Conservation of momentum in the COM frame amounts to the requirement that p = 0 both before and after collision. In the Newtonian analysis, conservation of mass dictates that ⁠ m = m 1 + m 2 ⁠. In the simplified, one-dimensional scenarios that we have been considering, only one additional constraint is necessary before the outgoing momenta of the particles can be determined—an energy condition. In the one-dimensional case of a completely elastic collision with no loss of kinetic energy, the outgoing velocities of the rebounding particles in the COM frame will be precisely equal and opposite to their incoming velocities. In the case of a completely inelastic collision with total loss of kinetic energy, the outgoing velocities of the rebounding particles will be zero.