Falling chains

Details Falling chains Falling chains

2005-07-31

arxiv.org/abs/physics/0508005v3

Am. J. Phys. 74, 490 (2006)

Physics

Classical Physics

9 pages, 1 figure; the Abstract has been shortened, three paragraphs have been re-written for greater clarity, and textual imp

Scientific paper

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.

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