Consider a point mass of mass m going with velocity v towards a point mass also of mass lying still. Now conservation of momentum allows any combinations og mass times velocities that add to the total momentum before the collision. So for instance ½mv + ½mv would be good. This is where the masses collide until they have the same velocity. For me it makes sense that this would happen since the first mass is not able to push against the other as soon as the mass originally lying still is going faster than the other - which happens infinitesimally later than when their velocities are the same. However, if energy was to be conserved the above would not hold, since E is proportional to v squared. My question is: How can energy have influence on when our two masses geometrically are able to push against each other or not? - like if energy was conserved in the above they would still be pushing against each other even though the first particle would be slowing down as seen from the second particles frame.