How Is the Coefficient of Restitution Linked to Conservation of Energy?

[Generally Confused]

Where does the Coefficient of Restitution equation come from, in terms of the Conservation of Energy?

The measure of efficiency is the velocity after the collision divided by the velocity before the collision, but how does it get to that point? I'm trying to view this focused on an object that is dropped from a specific height.

I believe it has something to do with 1/2mv^2=mgh (kinetic energy and gravitation potential energy put into Ei=Ef+Wnc) but I'm not sure how the transformation occurs.

Let me know if I'm being too vague, as I'm not exactly sure how much information is necessary.

 

[jbriggs444]

It comes from the same place that the coefficient of friction does. It is an engineering approximation that holds over a useful range of conditions.

 

[Jnan]

The Coefficient of Restitution Is actually defined as such. It is actually the ratio of impact after and before collision. Since most of the times, we don't consider loss of mass of the colliding bodies we have only velocity as the parameter which will measure the impact of the collision. Hence, Coefficient of Restitution comes into scene.

 

[sophiecentaur]

It comes from the same place that the coefficient of friction does.

Actually, I would say that it is even more of an abstraction than the coefficient of friction. Most situations where people seem to want to use it are so far from 'ideal' that I would say its only use is for answering A level Mechanics questions. I wish that School Maths courses would introduce COR with a massive caveat from the start. It would help reduce the number of unanswerable questions on PF that we get about collisions. Steel balls and steel plates - OK. Anything else, treat it with care.