High School Question about the validity of Coefficient of Restitution

[Tyrone Sawyer]

Specifically as to the validity of CoR as a metric for the bounciness of an object. CoR is inherently a property of /two/ objects, say, the interaction between rubber and steel. Is it truly the case that given two objects, it's impossible to say that one object is bouncier than another? This is a topic for which I really can't find many people talking, likely because it's boring, useless, but also sort of easy.

My intuition tells me that if you have two objects, and two surfaces, than if object A bounces better than object B on surface C, than it should bounce better on surface D as well. Further, it should bounce better on /all/ surfaces.

My understanding is that CoR is really a very rough approximation of a whole bunch of chaotic interplay between systems, but my intuition strongly tells me that there should be a notion of bounciness; even if it can't necessarily be used to trace back to CoR without complex formulae, whatever those formulae are, they should be monotone increasing.

 

[haruspex]

Specifically as to the validity of CoR as a metric for the bounciness of an object. CoR is inherently a property of /two/ objects, say, the interaction between rubber and steel. Is it truly the case that given two objects, it's impossible to say that one object is bouncier than another? This is a topic for which I really can't find many people talking, likely because it's boring, useless, but also sort of easy.

My intuition tells me that if you have two objects, and two surfaces, than if object A bounces better than object B on surface C, than it should bounce better on surface D as well. Further, it should bounce better on /all/ surfaces.

My understanding is that CoR is really a very rough approximation of a whole bunch of chaotic interplay between systems, but my intuition strongly tells me that there should be a notion of bounciness; even if it can't necessarily be used to trace back to CoR without complex formulae, whatever those formulae are, they should be monotone increasing.

Think of each object as an imperfect spring. That is, each has two spring constants: a larger one during deformation (compression in this case) and a smaller one during relaxation (decompression).
See if you can derive the CoR for the combination in terms of those four constants.