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American Journal of Physics -- December 2012 -- Volume 80, Issue 12, pp. 1051

Modeling a falling slinky

R. C. Cross and M. S. Wheatland

School of Physics, University of Sydney, NSW 2006, Australia

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A slinky is an example of a tension spring: in an unstretched state a slinky is collapsed, with turns touching, and a finite tension is required to separate the turns from this state. If a slinky is suspended from its top and stretched under gravity and then released, the bottom of the slinky does not begin to fall until the top section of the slinky, which collapses turn by turn from the top, collides with the bottom. The total collapse time tc (typically ∼ 0.3 s for real slinkies) corresponds to the time required for a wave front to propagate down the slinky to communicate the release of the top end. We present a modification to an existing model for a falling tension spring [Calkin, Am. J. Phys. 61, 261–264 (1993)] and apply it to data from filmed drops of two real slinkies. The modification of the model is the inclusion of a finite time for collapse of the turns of the slinky behind the collapse front propagating down the slinky during the fall. The new finite-collapse time model achieves a good qualitative fit to the observed positions of the top of the real slinkies during the measured drops. The spring constant k for each slinky is taken to be a free parameter in the model. The best-fit model values for k for each slinky are approximately consistent with values obtained from measured periods of oscillation of the slinkies.

© 2012 American Association of Physics Teachers

Article Outline

  1. INTRODUCTION
  2. THE COLLAPSE OF THE TURNS AT THE TOP OF THE SLINKY
  3. MODELING THE FALL OF A SLINKY
    1. The hanging slinky
    2. The falling slinky with instant collapse of turns
    3. The falling slinky with a finite time for collapse of turns
  4. MODELING REAL SLINKIES
    1. Data
    2. Fitting the data and model
  5. CONCLUSIONS

KEYWORDS, PACS, and IPC

Keywords

continuum mechanics, physics education, springs (mechanical), teaching, wave propagation

PACS

  • 46.00.00

    Continuum mechanics of solids

International Patent Classification (IPC)

RELATED DATABASES

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History
Received Mar 2012
Accepted Aug 2012

PUBLICATION DATA

ISSN

0002-9505 (print)  
1943-2909 (online)

Publisher

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

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1119/1.4750489

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