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How does a bouncing ball loses energy? Are there different energy loss regimes, depending on the ball material/structure (e.g., tennis ball vs. a solid caoutchouc) and the surface from which it bounces (e.g., metal vs. concrete; assuming for now a solid surface)?

The question is somewhat similar to this one Why does a ball bounce lower?, however the answers do not go in depth regarding the loss mechanisms (see Remarks). Two possibilities come to mind:

  • The compression of the ball when touching the surface is not quasistatic, that is some energy is irreparably transferred to heat. I would appreciate a more detailed discussion here.
  • The bounce may excite sound waves in the surface, thus giving it some energy.

Answers supported by estimates and calculations are especially appreciated.

Remarks
The accepted answer, among other things suggests:

Of course for an air filled ball, there are losses associated with the compression of the air: while the air is (adiabatically) compressed, it heats up; while it is hot, it dissipates heat to the environment; and when it expands, it cools down again.

which I certainly disagree with (see my first bullet above): while the fast compression does not allow for the heat exchange, it is not a quasistatic process, i.e., not adiabatic in usual sense. Moreover, thermal exchange with the environment is likely neglideable.

Roger V.
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1 Answers1

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I basically agree with your two bullet points, with the additional embellishments below.

  • The compression of the ball when touching the surface is not quasistatic, that is some energy is irreparably transferred to heat.

I would prefer to say that the compression of the ball is not "elastic". Inelastic compression means there is internal friction which increases the temperature of the ball material, resulting in heat transfer to the cooler environment. This loss of energy is at the expense of the macroscopic kinetic energy that the ball had at the time of impact. That leaves less kinetic energy to be converted to gravitational potential energy when the ball rebounds, so the height of the rebound is less than the initial drop height.

  • The bounce may excite sound waves in the surface, thus giving it some energy.

Agree that sound energy is another loss of macroscopic kinetic energy. Though I believe it is much less a factor than inelastic behavior.

Hope this helps.

Bob D
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