Gravity effects in mass-spring-damper models of inelastic collisions

Abstract

A ball bouncing on a rigid surface is modeled as a mass-spring-damper system. We consider the effect of including or neglecting the force of gravity, extending previous work that shows that including gravity yields a velocity-dependent coefficient of restitution. This velocity dependence is most pronounced at low impact velocities and high damping. Previously-published models differ in defining the termination of the collision, with some referencing the ball's position and others noting when the contact force becomes zero. We propose a new model that combines aspects of these approaches. The various models are compared in their predictions for the coefficient of restitution and collision duration, and are compared to experimental data from a cart on an inclined track bouncing repeatedly on a spring. While the new model shows some improvement over the prior collision termination conditions, the inclusion of gravity is the more important consideration in modeling repeated bouncing.