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Suppose a spherocylindrical solid is let to fall from some height to a flat, solid surface, bouncing some height up after it reaches the surface. The object clearly loses some of its energy due to the collision with the ground, but which factors determine exactly how much energy is lost? Also, please make these factors quantitative so I can create a theoretical model to predict the amount of energy lost as a result of a spherocylinder's bounce on some surface, and hence compare the release height and the predicted bounce height.

Also, keep in mind that the object may be released with some rotational kinetic energy.

In case you're wondering why I am asking this, my goal is to theoretically predict how much energy a Tic Tac, which is the spherocylindrical object, will lose if it is let go to bounce on a hard glass surface.

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    $\begingroup$ You're looking for the coefficient of restitution. A separate issue is of course how much KE goes into translational vs rotational $\endgroup$ – Señor O Mar 3 at 22:09
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    $\begingroup$ Yes. The coefficient of restitution makes the difference in bounce of a rubber solid and a wet clay solid. Also to think about: Suppose you dropped it through air or through water. Suppose it was shaped something like a pancake or something like a pencil.These would change how much energy was lost to friction on the way down. $\endgroup$ – mmesser314 Mar 3 at 22:12
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    $\begingroup$ Note that I would like to do this theoretically, and not by actually performing an experiment. Why the emph. on the former and not the latter? Good science almost always combines both. Your problem requires knowledge of material constants of a TicTac that can really only be accessed by experiment. $\endgroup$ – Gert Mar 3 at 22:24
  • $\begingroup$ What I meant was that I need to create a theoretical model, and then test it with an experiment, and so I didn't want the answers to be heavily focused on the experiment, because I figured they would, since it would be easier to answer my question that way. $\endgroup$ – Matthew Tchouikine Mar 3 at 22:28
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    $\begingroup$ Actually, some of your rather strident stipulations are likely to scare potential takers away. $\endgroup$ – Gert Mar 3 at 22:38
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I think your question is related to the elasticity theory. If two bodies are perfectly elastic, they exchange momenta. In this case, you might expect a perfect bounce. The loss of energy after a collision is related to a fraction of inelastic interactions. Search for inelastic-elastic collisions in classical mechanics and the coefficient of restitution. Here some info. The energy loss after an inelastic collision goes to the heat generation and deformations. Now you have to say whether you want to go to the microscopic level or your model is going to be macroscopic.

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  • $\begingroup$ I would like my model to be microscopic $\endgroup$ – Matthew Tchouikine Mar 4 at 1:56
  • $\begingroup$ Also, I know that the coefficient of restitution would vary based on the angle of incidence (as Anthonym mentioned), but how could I model that variation quantitatively? $\endgroup$ – Matthew Tchouikine Mar 4 at 1:56
  • $\begingroup$ Furthermore, is there a way to predict the rotational kinetic energy of the body after it bounces, and if so, how? $\endgroup$ – Matthew Tchouikine Mar 4 at 1:57
  • $\begingroup$ It seems you what to start with overcomplicated model taking into account everything. The art of making simulations is to understand what can be neglected. Let us start with what your bodies are. Are they macroscopic bodies or atoms or nanoparticles? $\endgroup$ – freude Mar 4 at 2:37
  • $\begingroup$ Are you talking about rotations of massive bodies or nano-objects? In the later case, you might be interested in the scattering theory. $\endgroup$ – freude Mar 4 at 2:39
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The relevant parameters are:

  • Mass of the body
  • Translational speed on impact (function of drop height and air resistance)
  • Rotational speed on impact
  • Angle of incidence of the impact (2 rotational angles of the body matter here)
  • Coefficient of restitution (elasticity) of the body and surface
  • Horizontal coefficient of restitution (sliding friction) between the body and surface
  • Smoothness of the surface
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