Brun P-T, Audoly Basile, Goriely Alain, Vella Dominic
Department of Mathematics , Massachusetts Institute of Technology , Cambridge, MA 02139, USA.
Laboratoire de Mécanique des Solides , CNRS and École Polytechnique , UMR 7649, 91128 Palaiseau, France.
Proc Math Phys Eng Sci. 2016 Jun;472(2190):20160187. doi: 10.1098/rspa.2016.0187.
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 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.
连接在链条或绳子上的重物在无摩擦滑轮上的运动是基础物理学中的一个经典问题，用于理解力与加速度之间的关系。在此，我们考虑当其中一个重物被移除，从而一端以恒定加速度被拉动时链条的动力学情况。这个简单的变化对后续运动产生了显著影响：在有限时间内，链条从滑轮上“抬起”，自由端随后比被拉动的一端加速得更快。最终，链条经历了曲率的剧烈反转，让人联想到鞭子的噼啪声。我们结合实验、数值模拟和理论论证来解释这个动力学问题的关键方面。
