How does the mass of a ball affect the % of energy loss

[Drake M]

Homework Statement

I am wondering how the mass of a ball affects the percentage of energy loss when the ball bounces.

Homework Equations

Ep=mgh
eff=eout/ein x 100%

The Attempt at a Solution

1)I don't think it affects them because if the ball is heavier but still made of the same material it has the same elasticity and density only mass has changed. But if all of the starting Ep goes to Ek then it should have generally the same efficiency. If this is correct please tell me why its correct and if its wrong then explain it. Thanks in advance. Cheers

 

[haruspex]

Are you familiar with coefficient of restitution? If so, write down the equation for rebound velocity.

 

[Drake M]

No, we haven't learned that in class so we wouldn't be allowed to use it as a reason on a test or lab. I am just trying to think of a reasonable explanation as to why. I did the experiment but there didn't seem to be correlation between the two variables.

 

[Drake M]

Basically what I'm asking is why doesn't mass affect energy loss

 

[haruspex]

Basically what I'm asking is why doesn't mass affect energy loss

There is no lay-down reason. It comes out of the physics behind bouncing, as is described by the equation involving coefficient of restitution. I can offer an explanation of why it might not affect the percentage lost. Doubling the mass doubles the energy invested. If it also doubles the energy lost then the percentage doesn't change. Does it seem reasonable that doubling the energy in doubles the loss?

On the other hand, I can conceive of a physical behaviour in which the mass does affect the percentage loss. Imagine dropping an assembly consisting of a small mass stuck on top of an egg stuck on top of a rubber pad, just a short distance. If the mass is small enough the egg stays intact and you get a decent bounce. With a heavier mass the egg cracks and the bounce is less. You could also imagine an analogous behaviour at the nanoscale within a material.

 

[Drake M]

Thanks