Newton's Cradle Simulation

Live script simulation of various Newton's cradles.

A Newton's cradle is a linear array of simple pendulums, typically steel balls suspended by strings which in equilibrium are in close contact each other. When one end ball (1) is pulled out of equilibrium away from the array and released, it swings towards the array and collides with its neighbor (2). Magically, for Nelastic balls, balls 1,2,3,...N-1 then appear nearly stationary while the last ball (N) swings away from the array with nearly the full energy of ball (1). This phenomenon results from a rapid sequence of (nearly) elastic collisions. What happens if the balls are not in close contact and what if the collisions are inelastic? Why might a Newton's Cradle But With Wrecking Balls be a letdown?

This educational Live Script simulates Newton's cradle with any number of balls, ball radii and masses, and separations. It uses the small angle approximation to model each free pendulum motion and incorporates a coefficient of restitution to model energy loss in collisions.

This simulation may interest students and instructors of physics and the curious and requires only a background in introductory mechanics. 'Try this' suggestions, coding challenges, hyperlinks, and references are included for further exploration. Additional educational Live Scripts by the author are available here.