# Mechanics predict an infinite number of bounces, does this make sense?

If we bounce a ball in ideal conditions, so after each bounce it retains only 1/4 of the original kinetic energy, then the time between bounces diminishes in half after each bounce. This will predict that the ball will be at rest at time=2, after enduring an infinite number of bounces (a variation of the zeno paradox).

But contrary to zeno paradox, here the bounces can in principle be physically measured. If we limit our discussion to the newtonian framework, does it make sense that the ball will bounce an infinite number of times? or is this an example of the failure of Newtonian mechanics because it predicts infinities?

• Maybe it’s a failure of the model to have enough detail to represent reality? The ball isn’t a point, the speed of sound in the ball isn’t infinite, etc. Dec 22, 2019 at 16:05
• @BobJacobsen what you said makes sense, but I was thinking ideal newtonian mechanics in which those issues should not appear. Let us say it is a point particle. Well, still the bouncing cannot happen at unlimited short times I guess
– user65081
Dec 22, 2019 at 16:38
• @BobJacobsen: That should be an answer.
– user4552
Dec 22, 2019 at 16:42
• if you assume "ideal conditions" in a "newtonian framework" what would cause in each bounce to have the kinetic energy to be 1/4 of the previous one? Do you consider dissipation to be part of the ideal conditions within a newtonian framework? Dec 22, 2019 at 17:39
• @hyportnex yes, they are inelastic bounces
– user65081
Dec 22, 2019 at 18:33