Bounce of a ping pong ball vs bounce of other things (How does the material affect ?)?

Question

Yesterday I saw that a ping pong ball bounced nicely on a hard surface but poorly on a mattress.On the contrary ,I saw that other things (a pen for example) bounced poorly on a hard surface but nicely on a mattress Please I want to know the reason behind the motion and more importantly why the difference is there **EDIT:** I found that certain materials rapidly lose their Kinetic energy on striking hard surfaces but a mattress manages to store the kinetic energy of the object as elastic potential energy and returns it in accord with its elasticity. What I find intriguing now is the properties of the material which contribute to loss of KE. Any help is highly appreciated. **NOTE:** I ensured that the pen hit the surface with minimum area in contact (the side from which the nib comes out) and the nib was removed. The pen material didn't look like it could be easily be deformed.

Answer 1

A perfectly elastic collision is one in which energy is conserved. It is an ideal case that never happens in practice.

A related concept is called the "coefficient of restitution". The classic example is a ball dropped from a specified height. The coefficient of restitution is the ration of the "bounce" height to the "drop" height. It cannot be greater than 1, and--in the real world--is always less.

A coefficient of restitution of 1 is equivalent to saying that there is a "perfectly elastic" collision.

Anything dropped on something like a mattress will have a very LOW coefficient of restitution---meaning the the collision is very much INelastic. In fact, I would expect many objects dropped on a mattress to not bounce at all.

There are all manner of ways to see confusing and ambiguous results. For example, a very light object dropped on a soft surface (like a mattress) may in fact bounce. One plausible explanation is that any complex structure can have widely varying elasticity, depending on what it is interacting with. My HUNCH is that the coefficient of restitution between a mattress and a grain of rice is vastly different than with the same mattress and a cannonball.