dorsal/arxiv
View SchemaFalling chains
| Authors | Chun Wa Wong, Kosuke Yasui |
|---|---|
| Categories | |
| ArXiv ID | physics/0508005 |
| URL | https://arxiv.org/abs/physics/0508005 |
| DOI | 10.1119/1.2186686 |
| Journal | Am. J. Phys. 74, 490 (2006) |
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.
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"abstract": "The one-dimensional fall of a folded chain with one end suspended from a\nrigid support and a chain falling from a resting heap on a table is studied.\nBecause their Lagrangians contain no explicit time dependence, the falling\nchains are conservative systems. Their equations of motion are shown to contain\na term that enforces energy conservation when masses are transferred between\nsubchains. We show that Cayley\u0027s 1857 energy nonconserving solution for a chain\nfalling from a resting heap is incorrect because it neglects the energy gained\nwhen a transferred link leaves a subchain. The maximum chain tension measured\nby Calkin and March for the falling folded chain is given a simple if rough\ninterpretation. Other aspects of this falling folded chain are briefly\ndiscussed.",
"arxiv_id": "physics/0508005",
"authors": [
"Chun Wa Wong",
"Kosuke Yasui"
],
"categories": [
"physics.class-ph"
],
"doi": "10.1119/1.2186686",
"journal_ref": "Am. J. Phys. 74, 490 (2006)",
"title": "Falling chains",
"url": "https://arxiv.org/abs/physics/0508005"
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