The two-ball bounce problem

A popular classroom demonstration is revisited in which a light ball and a much larger heavier ball are vertically aligned and dropped together onto a hard surface. Careful experimental data obtained using a high-speed camera is compared to a lumped-mass Newtonian restitution model. Good macroscopic agreement is found, provided there is sufficient separation between the two balls as they are dropped. An alternative continuum model based on elastic membrane theory is developed to explain the limit in which the balls are initially touching. The model assumes the lower ball deforms to a truncated sphere upon its impact with the floor, exciting an elastic wave which subsequently launches the upper ball like a particle on a trampoline, before the lower ball leaves the ground. A favourable comparison with experimental data is found for the case of negligible initial separation between the balls.