I was just looking at the equation: $$v2-v1=-e(u2-u1).$$ This equation is to describe the collision between two masses, where $v$ is the final velocity and $u$ is the initial velocity, $e$ is the coefficient of restitution.
The collision is the most inelastic when $e=0$, however, it is not true that all motion stops in an inelastic collision.
Case one: Two objects of the same mass and same speed in opposite directions, when they collide they will stick together and stop- total momentum was zero before the collision, so should also be conserved after.
Case two: Two objects of the same mass. One mass is stationary and the other one is moving, they collide and stick together.For the momentum to be conserved, after they join, they move together with the half the initial velocity of the moving mass.
I was told that when $e=0$, all motion stops only in the centre of mass frame, because the total momentum is always zero in the centre of mass frame.
Please could someone explain why the velocity and the momentum always zero in the centre of mass frame?