Suppose I have a system which contains two bodies m1 and m2 with initial velocities v1 and v2 , respecitvely.
they hurl toward each other and make an inelastic collision. such that they are now one body of mass
m1 + m2
I know that the difference in momentum is conserved before collision and after collision, so that: ΔP = 0
but during that time of collision , non-conservative force Fnc act on both bodies and thus the difference in mechanical energy before the collision and after the collision is not conserved ,so that : Eb - Ea = Wnc
Eb = mechanical energy after collision
Ea = mechanical energy before collision
Wnc = Work done by non conservative force
However , I have a problem at understanding why the energy is not conserved , If during the time of collision, both bodies have a non-conservative force ' Fnc ' acting upon them , and this force is equal in magnitude but opposite in direction on each body ,then how can it be that these two forces do not cancel out each other ( the sum of internal forces equals to zero ) so that the total work done by the sum of non-conservative forces is zero? I say that Wnc = 0 since I suppose that Wnc = ∫( -Fnc + Fnc)dr = 0 ( the forces and dr are vectors , and the integral is path integral )
So since Wnc = 0 by the sum of internal forces , then the diffrence in mechanical energy should be conserved so that Eb - Ea = 0 , but this is not the case , why?
Eb - Ea = Wnc
The Attempt at a Solution