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American Journal of Physics -- August 2010 -- Volume 78, Issue 8, pp. 828

The weight of a falling chain, revisited

Eugenio Hamm1 and Jean-Christophe Géminard2

1Universidad de Santiago de Chile, Av. Ecuador 3493, 9170124 Estación Central, Santiago, Chile and Center for Advanced Interdisciplinary Research on Materials, CIMAT, Av. Blanco Encalada 2008, Casilla 487-3, 8370415 Santiago, Chile
2École Normale Supérieure de Lyon, CNRS, Laboratoire de Physique, Université de Lyon, 46 Allée d’Italie, 69364 Lyon Cedex 07, France

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A vertically hanging chain is released from rest and falls due to gravity on a scale pan. We discuss the various experimental and theoretical aspects of this classic problem. Careful time-resolved force measurements allow us to determine the differences between the idealized problem and its implementation in the laboratory. We observe that, in spite of the upward force exerted by the pan on the chain, the free end at the top falls faster than a freely falling body. Because a real chain exhibits a finite minimum radius of curvature, the contact at the bottom results in a tensional force, which pulls the falling part downward.

© 2010 American Association of Physics Teachers

ACKNOWLEDGMENTS

The authors would like to thank R. Freund for introducing them to the problem and H. Gayvallet and B. Castaing for fruitful discussions. E.H. thanks the ENS de Lyon for having invited him as a professor in July 2009, during which this work was done.

Article Outline

  1. INTRODUCTION
  2. THEORETICAL BACKGROUND
  3. SETUP AND PROTOCOL
  4. RESULTS AND DISCUSSION
    1. Air friction
    2. Initial tension of the chain
    3. Finite bending limit of the chain
  5. THEORETICAL ANALYSIS
  6. DISCUSSION AND CONCLUSION

KEYWORDS and PACS

Keywords

chains, force measurement, physics education, student experiments

PACS

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History
Received Sep 2009
Accepted Apr 2010
Online Jul 2010

PUBLICATION DATA

ISSN

0002-9505 (print)  

Publisher

$abstract.society.value is a Member of CrossRef American Association of Physics Teachers

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1119/1.3429983

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