title: 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 acceleratesfasterthan 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.
authors.affiliation: Department of Mathematics , Massachusetts Institute of Technology , Cambridge, MA 02139, USA.
authors.forename: P-T
authors.identifier: 0000-0002-4175-0604
authors.initials: PT
authors.lastname: Brun
authors.affiliation: Laboratoire de Mécanique des Solides , CNRS and École Polytechnique , UMR 7649, 91128 Palaiseau, France.
authors.forename: Basile
authors.initials: B
authors.lastname: Audoly
authors.affiliation: Mathematical Institute , University of Oxford , Oxford OX2 6GG, UK.
authors.forename: Alain
authors.identifier: 0000-0002-6436-8483
authors.initials: A
authors.lastname: Goriely
authors.affiliation: Mathematical Institute , University of Oxford , Oxford OX2 6GG, UK.
authors.forename: Dominic
authors.identifier: 0000-0003-1341-8863
authors.initials: D
authors.lastname: Vella
keywords: Atwood machine; curvature-reversal; dynamic contact mechanics; strings and chains; whip