A New Look at an Old Problem: Newton’s Cradle

Abstract

In this paper we consider the most basic multi-impact system, the so-called “Newton’s Cradle.” The task of developing an analytical method to predict the post impact velocities of the balls in the cradle has baffled investigators in the field of impact research for many years. The impulse-based rigid-body body as well as the alternative compliance-based time-base approaches have failed to produce valid solutions to this problem. Here, we present a new method that produces energetically consistent solutions to the problem. Our method is based on the traditional impulse-momentum-based rigid-body approach. We do, however, resolve the nonuniqueness difficulty in the rigid-body approach by introducing a new constant called the Impulse Transmission Ratio. Finally, we verify our method by conducting a set of experiments and comparing the theoretical predictions with the experimental outcomes.