The surprising dynamics of a chain on a pulley: lift off and snapping.

Abstract

The motion of weights attached to a chain or string moving on a frictionless pulley is a classic problem of introductory physics used to understand the relationship between force and acceleration. Here, we consider the dynamics of the chain when one of the weights is removed and, thus, one end is pulled with constant acceleration. This simple change has dramatic consequences for the ensuing motion: at a finite time, the chain ‘lifts off’ from the pulley and the free end subsequently accelerates faster than the end that is pulled. Eventually, the chain undergoes a dramatic reversal of curvature reminiscent of the crack, or snap, of a whip. We combine experiments, numerical simulations, and theoretical arguments to explain key aspects of this dynamical problem.