I am having a bit of a conceptual problem with the conservation laws. Consider a system of two bodies of mass m each. One moving at speed V1 towards the second body which is at rest. For the case of an inelastic collision, I understand that the total kinetic energy of the system is not conserved but the total momentum of the system is. What is bugging me is how can this be if both KE and the momentum, P depend on the mass and velocity of the body. If the KE before and after the collision is different, how can the momentum which also depends on m and v be the same? In the case of an inelastic collision, energy is lost to the surroundings: if momentum conservation stems from the conservation of energy, how can the momentum be conserved?