# Energy loss mechanisms for a bouncing ball

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.

• I don't know about "quasistatic," but "elastic" and/or "inelastic" are good words to use. The impulse that the ball exerts on the floor as it explands is less than the impulse when it was being compressed. The missing energy was converted to heat in the body of the ball. (Sorry, but I'm not going to make this an answer because I don't know the atomic-scale explanation for why that happens.) Commented Jan 14, 2022 at 13:51

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.

• I used quasistatic while thinking about a ball filled with air in thermodynamic terms. Inelastic is probably more general term indeed. Commented Jan 14, 2022 at 14:23
• @RogerVadim I hadn't thought but I like it. Quasi-static refers to a process that is carried out very slowly so that the system is always in equilibrium with its surroundings. It is a necessary but not sufficient condition for a process to be reversible. The other is that there is no friction. So, in that. sense, inelastic behavior includes friction whereas quasi-static behavior doesn't necessarily include friction. Commented Jan 14, 2022 at 14:36
• The answer quoted in the OP claims the compression to be adiabatic, which is what I disagreed with, since the compression is fast. I think that during compression one can neglect the heat exchange with the environmet, but it is also too fast for a temperatuire change. So one could, in principle, calculate the entropy production. Then the expansion is probably a quasistatic process... but I am not sure. I am neglection friction here - thinking only of the air inside... like a bouncing baloon. Commented Jan 14, 2022 at 14:44
• It is adiabatic during the compression because the compression happens so fast. But because the compression occurs so fast it is irreversible because to be reversible it must be quasi-static (a very slow process). IMO the important point is macroscopic kinetic energy is converted to microscopic kinetic energy so the ball keeps losing height each time it bounces. Commented Jan 14, 2022 at 15:10
• Yes I believe we agree. For what it's worth, I was never happy with the ideal of a process being called adiabatic simply because it happens quickly because once the event is finished there is heat transfer. That's not the case for a truly insulated system. Commented Jan 14, 2022 at 15:52