I'm looking to fill some apparent gap in knowledge I have. I may have a bit of difficulty in properly conveying my issue, so I hope a discussion can clean it up. Looking at perfectly inelastic collisions, I am somewhat taken back by the fact that kinetic energy is not conserved? Looking at a simple model. Two bodies, one of mass and the other are bound for collision with velocities , and 0, respectively. after the collision they join together and continue with velocity
From conservation of momentum we have: , which means that
At this point lets look at the kinetic energy before and after the collision.
Then taking the ratio of after to before , meaning
So is someone going to tell me the quantity of energy has been lost as heat ( some seemingly divine intervention of the Second Law of Thermodynamics )? I wasn't aware that I was operating under the pretext of entropy in this idealized case? We know absolutely nothing of the internal collision mechaincs that would generate said heat and potential energies of various forms, yet some how this example dictates a quantity of transformed kinetic energy in this collision? For instance, In Newtons Laws ( and even conservation of energy - as far as the models are concerned ) you can simply "turn off" entropy, and the mechanics will yield a limiting case. But here, the limiting case of conserved kinetic energy seems to be impossible to show. So what is going on here?
Any help greatly appreciated.