Falling chains
Abstract
The one-dimensional fall of a folded chain with one end suspended from a rigid support and a chain falling from a resting heap on a table is studied. Because their Lagrangians contain no explicit time dependence, the falling chains are conservative systems. Their equations of motion are shown to contain a term that enforces energy conservation when masses are transferred between subchains. We show that Cayley's 1857 energy nonconserving solution for a chain falling from a resting heap is incorrect because it neglects the energy gained when a transferred link leaves a subchain. The maximum chain tension measured by Calkin and March for the falling folded chain is given a simple if rough interpretation. Other aspects of this falling folded chain are briefly discussed.
Cite
@article{arxiv.physics/0508005,
title = {Falling chains},
author = {Chun Wa Wong and Kosuke Yasui},
journal= {arXiv preprint arXiv:physics/0508005},
year = {2015}
}
Comments
9 pages, 1 figure; the Abstract has been shortened, three paragraphs have been re-written for greater clarity, and textual improvements have been made throughout the paper; to be published by the Am. J. Physics