Rocking Newton’s cradle

TLDR

Textbook accounts of Newton’s cradle predict that displacing one ball ejects a second while the rest stay still, but studies by Hermann and Schmälzle, Hinch and Saint‑Jean, and others reveal a more nuanced reality. The study aims to simulate Newton’s cradle to reproduce the line break at the first collision, the subsequent in‑phase motion of all balls, and to validate the model against experimental data. The simulation attributes the line break to the balls’ finite elastic response and the later collective motion to viscoelastic dissipation during impacts, while an ideal dissipation‑free model shows complex dynamics. The simulation accurately reproduces the line break and in‑phase motion observed experimentally, and the ideal dissipation‑free model reveals complex dynamics.

Abstract

In textbook descriptions of Newton’s cradle, it is generally claimed that displacing one ball will result in a collision that leads to another ball being ejected from the line, with all others remaining motionless. Hermann and Schmälzle, Hinch and Saint-Jean, and others have shown that a realistic description is more subtle. We present a simulation of Newton’s cradle that reproduces the break-up of the line of balls at the first collision, the eventual movement of all the balls in phase, and is in good agreement with our experimentally obtained data. The first effect is due to the finite elastic response of the balls, and the second is a result of viscoelastic dissipation in the impacts. We also analyze a dissipation-free ideal Newton’s cradle which displays complex dynamics.