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What are the factors on which coefficient of restitution depend? What is the reason for more coefficient of restitution of two glass balls (0.95) than for two lead balls (0.20)?

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The only factor is the capacity to return to the original shape when it is deformed by an external force.

An elastic object recovers its shape after it has been compressed and deformed, if you crush a plastic bottle and remove the cap it will partially return to his original length, a lead ball is almost completely irreversibly deformed.

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The Coefficient of Restitution measures the percentage of this capacity.

Here below you can watch an exceptional clip of a golf ball completely squashed flatten on a wall that completely recovers its shape

enter image description here

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  • $\begingroup$ Objects with high coefficient of restitution get back to original shape. Is it true? $\endgroup$ – pcforgeek Dec 13 '14 at 15:05
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    $\begingroup$ @pcforgeek, yes, you are seeing with your eyes a wonderful spectacle in the gif, how the golfball recovers his perfect original shape after being completely flattened, it is really amazing. $\endgroup$ – bobie Dec 13 '14 at 17:36
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Most of us will have discovered that a glass rings if you tap it, and the sound of the ring will persist for several seconds after hitting the glass. This shows that elastic energy stored in the glass is not dissipated fast.

I would guess that fewer people have tried the experiment with a lead beaker, but I have and I can report that the lead does not ring. As best you get a dull thud. This shows that elastic energy stored in the lead is dissipated fast.

And this explains the difference in the collisions. When the glass balls collide they deform, and the original kinetic energy is stored as elastic potential energy. Then as the balls spring back into shape most of the stored elastic energy is turned back into kinetic energy. So the final kinetic energy is almost equal to the initial kinetic energy and the coefficient of restitution is close to unity.

When the lead balls collide they deform, but much of the stored elastic energy is lost so the final kinetic energy is a lot lower than the initial kinetic energy. So the coefficient of restitution is a lot less than unity.

All very well, but the obvious question is why lead is so bad at storing and returning elastic energy. This is where I have to resort to arm waving, because the best I can say is that lead is soft. So when you attempt to elastically deform it you end up with a lot of plastic deformation. Even if the collision speeds are low, and there isn't any gross deformation, you'll lose a lot of energy to dislocation movements.

By contrast glass has no easy way to dissipate energy. It's very hard so it doesn't plastically deform, and it doesn't have mobile dislocations so it can't lose energy that way. The stresses involved are too low to excite molecular vibrations or electronic excitations. So you get back most of the elastic energy from glass because there's just nowhere for it to go.

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