Why does kinetic energy depend on the frame of reference?

[Marvin L]

I'm having this discussion with my engineering peers: A ball is sitting on top of a train traveling at, say, 10m/s. The ball has mass of 2kg, for simplicity. The ball's kinetic energy KE relative to ground zero is 1/2 m v^2, or 100J. A person riding on the train picks up the ball and tosses it ahead at 10m/s relative to the train, imparting an additional energy of 100J to the ball, for a total of 200J. Another person on the ground sees the ball traveling at 20m/s, apparently having 400J, or twice the energy 200J that we gave to the ball. Why does the person on the ground see twice as much kinetic energy in the ball? I'm guessing the mass of the ball changes according to relativity (?).

 

[weirdoguy]

It has nothing to do with relativity. Velocity is frame dependent in nonrelativistic mechanics and so kinetic energy is. That's all. The real thing is: why would you expect that it does not depend on reference frame?

 

[Orodruin]

Kinetic energy is not an invariant quantity, nor is energy. There is no reason to expect energy to be the same in different frames. This is true in relativity and classical mechanics alike. The same goes for momentum. Energy and momentum are conserved quantities, not invariant quantities. There is no such thing as "the energy in a system" unless you specify a reference frame in which the system is considered.

Why does the person on the ground see twice as much kinetic energy in the ball?

The amount of work done on the ball depends on the force and displacement. The displacement is also not frame independent.

I'm guessing the mass of the ball changes according to relativity (?).

This has nothing to do with it. In fact, you would do well to forget everything you heard about mass changing depending on speed. Physicists generally only talk about invariant mass. See also https://www.physicsforums.com/insights/what-is-relativistic-mass-and-why-it-is-not-used-much/

 

[Ibix]

The kinetic energy of the ball is the amount of energy you can extract from bringing it to rest. Since two frames don't agree what "at rest" means, it's not surprising that they don't agree what the kinetic energy of the ball is.

 

[Marvin L]

OK thanks folks. I got it.

 

[jbriggs444]

OK thanks folks. I got it.

While kinetic energy is not an invariant in classical mechanics, the gain or loss in kinetic energy due to internal forces within a system is an invariant. If you count the reduction in kinetic energy of the train together with the increase in kinetic energy of the ball, the sum is the same regardless of what reference frame you choose.