Physics Question #3314

Saurabh, a 15 year old male from New Delhi asks on March 8, 2006,

Gravity can produce motion in a body. Thus, it does work. But, for doing work, energy is needed. Does that mean every mass has energy? If not, which energy is responsible for gravity in a body?

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The answer

Jess Brewer answered on March 10, 2006

I will give three answers in the order that you would learn about gravity and mass in school. Note how the answer shifts around a bit and we slowly reveal what we lied about before....

ANSWER 1 (in terms of Classical Newtonian Mechanics): There is an attractive force between any two masses which we call the Force of Gravity. If one of the masses is really really big, like the Earth, and our distance from its centre is almost constant, then over small changes of that distance (what we call "altitude") it is almost a constant "downward" force proportional to the mass of the small body. Now, a mass sitting still at the bottom of a hill can be said to have no energy. (We get to define the zero of energy wherever we want.) If you would like to move the mass uphill you will have to push on it (exert a force) and move it through a distance parallel to that force, doing Work in the process. The Work you "invest" can be "withdrawn" by simply letting go. Assuming the mass can slide or roll back downhill without friction, it will arrive at the bottom of the hill again after a while, but this time it won't be at rest; it will be moving just as fast as if you had done the same amount of Work pushing it along a level surface so that it accelerated to that speed. We say it has a Kinetic Energy equal to the Work you did. But let's go back to the top of the hill: you have done all that Work to get it there, but it's at rest (no Kinetic Energy); so where did the Work go? We say it went into the Potential Energy difference between the bottom of the hill and the top of the hill: being further from the centre of the Earth means the Force of Gravity could potentially do work on the mass, accelerating it downhill and thus converting that Potential Energy into Kinetic Energy. (It could also be used to do some other kind of Work, like truning a mill wheel or a turbine.) So you see, the energy is not "in" the mass, it is something that we can manipulate using the mass as an agent. At the bottom of the hill it has no energy.

ANSWER 2 (in terms of Special Relativity): Ah, but Einstein showed that even a mass at rest has energy stored up in its very "massiness". You know the famous formula: E = m c2. Usually there is no way to get that energy out, but in certain nuclear reactions it is possible to convert a small fraction of the mass of the nucleus into energy, and we have seen that it is a lot of energy! Moreover, energy has mass! When the particle gets moving really fast (like at the bottom of a very long, steep hill) its Kinetic Energy gives it extra effective mass by the same formula. Even a box full of light is heavier than the same box empty. Cool, huh?

ANSWER 3 (in terms of General Relativity): Gravity is not really a force at all, it is a manifestation of the warping of spacetime in the neighbourhood of large energy concentrations (i.e. mass). (If you want to know more, you'll have to learn differential geometry and tensor calculus. :-)

You pick the answer you like best, but remember, they are ALL CORRECT IN CONTEXT. Good luck!

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