Determining kinetic energy loss in inelastic collisions

Question

I know there have been a lot of threads about this topic, but I haven't found one that answers my specific question. So if we have a case of two objects that stick together after colliding, with no external force present, then the momentum of the system is conserved. From that one can calculate the velocity of the combination of the two objects and use that to find the final kinetic energy (K.E.). We also know the initial K.E. as the sum of the K.E. of each object. The difference K.E.(final) - K.E.(initial) can be calculated and it is negative as some K.E. has been converted to heat. An example with equations can be found in @Bob D's answer here: Why do objects always stick together in perfectly inelastic collisions

What I'm wondering about is that it seems to me that if a variety of objects were used, all with different physical properties governing their deformation (elasticity, stiffness or whatever is appropriate), then that should affect how much K.E. is lost to heat. But the equations give one particular answer for K.E. loss. How do they "know" to do that without detailed knowledge of the objects' composition?

Answer 1

Pretty much expanding what Sandejo says: those physical properties that you mention are the ones that will determine what type of collision takes place. If two bouncy balls collide, they will undergo a nearly elastic collision, so their kinetic energy loss will not be the inelastic one that you reference, but rather much smaller. You could put glue on the surface of the balls to force them to stick together, but the glue is then part of the system too, and thus you have changed their physical properties. The elasticity of the balls might cause them to deform wildly as they try to bounce apart, but because they are stuck with glue, those waves will gradually dissipate into heat. Whereas, if two pieces of wet clay collide, they may stick together without much jiggling at all, ie. the energy is rapidly converted to heat. But objects with the wrong combination of properties will never undergo a perfectly inelastic collision.

Answer 2

Okay, I think I've reached the intuitive understanding that I was after. Just to summarize - for an isolated system, the conservation of momentum sets a value on the amount of K.E. lost in a perfectly elastic collision (for given values of mass and initial velocities). It was puzzling me how different materials will all have this same exact loss of K.E., given widely varying material properties. But their material properties come into play to determine the time it takes to convert that K.E. to heat, sound, etc.

We derive equations for the initial state, when the two objects are separated, and then for the final state when they have coalesced into one object and are moving with the same velocity. From those two equations we calculate the K.E. loss. There are, however, intermediate states when the two objects are in contact but are perhaps moving toward and away from each other, in which case the final K.E. value doesn't yet apply. So the particular material properties of the object come into play during this time.