Suppose that N sticky balls having masses m1, m2, m3, … , mN are arranged about a point in space with various distances and in various directions. The balls are all moving toward the point such that they will all arrive at the same moment. Since they are sticky balls, they will not rebound, but will adhere to each other in a lumpy cluster.
The amount of a particle’s momentum is proportional to the speed to the first power, but the amount of a particle’s kinetic energy is proportional to the speed squared.
Is it possible that the law of the conservation of momentum will require that the aggregate mass, after the collision of all the sticky balls, move in one direction, while the law of the conservation of energy will require it to move in a different direction?
