ONE-DIMENSIONAL BOUNCE OF INELASTICALLY COLLIDING MARBLES ON A WALL

n marbles with zero velocity are pushed away by a wall moving at constant velocity. The collisions are treated using an inelasticity coefficient eta and the equations of motion are numerically integrated until no more marbles collide with the wall. The principal investigated quantity is the relative kinetic energy E(k) of the bounced marbles. A model of `independent collision waves' is presented which predicts with a good precision the maximum of E(k) for eta-1 = 2(1-1/n) -1, and the value eta-2 = tan2 pi/4(1-(1/n)) at which the marbles stick to the wall. It is found that, for large n, the only important parameter is gamma = (1 - eta)n. Equivalent results are found when a marble is thrown against the column.