A unique pure mechanical system revealing dipole repulsion

We study multiple elastic collisions of a block and a ball against a rigid wall in one dimension. The complete trajectory of the block is solved as an analytic function of time. Near the turning point of the block the force carried by the ball is proportional to 1/x^3, where x is the distance between the wall and the block, in the limit that the block is sufficiently heavier than the ball. This is a unique pure mechanical system that reveals dipole-like repulsion.