The question is :
Heavier object A, initially at rest, is struck by lighter object B. Is it possible for object A to have a larger final momentum than the initial momentum of object B?
The answers is yes and the argument as follows:
Suppose a pingpong bouncing back upon hitting a stationary truck. The change in momentum of the ball is $ 2mv$. Conservation of momentum then requires the more massive object to have a momentum $2mv $ in the opposite direction.
But how is it possible? After the collision the ball retains same kinetic energy while granting some of it to the truck? Isn't it violation of the law of conservation of energy?
Best Answer
The ping pong ball would lose a tiny amount of kinetic energy to the truck. The truck ends up with a momentum of just under twice what the ping pong ball had. However, energy is 1/2 m*v^2 = 1/2(m*v)^2/m. Since the truck is much more massive than the ping pong ball, it carries much less energy for a given momentum. The end result is that the small amount of energy lost in the ping pong ball due to the momentum given to the truck is equal to the extra energy given to the truck (ignoring losses due to imperfect elasticity).