Originally Posted by

**Chotta**
Here's a quick paradox.

You've got a rod that's 1 light year long and weighs 1 kg(it's hypothetical :-) )

You push the end for 1 second with a force of 1 newton thus moving the rod 1 meter.

First off, since a = f/m and d= at^2/2, exerting one Newton for 1 sec on a 1 kg object moves it 1/2 meter not one meter.

Secondly, you cannot even assume that you are moving the end 1/2 meter, since you are only moving the end and not the whole mass of the rod. How much the end of the rod moves depends on how much it compresses from your exertion of force, which in turn depends on the material it is made of, and since the rod cannot be perfectly rigid the end will in all cases move more than the 1/2 meter.

So rather than assuming 1 Newton for 1 sec, let's just assume 1 Newton over 1 meter. Thus you are expending 1 Joule of energy. The rod compresses by 1meter in length, and the compression wave travels through the rod. This compression will also try to decompress the rod back out to its regular length. Which means the the end you pushed will tend to snap back at you. How much it snaps back at you depends on the total mass of the rod. IOW, the energy expended by you is stored by the compression of the rod.

If the rod remains whole that energy will be expended moving that mass resulting in a cetain final velocity of the rod.

It the rod is severed at the midpoint before the compression wave reaches that point, that energy will be expended on the remaining mass of the rod , resulting in a higher velocity

So the answer is the both the speed of light limit and energy is conserved.