Collisions with Springs: A Useful Context for the Study of Analytical Dynamics

A recent paper1 in this journal describes an experimental demonstration of the conservation of total momentum before, during, and after an elastic collision between two bodies. The experiment also appears to show that total kinetic energy is conserved in the process, including during the collision. There is a danger that this may give rise to some misconception given that, in any collision that takes place over a finite time, some kinetic energy must transfer to potential energy—albeit temporarily in the case of an elastic collision. Indeed, when a collision is observed in the c.m. frame, all kinetic energy is lost momentarily. The sequence of simple experiments described below, which can be performed using standard equipment available in undergraduate laboratories, was developed so that undergraduate students could study a collision process in some detail. It was designed to enable students to gain insight into a range of important ideas in elementary analytical dynamics, including conservation of momentum, energy transfer in inelastic collisions, and coefficient of restitution. An extension of the experiment also gives insight into wave propagation in elastic media.