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 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 the falling folded chain are briefly discussed.
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PAPERS| June 01 2006
Chun Wa Wong;
Chun Wa Wong, Kosuke Yasui; Falling chains. Am. J. Phys. 1 June 2006; 74 (6): 490–496. https://doi.org/10.1119/1.2186686
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