The falling chain of Hopkins, Tait, Steele and Cayley

Abstract

A uniform, flexible and frictionless chain falling link by link from a heap by the edge of a table falls with an acceleration $g/3$ if the motion is nonconservative, but $g/2$ if the motion is conservative, $g$ being the acceleration due to gravity. Unable to construct such a falling chain, we use instead higher-dimensional versions of it. A home camcorder is used to measure the fall of a three-dimensional version called an $xyz$-slider. After frictional effects are corrected for, its vertical falling acceleration is found to be $a_x/g = 0.328 \pm 0.004$. This result agrees with the theoretical value of $a_x/g = 1/3$ for an ideal energy-conserving $xyz$-slider.