suddenly turned into an electron-positron pair. For example, suppose that we have a 1.5 MeV (million electron volts, a unit of energy convenient for this kind of problem, look it up!) Now, the rest mass energy of an electron or positron is about mc²=0.5 MeV, so the photon could turn into a pair and that pair would have, in addition to their mc²energy, about 0.5 MeV of kinetic energy. That is pair production. (By the way, this will not happen spontaneously because a photon is a stable particle; instead you must "tweak" it which is usually done by shooting the photons into a strong electric field like that near the nucleus of an atom.

QUESTION:
im doing a project and im in 7th grade im trying to figure out how to measure the energy someone uses during the hours of a day i just dont know what the formula is to measure how much energy someone uses do you know?

ANSWER:
As a 7th grader, you should learn right now: physics is not about formulas, it is about thinking! Now, the question you ask can never have an answer because it all depends on how energy is used and what energy you want count in the your survey. For example, if I drive a car I would need to know how many miles I drove, what the energy content of a gallon of gasoline was, and how many miles per gallon my car consumed. I will give you one fairly simple example you can use if it is electrical energy you want to calculate. Most devices are rated by specifying their wattage; for example, a 100 watt light bulb comsumes 100 joules per second (a joule is a unit of energy). So, if I burn a 100 watt light bulb for one hour I consume 100 (joules'second) x 3600 seconds =360,000 joules of energy. So your formula is wattage x time (in seconds) = energy (in joules). A more familiar unit of energy is the kilowatt-hour. One kilowatt-hour is the energy consumed in an hour by a 1000 watt device (a kilowatt is 1000 watts) or 3,600,000 joules. If you look on your parents' electric bill you will see that each month you are billed by how many kilowatt-hours your household uses; a kilowatt-hour usually costs between 5 and 10 cents.

QUESTION:
I am a teacher (English teacher, though) writing a program to help visualize relativistic effects for college students (again, in English). I use it to help teach the Modernist worldview. To be accurate, my program needs a very precise definition of the speed of light. Apparently, the last time it was measured was in 1973, when it was 299792.4574 km/sec. My question is: has current technology not allowed us to refine this number to more decimals? I know that the current accepted value is an integer, but that is because in 1983 the uncertainty in the length of the meter was greater than the remaining uncertainty in C, so the meter was based on the then-current definition of C. But this doesn't touch the basic question of whether C has been refined since it was measured in 1973. Can you tell me the best current measurement of c in as many decimal places as possible?

ANSWER:
Well, here is some good news for you: the speed of light is exactly 299,792,458 m/s because the length of one meter is defined (since 1983) to be the distance traveled by light in 1/299,792,458 s.

QUESTION:
why there is no net charge on gaussian surface?

ANSWER:
There is no reason why there should be zero charge on a Gaussian surface. For example, imagine a conducting sphere on which I have placed a certain amount of charge. All the charge resides on the surface. If I say that Gaussian surfaces are concentric spheres, then the charged surface is one of them. Incidentally, any surface you choose to think about is a Gaussian surface as long as it is closed, that is encloses some volume; it just so happens that the most useful Gaussian surfaces are equipotentials.

QUESTION:
What is instantaneous velocity,and can you give me an aexmple using it?

ANSWER:
Average velocity is distance traveled divided by elapsed time. Instantaneous velocity is average velocity evaluated in the limit as the elapsed time becomes zero. This involves differential calculus which is why Newton had to invent calculus to do physics. If you are in a car which is speeding up and you look at the speedometer and it reads 20 mi/hr right now, that is your instantaneous velocity; a little earlier it was less, a little later it will be more. For simplicity I have not worried about the vector nature of velocity; I have assumed that travel is in a straight line like a long straight road. Things get a little more complicated if the path is not straight.

QUESTION:
Is the electromagnetic spectrum truly continuous such that for any two given frequencies, no matter how close together they are, there will always be another frequency between them?

ANSWER:
In principle, the answer to your question is a simple yes. In practice, there is a different answer. No real electromagnetic wave is comprised of a single frequency. Because of the uncertainty principle one needs an infinitely long wave to have a perfectly determined wavelength, therefore frequency. Or one can say that because of the uncertainty principle one needs to observe a wave an infinitely long wave to have a perfectly determined frequency, therefore wavelength. Real waves are of finite extent and therefore contain a distribution of all frequencies. (Determining the details of the distribution is called a Fourier analysis) However, you could have a distribution which peaked at a particular frequency and another which peaked at a frequency arbitrarily close to the first.

QUESTION:
This is somthing that has been getting to me for a while. If a long level is built with a horizontal vial on each end and that level is "calibrated" to work on the earth, will it work if I take it to the moon. Regardless of the moons off-center center of gravity. I Think that the curvature of the surface will be more sever and the distance to the center will be close and this will cause the bubbles to be slightly farther out from the center than they would be on Earth.

ANSWER:
You are correct if the length of the stick is not very small compared to the size of the earth or moon. Otherwise, the effect will be negligibly small.

QUESTION:
i know things don't fall faster at high altitude but it feels like it because there is lower air resistance (right?). In laymans terms, can you please explain to be why air is so thin at high altitudes which makes things appear and feel like the fall faster - Im things particularly in regards to skydivers - they seem to have a little more trouble landing and guiding their chutes in higher altitude.

ANSWER:
When there is less air resistance, things will go faster. If there were no air, the speed would continue getting larger without bound (well, not to the speed of light or higher!) The less air there is the faster an object will go before stopping its acceleration (called the terminal velocity). So, your main premise is wrong—you don't just feel like you go faster, you do go faster. The terminal velocity is also dependent on the mass and, particularly, the geometry; the reason a parachute works is because it has a lower terminal velocity than a rock. Yes, at higher altitudes there is less air resistance so a parachute is less effective; it would be useless if there were no air. The reason the air thins out at higher altitude is as follows. There is a certain amount of air in our atmosphere and, because it has weight, it arranges itself in a layer over the whole surface of the earth. But, the deeper you go into a fluid, the greater the pressure becomes; for example, when you go swimming you can feel the increased pressure by the pain in your eardrums as you go deeper. So, you are at the bottom of an ocean of air. There is a big difference between water and air, though, since air can be compressed and water cannot (for all intents and purposes), so the higher the pressure the denser the air will be. Therefore the air is dense at the bottom and gets less dense as you go up.

QUESTION:
If a spaceship leaves its engine on at full power, will it accelerate forever? (assuming it has endless fuel)

ANSWER:
Well, a really hypothetical question! Yes, it would continue accelerating but as it approached the speed of light there would be less and less velocity increase for each pound of fuel burned because the fastest possible speed is the speed of light. So the energy would keep increasing but the speed would hardly increase at all.

QUESTION:
I thought that magnetic and electric field lines were just convenient representations of how fields varied around charges and magnets, and, in reality the electric field, for example, would vary continously with distance. If this is the case, why do we see lines around bar magnets when sprinkled with ion filings, or lines between parallel plates in castor oil when sprinkled with semolina? What happens between the lines?

ANSWER:
You are right, the lines are just what we draw to convey what the field is like, there aren't really lines. Let me talk just about the iron filings around a magnet since both cases have a similar explanation (polarization). Focus your attention on an iron filing: it becomes polarized, that is it becomes a tiny magnet and it aligns itself with the magnetic field of wherever it is. Now, look at its neighbors: those near its ends will also be polarized but their N(S) pole will be close to the S(N) of our first filing, and they like that; but those alongside it will have their N(S) poles close to the N(S) poles of our first filing and will tend to be pushed away. The net result will be chains of filings separated from each other.

QUESTION:
I am an 8th grade Earth Science Regents student, and I am doing a project on the effect of the density of liquid on magnetism. The problem that I am having is that I cannot calculate the force of the magnet. If the magnet is too strong, it could pull out the object inside the liquid no matter what the density of the liquid is, and no difference will be present between the different types of liquid. How can I calculate the force of the magnet?

ANSWER:
You cannot calculate the magnetic field of a magnet, you have to measure it. It depends on its geometry, how far you are from it, what it is made of, how magnetized it is, etc. Do you have something ferromagnetic inside your liquids? You need to experiment so that your magnet is far enough away so that your sample will not be too strongly attracted but enough to measure. Not to be negative, or anything, but density is not the important quantity here but rather the nature of the liquid itself; is it paramagnetic, ferromagnetic, diamagnetic, etc.? Except for ferromagnetism, magnetic forces are very weak and you are going to have trouble getting reliable results without pretty sensitive equipment.

QUESTION:
When I go into my apartment in the winter, I am full of static electricity. If I touch my metal closet door first, I get an electric shock. I would rate this shock a "2" on a logarithmic 1 to 10 scale. However, if I first turn on the light, I get a shock that I would rate a "3" on the same scale. I do not get shocked by my outlets otherwise and I believe that I have the same static charge for both events. Why is there this difference in the amount of shock? What is the physics that causes additional shock? Is this related to what happens with lightning?

ANSWER:
Electrical codes require that there be a ground for all circuits, and this ground wire is connected to the metal parts of the appliance, lamp, whatever. So, even though one of the two leads to the "guts" of the appliance is also grounded, there is a separate ground for everything which is not electrical. Your door is not necessarily at ground potential. Also, the geometry of what you are touching matters. The door is flat and the lamp presumably has a curved surface; the electric charge on you hand induces a charge on the object you are about to touch which is has a larger charge density on the curved surface resulting in a greater potential difference. By the way, if it is a logarithmic scale, the difference between 2 and 3 is a factor of ten. Is that what you meant? For example, the Richter scale is logarithmic and an earthquake with a Richter scale of 8 is ten times stronger than one with a 7.

QUESTION:
what is a simple formula for calculating the beam divergence of a white light flashlight. Observationally it seems related to the ratio of emitter size to reflector size. E.g, lights with a large reflector diameter (and/or small emitter) seem to produce a more tightly focused beam. A WWII searchlight with a huge reflector produces a very tightly focused beam that converges for a long distance to a "beam waist", then diverges. Details: Assuming a typical white-light focusing flashlight (e.g, Mag-Lite) with a parabolic reflector focused to produce a convergent/divergent beam, how do I calculate the smallest achievable spot size (i.e, smallest beam cross sectional area) at a given distance? How does this vary with reflector diameter, focal length, and emitter source size? I can't just use angular field = arctan (source dia. / focal length), as the beam can be initially convergent then divergent.

ANSWER:
Ah, the neverending quest for simple formulas for a complicated world! There is no such simple formula Unless the source is a point placed exactly at the focus of a parabolic reflector; you must also ignore diffraction and any rays which exit without striking the mirror. In any other case you would have to have to do detailed raytracing which would require knowing the exact geometry of the source and where on the source the focus of the paraboloid was. You would also have to define criteria for quantifying what you mean as beam spot since there will never be a clear-cut spot. This would, of course, be best done with computers. Physics is not formulas!

QUESTION:
I teach AP physics in high school and had a question concerning the electrons of metals. What is the difference between the ionization energy of a metal and its work function ?

ANSWER:
The ionization potential refers to the energy required to remove an electron from an isolated atom. However, the properties of most materials are affected by being in a macroscopic solid, metals in particular. In a metal, the valence electrons are, for all intents and purposes, free to move around, that is they are already detached from the atoms of the metal. To remove an electron from a metal, though, means that you leave behind a positive charge which will attract the electron if you try to remove it, so it takes work to remove an electron from a metal; this is the work function.

QUESTION:
I know what Newton's first law of motion means but could you give me some examples of it? And please make sure they are comprehendible but good enough for a group of teachers.

ANSWER:
They are innumerable! I will give a few:

A spaceship is sent to Mars. Once it has escaped the earth's gravitation and not yet close to Mars, you do not have to keep burning your rockets to keep up your speed; Newton's first law (N1) says that with negligible force an object will move with constant speed in a straight line.

When you stand on a scale there are two forces on you, your own weight (the force the entire earth exerts on you) and the force which the scale exerts on you. Because of N1, the net force on you must be zero (you are at rest), so the force the scale exerts on you must be equal in magnitude to your weight but up. {To carry this a bit further, Newton's third law (N3) says that the force you exert on the scale is equal and opposite the force you exert on the scale and this is the force which the scale registers. A scale does not measure your weight, rather it measures the force you exert down on it which just happens in this case to be numerically the same. If you are in an elevator accelerating upwards, the scale will read something larger than your weight.}

You are pulling a box across a level floor with constant speed. The rope you are pulling on is horizontal. The force with which you must pull is equal in magnitude to the force of friction the floor exerts on the box.

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

ANSWER:
The gravitational force depends on the mass located near that place, so all you have to do is put a huge block of lead under the room to increase the gravity. But the gravitational force is so weak that you would be hard pressed to observe any change since the mass of the earth is so large. I estimate roughly that if you put a 10x10x10 m³ block of lead under your floor that the weight of something in the room would increase by about 2x10^-4%!

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

ANSWER:
The component of the ruler along the direction of motion is shortened from (l₀/√2) to (l₀/√2)√[1-(v²/c²)] while the component perpendicular remains (l₀/√2). You should be able to do the trigonometry from here.

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

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

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

ANSWER:
I have answered questions before which involve frost forming at temperatures above freezing. These involve both evaporative cooling and radiative cooling, so your fiancée has a good idea. However, I really find it hard to believe that this could be the answer to your question since a half inch of ice is a whole lot more than a little frost and the temperature is so far above freezing. I suspect a much more mundane reason: I have sometimes found ice on the top of a bottle of milk but only if the bottle has been put in a particular place in my refrigerator. Some locations of the refrigerator are colder than others because of proximity to cooling coils, a duct to the freezer section, or for other reasons having to do with how the refrigerator is engineered. And, the temperature you suspect, 38⁰, may be inaccurate so that the whole refrigerator is set too low making it even more likely that somewhere will be below freezing.

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

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

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

ANSWER:
Well, you are treading on some pretty difficult stuff here. There are certain aspects of this problem which can be solved using exotic mathematical functions called elliptic integrals, but I suspect you don't want to go there. So let us just say that this problem is one (as are most of nature's real problems) which cannot be solved in closed form in terms of standard mathematical functions. That is, y"+sin(y)=0 is not a differential equation which can be exactly solved. But if we approximate sin(y)≈y, as you have learned in your physics class, it can be solved. But, now you want to do better than that. So you have to use a better approximation for the sine function. Where did the first approximation come from? It came from a series expansion for the sine, sin(y)=y-y³/3!+y⁵/5!-… So, if y is not so small a better approximation would be sin(y)≈y-y³/6. Now you will find that the period is better approximated by T=T₀(1-(A²/8))^-1/2 where T₀ is the period in the small angle approximation and A is the amplitude in radians. For example, if A=90⁰=π/2, T=1.2T₀, about 20% longer. I should warn you that, unless you are pretty handy with differential equations, this is not trivial to deduce. In this day and age, one can solve problems of this type numerically on a computer.

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

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

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

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

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

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

ANSWER:
You're jokiing, right?

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

ANSWER:
First, let me say that your example (which I have not included here) is not a good one. Let me attempt to give an answer to the question regarding zero-g (sometimes referred to as weightlessness). Those terminologies are, strictly speaking, incorrect. What is your weight? It is the force which the earth exerts on you. It is not what is measured by a scale; a scale measures the force you exert on it, not the force the earth exerts on you. Of course, in every day life the force which you exert on the scale happens to equal your weight, but if you are in an elevator accelerating up the scale will read more than your weight. If you are in an elevator free falling down, the scale reads zero but your weight is still the same. If you say zero-g you imply that the gravitational field is zero but that is certainly not true anywhere near the earth (except at that point where the earth's and moon's gravity cancel). I presume that you have taught your students about centripetal acceleration. Anything which moves in a circle of radius R with speed v has an acceleration toward the center of the circle of v²/R. A satellite in a circular orbit has just the right speed such that this acceleration is equal to g so, as you correctly state, it is the same as the free falling elevator—you feel like there is no gravity. All this is standard physics.

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

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

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

ANSWER:
See an earlier answer.

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

ANSWER:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

http://en.wikipedia.org/wiki/Bicycle_and_motorcycle_dynamics
http://socrates.berkeley.edu/~fajans/Teaching/bicycles.html

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

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

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

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

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

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

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

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

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

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

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

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

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

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

ANSWER:
Yes, of course. Untold millions of atoms go both ways. But millions is a really small number compared to the total number of atoms in the objects (like on the order of 10²⁴). But, ultimately this is why clothes get dirty, clothes wear out, things have to be repainted now and then, etc. Also, electrons can go one way or the other which is why you sometimes have a static charge on you after rubbing on something.

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

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

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

ANSWER:
The key is to multiply by 1 so the units come out the way you want them. For example, suppose you wanted to convert 73 miles to centimeters: 73 mi(5280 ft/1 mi)(12 in/1 ft)(2.54 cm/1 in)=73 x 1.61 x 10⁵ cm =1.175 x 10⁵ cm; note that each quantity in parentheses is 1 even though it is numerically not 1. The ones you ask for are easier: N mm(1 m/1000 mm)=N/1000 m; N ms(1 s/1000 ms)=N/1000 s; N cm(1 m/100 cm)=N/100 m.

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

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

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

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

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

ANSWER:
The trouble with having a well-known equation like E=mc² is that it is often used when not appropriate. If you write E=mc², then this is the energy of a mass which is at rest; or else it means that the mass has a different meaning from what you usually think of when it is moving with speed v, namely m=m₀/√(1-(v²/c²)) where m₀ is the mass of the particle at rest, what you usually think of as inertial mass. As I have said in many earlier answers, I prefer to not think of mass as increasing with velocity, m to me just means rest mass. The correct equation for energy is E=√(p²c²+m²c⁴) where p is the linear momentum. So, if a particle is at rest, momentum is zero and E=mc²; if the mass is zero (as is the case for a photon), E=pc. So a photon has momentum even though it has no mass. One thing to be careful of, as explained in my earlier answers, is that momentum is no longer mv but rather mv/√(1-(v²/c²)).

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

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

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

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

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

ANSWER:
The first law is energy conservation. If you arrange so that no heat goes in or out of the gas, then the work done on the gas must equal the increase in energy of the gas. This is called an adiabatic compression (AC). It may be shown that for AC the pressure and volume are related by PV^γ=constant where γ=C_p/C_vand C_p and C_vare the specific heats of the gas at constant pressure and volume respectively. The work done on the gas when you go from P₁, V₁to P₂, V₂is W=(P₂V₂-P₁V₁)/(γ-1). One can easily relate this to the temperature change because work may also be written as W=C_v(T₂-T₁). All the details can be found in any introductory physics textbook. Your qualitative analysis of the moving piston speeding is the gas molecules is a good one. There is no reference in my remarks above about how you get from 1 to 2, so your expectation that the temperature change depends on how rapidly your compress the gas is not right; when you go slowly you give the molecules many little kicks but when you go rapidly you give them a few big kicks. In the real world we usually want the compression to be fast to guarantee that it is adiabatic because it is hard to make a really well insulated cylinder so if you compress slowly heat is more likely to leak out as the gas heats up. But, if it is well insulated it should make no difference. Regarding gravity, it does have an effect but, because the molecules are restless (they can't all settle at the bottom because they keep moving around if the temperature stays constant), the effect is smaller than you expect. In fact, the density of gas at the top of a container is very slightly smaller than at the bottom. You might find this difficult to believe, but it happens for the same reason that the density (pressure) of the air decreases with altitude.

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

ANSWER:
Your questions are not dumb. When we derive the ideal gas law we assume that the collisions of the molecules with the wall are elastic, that is no energy is lost or gained in a collision. This is not necessarily true for any given collision but, if the gas and the walls are in thermal equilibrium, it will be true on the average, just as many collisions gaining energy from the walls as those losing energy. When you are dealing with something like 10²⁴ atoms, the average is what matters, not one particular event.

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

ANSWER:
This question has been previously answered.

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

ANSWER:
Imagine that you are in empty space where angular momentum must be conserved. You start with angular momentum L₀ which is parallel to your spine, say. Later the wheel has angular momentum L₀ perpendicular to the original direction of your spine. So the change in angular momentum of the wheel is in a direction 45⁰ relative to the original direction of your spine so that is the axis along which your angular momentum must have to conserve angular momentum. When you do this experiment you should feel like something is trying to push you off the stool but you can only rotate about an axis parallel to your spine so angular momentum is not actually conserved; the friction between you and the stool exerts an external torque.

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

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

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

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

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

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

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

ANSWER:
The diameter of the ball along the direction of motion will get smaller so the ball will not be a sphere. The volume therefore gets smaller as measured by an observer seeing it zip by. The volume will be reduced by a factor of √(1-v²/c²). That is the easy part of the question. The question concerning the pressure is a very difficult one and I have not found anybody who can give me a definitive answer. I have done a little research and have found more information about temperature than pressure in special relativity. There is a what is called the Planck-Einstein transformation for temperature: the temperature of the gas in the passing ball is reduced by the same amount as the length, that is √(1-v²/c²). So if we now assume that the ideal gas law, PV=NkT, is correct in the moving system, then if V'=V√(1-v²/c²) and T'=T√(1-v²/c²), it follows that P'=P; the pressure is unchanged. That is all well and good, but recent research has shown that the Planck-Einstein transformation is incorrect. In fact it appears that there is no Lorentz transformation for temperature which essentially means that temperature as we define it is not a useful variable in relativity. I suspect that the same could be said for pressure, that is it is not a variable which we could transform into a moving system, there would not be a way you could measure pressure in your moving ball. That is the best I can do with this question. If you get a better answer somewhere, I would be most interested in learning what you learn.

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

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

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

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

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

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

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

ANSWER:
This is really too technical a question for the purposes of this web site. I can tell you that a physically observable quantity may be characterized by how it transforms under certain tranformations; examples of transformations are translations, rotations, space reflection. If you are doing physics in an N-dimensional space then you need one number to specify a scalar quantity, N numbers to specify a vector, N²to specify a tensor (although symmetry proporties usually reduce this number, maybe something like T_ij=T_ji), etc. I do not know how to answer the question "what does it mean", it simply is what is mathematically necessary to describe accurately something in nature. An example more accessible than gravity is perhaps electromagnetism. Here we may describe the electromagnetic field by specifying two 3-dimensional vectors, the electric and magnetic field; this requires 6 numbers. However, the field may be alternatively represented by a single quantity, the field tensor, also containing six numbers but having the elegance of a single quantity rather than two.

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

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

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

ANSWER:
Let D be the intensity in decibels and I be the intensity in W/m². Then the definition of the decibel gives D_woman=D_man+10 log(I_woman/I_man). Then D_woman-D_man=6 dB=10 log(I_woman/I_man). So log(I_woman/I_man).=0.6 and solving I find I_woman/I_man=3.98 .

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

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

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

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

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

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

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

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

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

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

QUESTION:
Is hinge a simple machine?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

ANSWER:
Because of capillary action.

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

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

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

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

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

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

Background radiation is relatively weak and difficult to receive reliably.

Background radiation is a whole spectrum of wavelengths, some of which would go through, some of which would diffract efficiently around the aircraft.

Because it is a whole spectrum, your detector would have scan frequencies or lock in on one you like, which would further enormously reduce the intensity.

The radiation comes from all directions so you would need very tight directional detection, again greatly reducing the already tiny intensity.

Overall, it is not practical.

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

ANSWER:
I have previously answered this question.

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

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

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

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

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

ANSWER:
Wow, either you misunderstood your instructor or else he has no business being a physics instructor. What you describe is called a perfectly inelastic collision but in any collision where there are no external forces (the only relevant forces here are the forces the two blocks exert on each other) the linear momentum must be conserved, that is remain constant. The linear momentum is the mass times the velocity, and it must be the same before and after the collision. Before the collision the momentum is mv₁ and afterwards it is mv₂+mv₂=2mv₂. Therefore, mv₁=2mv₂or v₂=v₁/2, exactly like your intuition told you. What is not conserved is the energy. Before the collision, E₁=½mv₁²and after the collision, E₂=½(2mv₂²)=¼mv₁². So, you see, exactly half the energy was lost and most of this will show up as thermal energy.

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

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

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

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

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

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

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

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

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

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

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

ANSWER:
And the point of this experiment would be…? Gravity is one of the best understood of nature's phenomena and there is really no need to verify each cute little example which has been dreamed up. The idea of drilling a hole all the way through the earth will obviously not work not to mention that the earth is not really a uniform sphere. To do as you suggest is really hard because the Eötvös experiment is one of the hardest around to perform with precision (a group of renoun experimentalists at the University of Washington has been working for years to measure G with great precision this way). The main reason is that gravity is so weak even for objects of mass of tens of thousands of kilograms which you might be able to do an experiment with will experience forces so weak that it might take years for one oscillation to occur. Similar experiments are much easier with electric charges which are also 1/r² forces.

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

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

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

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

QUESTION:
I have some questions regarding strength of an electromagnet
1) Does the size and the material of the core affect the strength of an electromagnet?
2) Does the thickness of the coil affect the strength?
3) The electromagnets I've seen so far had only one layer of coils wrapped around them. Would the electromagnets become stronger if I warp a multiple layer of coils around them?

ANSWER:

The field is proportional to the current around the core and the number of turns per unit length. Therefore the strength is not greater but there is more of it over a larger area. However, the material certainly matters and a ferromagnetic material, usually iron, works best.

Answer 1 covers this.

Again, answer 1 covers this because if you wrap two layers around you are essentially doubling the current.

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

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

QUESTION:
Are metals more efficient as thermocouples or alloys?

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

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

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

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

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

QUESTION:
I have a problem with making a contraconcave mirror. Please refer to these links if my question is somewhat incomprehensible...I seem to be having a hard time wording this question...
http://ec.hku.hk/schoolscience/Volumes/Vol_3/SSHK_Vol_3_03.pdf
http://www.wfu.edu/physics/demolabs/demos/6/6a/6A2035.html
http://www.i-am-bored.com/bored_link.cfm?link_id=17162
Anyways, it seems fairly simple enough to make this, however, I am facing two major problems. These are:
1. How can one find out the focal length of any given concave mirror? Is there a formula defined for this?
2. How would the size of the hole in the top mirror affect the mirage produced? If the hole has to be of some exact size, how can one find out what size should it be when making a contraconcave mirror?

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

QUESTION:
I work in an industrial plant and we have air diffusers which are round and have small holes punched in them in a regular pattern. So think of it as a tube about 2 feet in diameter standing on end. The small holes (.125 inch or so) are regularly spaced about .375 inch or so apart. When you stand back from the diffuser you see a pattern that changes depending on your orientation to the diffuser, you see a pattern of much larger light and dark areas that seem to match the pattern of holes in the diffuser (tube) the patterm remains the same, but the size of the pattern will change with distance from the object. I've also seen this same effect when I lay one material with a pattern on top of identical piece of material with the same pattern that is back lit, as you change the orientation relative to each other you see the pattern seem to shift and expand in size. Is this just a complicated version of the interference pattern from the famous 2 slit experiment that proves that light has the properties of both a wave and a particle? file:///C:/Documents%20and%20Settings/todd/Desktop/moire.jpg

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

ANSWER:
When light is acted on by gravity it does not accelerate like matter does but it does have its energy changed. Light falling into a black hole gains energy so its wavelength gets shorter. But all electromagnetic radiation moves with the same speed in vacuum. And x-rays are no different in this respect. No radiation, regardless of energy, can escape a black hole. And no electromagnetiic wave in a vacuum moves with a speed other than 3 x 10⁸ m/s.

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

ANSWER:
The implications of your question emphasize that it is really unphysical. Suppose we make the halo as light as possible: I reckon that the number of atoms if the halo is a single chain of atoms would be about 10³¹ and the mass would be on the order of 1,000,000 kg. And this would not be very strong would it? Anyhow, the motion at the other side cannot happen faster than the speed of light and it would not even come close to the the speed of light, more like the speed of sound in the halo. I have previously answered a similar question.

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

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

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

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

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

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

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

ANSWER:
Bernoulli's equation is ½ρv²+ρgh+P=constant. Here ρ is the density of the fluid, h the height above some reference, and P the pressure. In this case h is about the same for fluid inside and outside the piston. The pressure outside is atmospheric regardless of what happens inside, so the constant is the same regardless of which opening you use. The half inch opening has an area 16 times smaller than the 2 inch opening, so the velocity will be 16 times greater for the same rate of flow. Therefore ½ρv²+P_2"=½ρ(16v)²+P_½". So P_½"=P_2"-½(255)ρv² so the pressure for the smaller opening must be much lower to move the fluid at the same rate which means you have to pull on the piston much harder. This analysis neglects things like viscosity, compressibility, etc. but gives a reasonable qualitative explanation.

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

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

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

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

QUESTION:
Is gravity a form of energy?

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

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

ANSWER:
I make the following assumptions: the fluid is ideal, i.e. laminar flow, incompressible, no viscosity. Then the operative equation is Bernoulli's equation, ½ρv²+ρgh+P=constant. Here, the pressure P is the same at both the surface of the reservoir and the surface in the tube so we may use ½v²+gh=constant; I will choose g to be about 10 m/s² to simplify my arithmetic. Choose h=0 at the bottom of the tank and note that the velocity in the 2 m² tube is 25 times the velocity of the surface of the reservoir. Then ½v²+10 x 10=½(25v)² and so the speed v at the surface of the reservoir is v=0.566 m/s and the speed at the hole is 14.2 m/s. Now, for your second question, we are interested in what the heights of the two surfaces are when the velocities of the surfaces are zero. From the equation ½v²+gh=constant you can see that when the velocities are zero the heights must be equal. The relative heights of the surfaces will depend on the details of the shape of the tube below the reservoir (your descriptions are a bit ambiguous). I estimate that the volume below the bottom of the reservoir is about 31 m³ and so 100h+31+4h=1000, so h=9.32 m. So the fluid will never rise even to the top of the reservoir.

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

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

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

ANSWER:
E=mc² applies only to a particle of mass m at rest; a photon has no mass and is never at rest. The general relation is E=√[m²c⁴+p²c²] where p is the momentum. (See an earlier answer for the definition of relativistic momentum.) So a massless particle has energy E=pc. The energy of a photon is also related to the frequency f of the corresponding electromagnetic wave by E=hf where h is Planck's constant.

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

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

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

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

ANSWER:
The problem is that you are treating a two-dimensional problem as a one-dimensional problem. A vector may be uncertain with respect to either its magnitude or its direction but in one dimension only the magnitude can vary. In the case you describe, the narrower the slit becomes the more uncertain the direction of the photon becomes because of uncertainty in the magnitude of the x-component of the momentum. However, there is still the constraint that the total momentum be unchanged, so the maximum value of p_x is p when the angle with the z-axis is 90⁰. As the slit approaches zero width, the direction of the momentum becomes completely uncertain as required by the uncertainty principle.

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

ANSWER:
Such force would be so small as to be unmeasurable

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

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

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

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

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

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

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

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

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

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

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

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

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

ANSWER:
(Your first sentence is a little difficult to read; I assume you are referring to the velocity of light.) You cannot use classical kinematics to do this problem because it is incorrect for high speeds. Instead of writing F=m[dv/dt] you must write F=dp/dt where the momentum is defined as p=mv/√[1-(v²/c²)] (not p=mv) where c is the speed of light. If you now exert a force of 3x10⁴ N as you propose (for a 1 kg object), the time to reach speed v is given by t=v/√[1-(v²/c²)]/3x10⁴. So, for example, to reach speed c/2, half the speed of light, it would take, by my calculation, about five and a half years. It would take infinite time to reach the speed of light. When the speed of the particle is large, adding energy by doing work increases the energy of the particle but it changes the speed by almost nothing. (I have always thought that high energy particle accelerators should be called energizers, not accelerators!) You might find the answer to an earlier question interesting regarding why momentum has to be redefined in relativistic mechanics.

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

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

There is no friction before you begin to push, but when you start to push a little the (static) friction turns on, the net force is zero and there is no acceleration.

As you push harder, so does the friction, so still no accereration.

If you aren't strong enough, you will never be able to move it; for example, maybe the boulder is Mount Everest which you will never be able to budge.

But there is a limit to how big friction can get, and if you are strong enough or the floor is slippery enough eventually it will accelerate since you will now be pushing with a force bigger than the frictional force which is trying to slow it down.

If you stop pushing, the frictional force will cause an acceleration opposite the motion and it will slow down and stop.

When it stops, friction dissappears again.

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

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

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

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

ANSWER:
This is a pretty complicated question and the answer depends on what assumptions you make in modeling the atmosphere. I will assume that the density of the atmosphere is independent of temperature and that the areal density (the mass above a given area of the "planet") is the same as for the earth. You say that it "will attract and hold an atmosphere". Hold an atmosphere, yes, but it wouldn't attract an atmosphere since space is essentially empty so whatever it has would have to have already been there or to get there somehow. It is fairly easy to show, given the mass of the sun and its radius, that the acceleration due to gravity at the surface would be about g_S=270 m/s² compared to the earth's approximate g_E=10 m/s², about 27 times bigger. If we assume the density ρ of the compressible atmosphere is proportional to the pressure P, ρ=ρ₀P/P₀where P₀ and ρ₀are the pressure and density respectively at the surface of the planet, we find that pressure as a function of height h is P=P₀exp[(-gρ₀/P₀)h]. Because the areal mass density is the same as on earth, one may now show that the pressure and density at the surface are about 27 times greater than on earth. Similarly, the height at which the density would drop to some fraction of what it is on the surface would be 27 times smaller than on earth. The question regarding index of refraction is too technical for this site and depends on assumptions; clearly, the index would be larger than for earth's for my model because the gas is much more dense.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

QUESTION:
what is RADAR,end howe did worked

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

ANSWER:
Hot, cold, warm, cool, tepid, lukewarm, scalding, icy,… These are all qualitative words which give us qualitative information about the temperature of something. So, the pertinent question is: what does temperature measure. In physics, temperature is a measure of the average kinetic energy per molecule of the object. (Kinetic energy of a mass m with a speed v is ½mv².) This is actually what temperature is for a gas; for a solid it is a little more complicated but essentially comes down to average energy per molecule. So, when we say one object is colder than another it does not mean that it has more of something called coldness as suggested by your friends; rather it means that it has less internal energy per molecule, the molecules are jostling around with less speed than something not so cold. Incidentally, your use of the word heat is incorrect; but don't feel badly because lots of physicists use it incorrectly too. Heat (Q) should be reserved for energy which is transferred from one object to another whereas the temperature of something is determined by its internal energy (U). The first law of thermodynamics is essentially energy conservation. The change in internal energy of a system equals the heat which flows into the system plus the work W done on the system, ∆U=∆Q+W.

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

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

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

ANSWER:
No.

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

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

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

ANSWER:
I have answered similar questions twice before. There are two important factors in frost formation at temperatures near the freezing point, radiation cooling and evaporative cooling. My research has led me to believe that radiation cooling is more important. If you read my earlier answers, which are much more exhaustive than this answer, you will see that all things radiate away energy and that tends to cool them. However, there are also many things in the environment which are also radiating energy and this energy will be absorbed by its neighbors, and so everything will tend to be in thermal equilibrium. So, look at the car in the garage: it, the walls, and the roof are all at, say, 34⁰ and radiating but also absorbing so all stays at 34⁰ and no frost forms. Now look at the car outside: its environment is at 34⁰ and it is radiating accordingly but it does not have the walls and roof from which to absorb energy and so it cools to a lower temperature and frost forms. The second factor is evaporative cooling. As you probably know, since it takes energy to evaporate water, evaporation cools; just take a damp rag and twirl it around and you will see that it gets cold. If there is a breeze which would hasten evaporation and the car in the garage is sheltered from the breeze, this would again give the outside car the cooling advantage. I have noticed this effect even if one car is parked in the vicinity of a house and the second is not.

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

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

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

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

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

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

To the best of our knowledge, the gravitational force propogates with the speed of light. The neutron, being a particle with mass, cannot travel the speed of light. In fact neutrons, having no charge, are quite difficult to accelerate and are usually relatively slow in nature.
The neutron is not a stable particle unless it is bound inside a nucleus; a free neutron has a lifetime on the order of 15 minutes at which time it will decay into a proton, and electron, and an antineutrino. This would not be very good for communication of the gravitational force between, say, the sun and Jupitor would it?
Forces which have carriers with mass, for example the strong nuclear interaction with mesons as field quanta, are very short ranged. Gravity is a long-range interaction like electromagnetism, that is it falls off like 1/r². The force carrier for electromagnetism is the photon which is massless and one would therefore expect the graviton to be massless.

QUESTION:
is energy quantized ?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

QUESTION:
How to derive E=m.c.c?

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

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

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

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

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

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

ANSWER:
Nobody is even considering trying to develop such a weapon. The reason is very simple—we do not have access to the amount of energy it would take to operate it. If you were to totally blow apart an earth-sized planet the total energy you would have to supply is about 10³² J; to calculate this, just use the magnitude of the total gravitational potential energy of a uniform sphere is, 3GM²/(5R). Now, the death star took about one second to blow up the planet, so the power had to be 10³² W=10²⁶ MW. The entire power output of the US is about 10⁶ MW, about a million megawatts. So it takes a mere 10²⁰ Americas delivering all their energy in a second to fuel the death star laser.

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

ANSWER:
The third.

QUESTION:
What happens tp particles at 0K?

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

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

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

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

ANSWER:
I think you must mean megarad. One rad is the amount of radiation which will deposit 0.01 J of energy in 1 kg of material. So, you see, a different amount of radiation will be 1 rad for steel than for human flesh. A megarad would be 10⁶ rad. Incidentally, the rad is an obsolete unit and radiation doses are now more often quoted in Grays (Gy) where 1 Gy=100 rad.

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

ANSWER:
I really do not understand what the first part of your question is asking. Certainly the velocity of any object in orbit around the sun depends on the orbit and where the object is on that orbit. If we view the velocity of a meteoroid on the earth, then the velocity we see will be the the velocity of the meteoroid relative to the sun minus the velocity of the earth with respect to the sun, v_ME=v_MS+v_SE=v_MS-v_ES where, for example, v_MS is the velocity of the Meteoroid relative to the Earth. This ignores the fact that we also have a velocity due to the earth's rotation about its axis.

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

QUESTION:
What is gravity at the sub-atomic level

ANSWER:
Negligible.

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

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

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

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

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

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

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

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

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

ANSWER:
For starters, your terminology needs some touching up: a light year is a distance, not a time; it is the distance light will travel in one year. Second, no material object may go the speed of light, so your question technically has no answer. Now, Andromena galaxy is about 2.5 million light years from earth. Now, let's assume that the spaceship is going 0.99999 the speed of light. Then from earth's perspective it will take almost exactly 5 million years for the round trip so the earth will be that much older. The ship, however, will see the distance to be only 2.5√(1-.99999²)=0.011 million light years=11,000 light years so the time for the trip as measured by clocks on the ship would be about 22,000 years.

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

ANSWER:
I believe the key here is length contraction. A train with speed v will measure the distance to the light source not as 1000 m but as L=1000√(1-(v²/c²)) where c is the speed of light. He will see the light approach him with speed c regardless of what v is (the basic postulate of special relativity) and, while the light approaches him he is approaching to meet it. So, calling t the time (measured by the train) until the light is seen, we can write ct=L-vt. Doing a little algebra, you will find that t=(1000/c)√[(c-v)/(c+v)]. Note that the larger v is, the smaller t is; so, as measured by the clocks on the trains, the faster train sees the light first.

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

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

QUESTION:
Does gravity cause an elrctron to orbit

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

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

ANSWER:
In no measurable way. Magnetism is totally negligible here.

QUESTION:
does Atmospheric pressure effect ones weight on a plant.

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

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

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

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

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

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

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

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

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

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

ANSWER:
First of all, subatomic particles do not have well-defined sizes (they are sort of smeared out over space) so "touching" each other does not really have a definite meaning. However, if we suppose the protons and neutrons in a nucleus are just touching, we can compress the whole earth so that its density becomes that of nuclear matter (the mass of a typical nucleus divided by its volume) and see how big it is. The density of nuclear matter is about 10¹⁸ kg/m³ and the mass of the earth is about 6x10²⁴ kg. So the volume of the earth compressed to nuclear matter density would be about 6x10⁶ m³. This would correspond to a radius of about 113 m, pretty small! Incidentally, this is what happens to a star when a neutron star forms in stellar evolution.

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

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

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

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

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

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

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

QUESTION:
I am an 8th grade teacher trying to teach Physics. When I make up word problems for force, am I always using acceleration due to gravity. For example: I can say a 15 kg object is being accelerated 9.8m/s², what is its force? But can I say a 20 kg object is moved 2m/s² what is its force? Are not all force problems using gravity as acceleration?

ANSWER:
The basic law is Newton's second law, F=ma which relates the net force F experienced by a particle of mass m which has an acceleration a. When a 15 kg object is freely falling the only force on it is its own weight (assuming no air resistance), so if we measure its acceleration to be 9.8 m/s² the weight must be 15x9.8 kg m/s²=147 N (newtons)=33 lb. For the object of mass 20 kg which is measured to have an acceleration of 2 m/s², the net force on it must be 40 N which is about 9 lb; since its weight is 20x9.8=196 N, there must be other forces on this object. An object may certainly have an acceleration different from 9.8 m/s². For example, a box sliding across the floor might have an acceleration of magnitude 2 m/s², that is as each second ticks by the speed gets smaller by 2 m/s so if it starts with a speed of 10 m/s it takes 5 s to stop. (We usually say that the accerleration is, in such a case, negative, but the important thing for 8th graders to understand, I think, is that acceleration tells you how the speed changes, so you should think of an acceleration of 9.8 m/s² as 9.8 (m/s)/s so that if you drop something it has a speed of 9.8 m/s one second later, 19.6 m/s two seconds laterr, etc.) If you are in the US, it would probably be helpful for your students to know that 1 N=0.225 lb since they probably think in terms of pounds; so a newton is about a quarter of a pound.

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

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

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

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

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

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

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

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

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

ANSWER:
I have previously answered this question.

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

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

QUESTION:
Does noise require energy to happen?

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

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

ANSWER: {this answer is not complete yet, I have to go to a concert!}
Your question is closer to breaking groundrules for not being concise and well-focused than being too technical. However, I will answer it because it is interesting. If you work with MRI, I am afraid I must tell you that you do not really understand what is going on. If a classical magnetic moment is placed in a uniform magnetic field it will align with the field. That is what it wants to do. If it is a quantum mechanical particle (that is it has a spin angular momentum) it cannot align with the field because the component of the total angular momentum (which is J=ħ√[3/4]) along the field direction may be only ±½ħ. That is where your angle comes from, cos(54.7)=½/√[3/4]. It is not really correct to say that the proton precesses; it is more correct to say that it is equally probable to be at any azimuthal angle and so many texts describe this situation as precession. Go ahead and think of it as precession, but it certainly does not radiate energy. Note that the moment is "up", that is 54.7⁰ relative to the field direction. Its other state, 54.7⁰ relative to the opposite direction ("down") is at a higher energy because it takes work to take the "up" aligned moment and turn it to a "down" moment. Let us say that it takes an energy E (which depends on the field strength) to flip the moment from up to down. In an MRI what happens now is that we shine in some electromagnetic radiation. If the radiation is of just the right frequency, that is f=E/h, there will be a high likelihood that the radiation will be absorbed resonantly (hence the "R" in MRI, magnetic resonance imaging). This absorption is what is detected in MRI. This is a very simplified overview, but it gives the basic physics principles. The details of how the whole imaging process is very much more complicated because of the problem of locating where the absorption is taking place.

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

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

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

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

ANSWER:
Both of these questions are unanswerable because the force is proportional to the acceleration, that is the time rate of change of velocity. So knowing the velocity when an object hits and the fact that it is at rest afterward gives you the change in velocity but you cannot compute the rate of change of velocity without a time. So, if an object changes its speed by 500 ft/min =2.54 m/s, its mass is 100 kg, and it stops in 0.5 s, the average acceleration is 2.54/0.5=5.08 m/s² and the average force experienced is ma=100x5.08=508 N=114 lb. Since the weight of 100 kg is about 220 lb, the force of the ground must be 114+220=334 lb. So the force you would feel is larger than your weight by 334/220=1.5, so you would feel a 1.5 g-force. This is an example, but if either of these questioners really wants an answer, more data are needed.

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

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

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

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

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

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

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

ANSWER:
The key is to understand the relationship between the energy (E) of a photon and its frequency (f). The photon is the quantum of light emitted when a transition occurs. This is the famous relationship Einstein discovered in his theory of the photo electric effect, E=hf where h is Planck's constant, h=6.62×10^-34 m²kg/s. Hence, if an atom makes a transition from a state with energy E₁to a state with energy E₂, the frequency of the emitted radiation is f=(E₁-E₂)/h. Then the wavelength (l) is just l=c/f where c is the speed of light.

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

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

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

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

ANSWER:
I have previously answered this question.
PS there is no such thing as a perfect vacuum either.

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

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

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

ANSWER:
OK, I will take a stab at this. But, I am not an engineer and do not really know for sure how much information one must receive to be able to put together a tv picture. I will assume that, since the wave nature of the radio waves carries the information, we will need at least one million photons per cycle of the wave. My thinking is more in line with AM radio waves where there is one constant frequency of carrier waves and the information is carried by the amplitude of the wave; I realize that this is not really what tv is but it should give an order of magnitude estimate. The typical power of a tv station is about 100 kW=10⁵ J/s. The energy of a single photon is hf=6.6x10^-34x10⁸=6.6x10^-26 J/photon so for our power source we have N=10⁵/6.6x10^-26=1.5x10³⁰ photons per second. The frequency of a tv station is about 100 MHz= 10⁸ s^-1. To get 10⁶ photons per cycle we therefore need 10⁶x10⁸=10¹⁴ photons per second. 4.7 ly=4.4x10¹⁶ m so the intensity (in photons/second/square meter) at Alpha Centauri will be about 1.5x10³⁰/[4p(4.4x10¹⁶)²]=6x10^-5photons/s/m². We therefore need an area of 10¹⁴/6x10^-5=1.7x10¹⁸ m². That is about an 800,000 mile square. This hinges mainly on my assumption of needing 10⁶ photons per cycle of the wave which might be wrong by several orders of magnitude.

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

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

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

ANSWER:
I only need the kinematic equations y=y₀+v₀t-½gt² and v=v₀-gt and I use g≈10 m/s² for calculational ease. First, find out where the first arrow is and how fast it is going after 1 s. y(1)=30x1-5x1²=25 m and v(1)=30-10x1=20 m/s; the purpose of this step is to find the initial conditions for arrow #1 to use in the next step of the problem. Now write the y equations, choosing t=0 when the second arrow is shot, for each arrow. y₂=40t-5t² and y₁=25+20t-5t² (we don't need the v equations since we are not asked for any speeds). Now set y₁=y₂ and solve for t and find t=1.25 s. Put this t into either y equation and find y=42.2 m. You could go on and write the v equations to find out the velocity of each when they collide. v₁(1.25)=20-10x1.25=7.5 m/s and v₂=40-10x1.25=27.5 m/s.

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

ANSWER:
This is atrociously poorly written! Believe me, centrifugal force is not a real force. In even the most elementary physics course we learn that a force perpendicular to the velocity (as in an orbiting particle) causes the direction, not the speed, to change. Hence there is no reason to ask the ridiculous question of what "keeps the two particles from coming into contact with each other" since the orbiting particle just orbits. Let me try to clarify what centrifugal force is. As I have alluded to above, we easily calculate a circular orbit for a particular force and velocity using Newton's second law, F=ma, where F is the electrostatic attraction to the nucleus, m is the electron mass, and a is the acceleration where a=v²/r for circular motion and r is the orbit radius. Now, suppose that you are standing on the electron; how do you describe the situation? Well, Newton's laws are not true in an accelerating system which is the case here. And it is really obvious that they are not valid because there is only one force and yet, if you are in the electron's frame of reference, no acceleration. But suppose that you insist on using Newton's laws to describe your motion; the only way you can do that is to invent fictious forces to make things work out. In the case we are discussing the electron is not accelerating and there is one real force pointing toward the nucleus of some magnitude F (this is referred to as the centripetal force, center seeking if you know your Latin); but the sum of all forces must be zero and so you must postulate the existence of a force which has magnitude F and points away from the nucleus (centrifugal force, center fleeing if you know your Latin). That is not really there but it is often very much to our advantage to force Newton's laws to be true in accelerating (so called noninertial frames of reference) for computational reasons. Let me give you a couple of other examples of fictious forces.

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

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

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

ANSWER:
You are right, it is p=mv. The reason that ma sticks in your head is that Newton's second law may be written F=ma. There is another connection: since a is the time rate of change of v, dv/dt (do you know calculus?), Newton's second law may be written F=dp/dt, that is, force is the time rate of change of momentum. This is how Newton originally expressed it and is the way you must express it in special relativity, that is F=ma is not true in special relativity. In special relativity, though, momentum must be redefined to be p=mv/√(1-(v²/c²)) where c is the speed of light. Note that when v<<c, p≈mv.

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

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

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

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

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

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

QUESTION:
How do you go from the fully relativistic form for Kinetic Energy, to the more well known ke=1/2mv²?

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

KE=m₀c²[(1-b²)^-1/2-1]≈m₀c²[1-(-½)b²+…-1]≈½m₀v²where b=v/c and c is the speed of light. I have used (1+x)ⁿ≈1+nx+… for small x.

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

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

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

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

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

QUESTION:
is there pure concussive effect of an explosion in a vacuum

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

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

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

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

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

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

ANSWER:
Suppose that we assume that the atmosphere gets completely mixed up by weather patterns after a relatively short time, say a year; this essentially means that a molecule here today is equally likely to be anywhere else in the world in a year. Now, I calculated the volume of the atmosphere assuming it to be 20 km thick; that would include most of the molecules. Now, I assumed a typical human breath is about 1 liter; then I find that the number of lungs full of air there are in the atmosphere is roughly 1.5x10²¹. Next I roughly estimate the number molecules in one lung full of air to be about 3x10²². So, if I take one breath and redistribute the air over the whole atmosphere, I will find about 20 molecules of that air in any other breath. So, very roughly speaking, each breath you take will have 20 molecules of the last breath John Kennedy took before he died. But, we might more likely be interested in the number of molecules over a lifetime; taking Leonardo da Vinci, who lived to age 67 as an example, the number of molecules breathed in his lifetime was about 7x10⁸(I assumed about 20 breaths/minute), so every breath you take will contain about 1.4x10¹⁰ molecules (that is about 14 billion) that were breathed by da Vinci! Keep in mind that my calculations are very rough but they should give a good approximation of orders of magnitude.

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

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

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

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

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

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

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

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

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

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

QUESTION:
Who was most responsible for the Grand Unification Theory?

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

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

ANSWER:
I have previously answered this question.

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

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

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

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

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

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

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

ANSWER:
The answer is yes, but the effect is very small, probably not measurable. I calculate the acceleration due to gravity at the earth's orbit due to the sun to be about 6x10^-3 m/s². Assuming that g=9.8 m/s², the two values would be 9.806 and 9.794 at the equator, less than 0.1%. This is small compared to variations in g due to the nonsphericity of the earth, local mass variations, the rotational motion of the earth and other effects.

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

ANSWER:
I have previously answered a similar question.

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

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

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

ANSWER:
You have several very different things jumbled up here.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

ANSWER:
If you measure the force between two point charges separated by a distance r, this force is found to be proportional to product of the charges and inversely proportional to r². If you measure the charge in Coulombs and the distance in meters, then k=9x10⁹ Nm²/C² as you state. This is simply an experimentally measured number, that is the force between two charges each 1x10^-3 C and separated by 1 m would be 9000 N, a number you could measure to get k. Suppose that you have a number N and you want to define a new number M=2N; that is all permittivity is, a redefinition of k, e₀=1/(4pk). Your last question is most interesting. The permeability of free space is m₀=4px10^-7Ns²/C² and, like k, it is just a proportionality constant which tells you the magnetic force between two current carrying wires. Now, it turns out that when you do the mathematics you find that the equations of electricity and magnetism (called Maxwell's equations) predict waves which have a speed of c=[e₀m₀]^-1/2 and this speed just happens to be the speed of light in a vacuum. And so if you now do the simple algebra, you find that k=10^-7/[e₀m₀]=c²x10^-7.

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

ANSWER:
You are referring to virtual particles as you indicated in a later message. How can a particle, with energy mc², simply appear from nothing? The answer is that you can violate energy conservation as long as you also obey the Heisenberg uncertainty principle, i.e. as long as the time during which you violate energy conservation is short enough. Quantitatively, The product ET (energy time time) must be on the order of about Planck's constant which is a very small number (on the order of 10⁼³⁴ in SI units). So, you may spontaneously create 1 Joule of energy as long as it does not exist longer than 10^-34 seconds. This picture has done remarkably well in understanding virtual particles. (Incidentally, you cannot have a virtual electron, for example, because that would violate conservation of electric charge; instead you must have a vitrual electron-positron pair.) Could they be understood as evidence of higher dimensions? Scientists are loathe to say anything is not possible, but more than simple conjecture would be needed to convince anybody—predictions of nature are required for acceptance of a hypothesis.

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

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

QUESTION:
I've been looking at various videos on Youtube about homompolar motors. In some videos a battery is used and in other there is not, but in both types of set-ups... What is it that causes the spinning action. I can some what understand the spinning when a battery is used. In a battery set-up there is a current in the wire that makes a magnetic field around the wire, or wires, and it is this magnetic field that conflicts with the current in the wire causing it to be pushed away. But in the videos that don't use a battery what is making the whole assembly spin? I is my understanding that magnetic flux fields are stagnant. So when a charge is applied to the "no battery" homopolar motor is there a current traveling along the flux lines causing it to spin? I've attached some links to clarify my question:
http://www.youtube.com/watch?v=2hHfkK4iGBQ
http://www.youtube.com/watch?v=hXbFfMBW97A&mode=related&search=

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

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

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

The instant that the ball leaves the hand the hand must be moving with speed 100 mi/hr and, as you note, must experience a force to stop it.
But the hand does not stop in a fraction of an inch, it probably travels a couple of feet or more.
Understanding this you can see one of the reasons for "follow through" in throwing balls, golf swings, etc.
A rough calculation of the force is: let the time to stop be 0.2 s, the initial velocity be 100 mi/hr=45 m/s, the mass of the hand be 1/2 lb=0.23 kg, and the distance traveled be 1 m=3.3 ft. Then the average acceleration is 45/.2=225 m/s²=503 mi/hr/s. Then the average force is 225x0.23=52 N=12 lb. The source of the force on the hand is the wrist. Note that the distance does not factor into calculating the acceleration, just the change of speed and the time. The distance and time are not independent and making the distance larger makes the time larger which makes the acceleration and force smaller.

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

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

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

ANSWER:
What the terminal velocity is depends on a number of things including the skydiver's weight, the density of the air, and how he orients himself relative to his fall. If he orients in a belly flop position he will have a lower terminal velocity than if he falls feet first. Also, he technically never reaches the terminal velocity but just approaches it asymptotically. But you can estimate when he is within, say 95% of the terminal velocity. The details of the physics are given in a previous answer; I will just give you the results for your situation here. Choosing the mass to be 100 kg (about 220 lb), the air density to be 1.3 kg/m³, cross sectional area to be 1 m² (more like the belly flop position), and the drag coefficient 1.2, I find a terminal velocity of about 35.4 m/s (about 79.4 mi/hr). The characteristic time is about 3.6 s; this is the time it takes the speed to go to about 76% of the terminal velocity. If you wait twice the characteristic time, about 7.2 s, you will reach about 96% of the terminal velocity. The characteristic distance is about 64 m; this is the distance it takes the speed to go to about 63%. If you go three characteristic distances, 192 m (about 630 ft), you will reach about 95% of the terminal velocity. If you are interested, the characteristic time is v/9.8 s and the characteristic length is 19.6/v² m where v is the terminal velocity in m/s. It is interesting to note that cats that fall out of skyscrapers usually survive because their terminal velocity is slow.

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

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

QUESTION:
Do electrons maintain a standard orbit about the nucleus?

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

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

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

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

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

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

ANSWER:
(I will take the 10 billion light year distance; everything is half as large for 5 billion light years.) The first velocity you quote, 250,000 km/hr is about 0.00023=0.023% the speed of light, so both observers would see the same elapsed time which would be 10x10⁹/2.3x10^-4=4.3x10¹³ years, about 43,000 billion years. The case of a speed 99% the speed of light, we would see it take about 10 billion years (just a hair longer) but the observer in the space craft would see much less time elapse. He would see the distance to the hole to be contracted to 10x(1-.99²)^1/2=1.4 billion light years; so the time it would take him, according to his clocks, would be 1.4/.99=1.42 billion years.

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

ANSWER:
In principle, this is a simple free fall problem. In practice, we need to worry about air resistance since that becomes important in real life at high speeds. However, there is very little air above about 60,000 feet, so let's assume that there is no air resistance and see how far he has to fall to reach a speed of 600 mi/hr and if it is less than about 40,000 feet he probably achieved that speed. The acceleration due to gravity is about 21.8 mi/hr/s; that is a freely falling object will gain about 21.8 miles/hour as each second clicks by. One pertinent physics equation is v=at where v is the speed (assuming we start from rest), a is the acceleration, and t is the time. So, putting 600 in for v and 21.8 in for a we can solve for t: t=27.5 s; in other words, after about a half a minute the object will be going 600 mi/hr. The second pertinent equation is s=½at² where s is the distance traveled in time t. Solving for s I find s=12,000 ft, that is he will have a speed of 600 mi/hr when he is at about 90,000 ft, still far above where there is signficant air. (Incidentally, in the second calculation I used a=32 ft/s/s so the units would come out right, viz. feet.) So, I would say that yes, he must have gone at least 600 mi/hr. I did a little research and saw 714 mi/hr quoted as the highest speed he achieved. Once he starts encountering significant amounts of air he will begin slowing down.

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

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

Here are the facts, as presented in an article at http://www.centennialofflight.gov/essay/Explorers_Record_Setters_and_Daredevils/Kittinger/EX31.htm
1. Kittinger jumped from 102,800 ft.
2. His weight is approximately 300 lbs.
3. He was falling in a backward orientation
4. After falling for 13 secs, a small chute, 6 ft. in diameter, opened.
5. He feel for 4 min. and 36 secs more bringing him to 17,500 ft.

ANSWER:
Your friend certainly makes some quite good points, although he is maybe a bit overemotional and maybe a little hostile to us college professors. It is true that we often simplify problems to get to the core of a problem. So let me be a little more careful and go over the calculation of your friend the way I would do it since some of the numbers he quotes are undocumented and some of them (in particular slugs/ft³) are completely incomprehensible to a modern physicist! Your friend must be an engineer. His equation is quite correct, that is the terminal velocity is given by v=[(2mg)/(rAC_p)]^1/2 . Now it is easy to see how disputes can arise because the answer, of course, depends the choice of constants some of which are not easy to estimate (for example, I would say approximating the man as a brick is what some nutty college professor might do). The density of the air at 100,000 ft is about 1/100 the density at sea level and, since the density at sea level is about 1.3 kg/m³, I will take r=1.3x10^-2 kg/m³. I searched the web for tables of drag coefficients and found that a parachutist has C_d=1-1.4 (not 2.1 as your friend assumed); I will use 1.2. The cross sectional area also requires a rough estimate since it depends on whether he is falling, for example, feet first or is falling "belly flop" orientation. I will assume the latter so as to get as small a speed as possible and I will estimate the area as about A=2 m x 0.5 m=1 m² (your friend uses 15 ft², about 1.4 m²). Using m=136 kg (300 lb) and g =9.8 m/s², we are ready to estimate v; I get v=413 m/s= 924 mi/hr.

But, there is important information which you did not tell me the first time through--the opening of the small chute. So now the cross sectional area is about 2.5 m² and the drag coefficient is about 1.42 (I model it as an open hemisphere into the wind). So now I get a reduced terminal velocity of v=240 m/s= 537 mi/hr.

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

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

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

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

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

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

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

ANSWER:
Almost anything will relfect electromagnetic radiation. The real problem here is the intensity. The intensity of radio waves emitted from the earth will fall off approximately like 1/r² where r is the distance. So, if you have a certain intensity 1,000 miles from earth, the intensity 1,000,000 miles away will be (10⁶/10³)²=1,000,000 times weaker; and 1,000,000 miles is a very small number compared to the distance to a star. And the reflected signal will lose just about the same fraction coming back. My guess is that the intensity would be so low that no information could be obtained from it.

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

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

QUESTION:
What is the speed of gravity?

ANSWER:
This quetion has been previously answered.

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

ANSWER:
There is, of course, no way to calculate it. You could estimate it, however. I am not a geologist, so I really don't know how much sand there is in the world but it must be a lot. I will take a wild guess that there is enough sand to cover the entire earth to a depth of 10 cm =10^-1 m (there is probably more than that). The surface area of the earth is about 5 x 10¹⁴ m² (from A=4pR²) so the total volume of sand is about 5 x 10¹³ m³. Now, I will guess that a typical grain of sand would have a diameter of maybe 0.1 mm=10^-4 m so the volume of a typical grain of sand would be about 10^-12 m³. So the number of grains of sand would be the ratio of the volumes (volume of sand/volume of one unit of sand), about 5 x 10²⁶, quite a lot! This is comparable to about how many atoms there are in your pencil.

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

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

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

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

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

ANSWER:
Have you thought about the implications of your question? I figure the mass of the rod would be about 10¹⁰ kg. Suppose that you exert a constant force such that after 0.1 s it is moving with a speed of about 0.5 m/s; it would have moved about an inch in this time. The force is the change in momentum divided by the elapsed time so, roughly speaking, the required force is about 10¹² N. Where are you going to get such a force? Anyhow, to the meat of your question: no, the other end would not start moving instantaneously. It could not begin moving until at least one second later than your end started moving for the reason you state: no information can travel faster than c. In reality, it would be much longer than one second because your "mighty whack" will compress the rod and this compression will move with the speed of sound in the metal and this compression is what travels to the other end to move it.

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

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

ANSWER:
What hitting with a hammer will do is cause an acceleration. How big might that acceleration be? First let's assume we want the object to move (to be continued)

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

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

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

ANSWER:
Yes, the magnets will be more massive after you have separated them. But, the amount will be unmeasurably small. Suppose that you do 100 J of work to separate them. Then the mass increase will be Dm=100/(3x10⁸)² kg, about 10^-15 kg!

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

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

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

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

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

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

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

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

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

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

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

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

ANSWER:
First, allow me a little rant! It is utterly ridiculous that this problem is part of a high school curriculum. Coefficient of restitution (COR) is one of the least important concepts in classical mechanics. Furthermore, it is nearly always defined in terms of a one-dimensional collision which the collision in your problem is not, so it looks like the problem writer is trying to confuse the reader (which I consider to be poor educational method). Furthermore, I find that I do not get 1/2 for the coefficient of restitution when I work the problem. I will outline the solution to the problem and give my results. You can reconstruct the solution and see if I have made any errors. First, the COR e is related to the energy loss Q in the collision by Q=½mv²(1-e²) where m=m₁m₂/(m₁+m₂) (reduced mass) and v is the incident velocity (if one of the two particles is at rest as it is here). It makes no difference what the actual masses are since they are equal, so I shall choose m₁=m₂=1 kg such that Q=31.25(1-e²) J. (I have used v²=125 m²/s² as given in the problem.) Now, just calculate Q to get e. The information given about the recoiling velocities is their directions, not their magnitudes; to get the speeds you must do momentum conservation. The red ball moves at an angle of 53.1⁰ above the negative x axis and the white ball moves at an angle of 63.4⁰above the positive x axis. Conserving momentum in x and y directions I now find the speeds of the red and white balls: v_r=7.5 m/s and v_w=5.59 m/s. Hence the energy after the collision is 43.75 J and before the collision 62.5 J, so Q=18.75 J. Solving now for COR: 18.75=31.25(1-e²), e=0.63, not ½.

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

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

ANSWER:
For starters, you would not be here to ask this question. The existence of life as we know is very sensitive to the values of the most important physical constants, the speed of light, c, being one of them. The easiest way to see dramatic effects is from good old E=mc². If c were 10x bigger, the energy equivalent of mass would be 100 times greater, so the energy being produced by the sun would be 100 times what it is; talk about global warming! Assuming that protons and electrons still existed you could still have hydrogen since atomic physics is not very affected by relativity, but when you tried to make a nucleus you would find that the masses of the nuclei were very much less than the sum of its components due to the enormous binding energies. In fact, I do not think you could have a neutron so you could make no nuclei and therefore you would have no chemistry and the stars would not be able to make energy using fusion.

QUESTION:
What is the basic physics behind laser cooling.

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

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

ANSWER:
When you say to forget about "quantum mechanical complexities" you guarantee that the answer to your question is no. However, "complete information" really means detailed wave functions of hydrogen and oxygen atoms; given that information, excellent predictions of the properties of H₂O may be calculated.

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

ANSWER:
The voltage you quote is for a point charge, not parallel plates. For parallel plates the electric field E is uniform and so the potential difference is V=Ed where d is the spacing between the plates. The field is determined by the charge Q on the plates and the area A of the plates, E=Q/(e₀A) so the field stays the same when the plates are separated.

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

ANSWER:
Freezing the water will not affect its weight so both bottles will weigh the same after one has been frozen. So, the condensation will cause the cold water to be heavier. [A technicality: because E=mc², the frozen bottle, because energy has been taken from it to cool and freeze the water, will actually be lighter. However, the amount by which it will be lighter will be unmeasurably small, so it may be ignored. A rough estimate: suppose that 1,000 J of energy are removed in doing the freezing; the mass equivalent is 10³ J/(3 x 10⁸ m/s)² which is about 10^-14 kg!]

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

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

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

ANSWER:
The law is that the speed of light in vacuum is the same for all observers. Light, when passing through matter, moves slower.

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

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

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

ANSWER:
It depends on where the strings are attached to the rock. If one is directly above the center of mass, it will carry all the weight and the other will have zero tension. If they are equal horizontal distances from the center of mass, each will carry half the weight. The thing is that the sum of all the torques about the center of mass must be zero. So T₁d₁=T₂d₂ and T₁+T₂=W. where d is the distance of each string horizontally from the center of mass.

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

ANSWER:
The power P dissipated in a resistor R is P=IV; if you increase the voltage and keep the power the same, the current becomes small. But, in the transmission line, if you use Ohm's law V=IR, P=I²R, so low current means low power loss.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

ANSWER:
I assume they are identical. I will also assume that the light intensity is proportional to the power dissipated by the bulb; this is not a very good approximation because the resistance of tungsten wire is dependent on its temperature which is in turn dependent on the current through it. Then brightness depends on power which is proportional to V² where V is the voltage across the bulb. The bulbs in series will have only 1/3 the voltage across each as the bulbs in parallel, so they will be only 1/9 as bright.

QUESTION: ;
Is there a scientific proof that the atom is neutral?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

ANSWER:
To see something, your eye (or telescope) must detect light which was emitted from that object (or reflected from it). So, when you look at a friend who is 100 m away, you are not seeing him as he is right now but how he was 100/3 x 10⁸=3.3 x 10^-7s ago. 1/3 of a millisecond is a quite measurable time. Now suppose you are on a planet which is 100 light years from earth. When you see the earth you are seeing as it was 100 years ago because a light year is the distance light travels in a year. The moon is 1.3 light seconds from the earth and the sun is 8.3 light minutes from the earth. So, when you see the moon you are seeing it as it was 1.3 seconds ago. If the sun were to blow up right now, you would not know it for 8.3 minutes.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

ANSWER:
Let's look at the pressure fluctuations in a sound wave. At the threshhold of pain, the loudest sound you can hear without feeling pain, the pressure variations amount to about 30 N/m²; compare this to the pressure of the air, about 100,000 N/m². I believe that the resulting local temperature fluctuations would be negligible.

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

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

QUESTION:
Why does a diamond glitter so much?

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

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

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

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

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

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

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