Why does kinetic energy depend on the frame of reference?

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Discussion Overview

The discussion revolves around the dependence of kinetic energy on the frame of reference, particularly in the context of a ball tossed on a moving train. Participants explore the implications of this dependence in both classical mechanics and relativity, examining how different observers perceive kinetic energy differently based on their reference frames.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant calculates the kinetic energy of a ball on a moving train and notes the discrepancy in energy observed by a stationary observer, questioning why the ground observer sees twice the kinetic energy.
  • Another participant asserts that kinetic energy is frame dependent in nonrelativistic mechanics, emphasizing that it is expected to vary with the reference frame.
  • A third participant clarifies that kinetic energy and momentum are not invariant quantities and that energy conservation does not imply invariance across frames.
  • One participant explains that the kinetic energy is related to the work done to bring the ball to rest, highlighting the frame-dependent nature of "at rest."
  • Another participant mentions that while kinetic energy is not invariant, the total change in kinetic energy due to internal forces within a system remains invariant across frames.

Areas of Agreement / Disagreement

Participants express differing views on the implications of frame dependence for kinetic energy, with no consensus reached on the underlying reasons for these differences. Some participants focus on classical mechanics, while others reference relativity, indicating a mix of perspectives.

Contextual Notes

Participants discuss the concept of invariant mass versus relativistic mass, with some suggesting that the notion of mass changing with speed is misleading. The discussion also touches on the importance of specifying a reference frame when discussing energy.

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 (?).
 
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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?
 
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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.

Marvin L said:
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.

Marvin L said:
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/
 
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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.
 
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OK thanks folks. I got it.
 
Marvin L said:
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.
 
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