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 (COR). 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 COR 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.