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I've recently been looking for information on how to describe elastic and inelastic collisions in a way that spans the full set of possibility of different levels of elasticity between objects.

In both of my physics textbooks I was only able to find quantified information on the two extremes, perfectly inelastic and perfectly elastic. Eventually I found an equation that seems to span the full range between them.

I found it on Wikipedia actually, should have looked there earlier. Here's the link:

http://en.wikipedia.org/wiki/Inelastic_collision" [Broken]

I'm referring to the first two equations, Va and Vb.

My concern with the given equations is that the pair contains only one coefficient of restitution (i.e. only one measure of elasticity). In the context in which I want to do collisions, I want to specify a particular elasticity for every object in the system.

Thus, if two objects in my system collide then I have

I've been trying to think about it by example to see if I can derive it myself.

For example, suppose a steel ball (nearly perfectly elastic) collides with mud (nearly perfectly inelastic). In that case the steel ball should get stuck to the mud and most of the energy will get transferred to deformation of the mud. In other words, it would behave like an inelastic collision despite the steel ball's elasticity. This implies that inelasticity is more of a dominate factor than elasticity is in collisions, in some sense.

My problem is I don't know how to extend this to the more general cases to correctly model how different values of elasticity interact with each other during collision.

What's the general solution? Will each object be effected by

In both of my physics textbooks I was only able to find quantified information on the two extremes, perfectly inelastic and perfectly elastic. Eventually I found an equation that seems to span the full range between them.

I found it on Wikipedia actually, should have looked there earlier. Here's the link:

http://en.wikipedia.org/wiki/Inelastic_collision" [Broken]

I'm referring to the first two equations, Va and Vb.

My concern with the given equations is that the pair contains only one coefficient of restitution (i.e. only one measure of elasticity). In the context in which I want to do collisions, I want to specify a particular elasticity for every object in the system.

Thus, if two objects in my system collide then I have

*two*measures of elasticity but the equation I've found for working out the collisions only has*one*. So, my question is, how do I correctly implement both of the elasticitys of the objects?I've been trying to think about it by example to see if I can derive it myself.

For example, suppose a steel ball (nearly perfectly elastic) collides with mud (nearly perfectly inelastic). In that case the steel ball should get stuck to the mud and most of the energy will get transferred to deformation of the mud. In other words, it would behave like an inelastic collision despite the steel ball's elasticity. This implies that inelasticity is more of a dominate factor than elasticity is in collisions, in some sense.

My problem is I don't know how to extend this to the more general cases to correctly model how different values of elasticity interact with each other during collision.

What's the general solution? Will each object be effected by

*different*elasticities or will it be merged into one value Cr applied to both somehow?
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