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New insights on the falling ladder problem

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Abstract

A classical mechanics approach of the falling ladder problem with and without friction is presented. The ladder falls freely under the influence of gravity. As the ladder slides on the floor, it is free to lose its contact with the wall. The general nonlinear differential equation of motion is derived and solved numerically using the Runge–Kutta method implemented by MATLAB. The variation of the contact force with the wall is calculated and used for detecting the angle of separation from the wall. The motion after separation has two degrees of freedom and it is also solved by the Runge–Kutta method. It is shown that the separation time from the wall and the reaction forces are higher than the corresponding no-friction values.

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Data availability statement

The datasets generated during and/or analysed during the current study are not publicly available, but are available from the author on reasonable request.

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Acknowledgements

The author appreciates the fruitful conversations he has had with Ali Ghorashi (his co-author in reference [2] and a physics Ph.D. candidate at M.I.T.); as well as the constructive comments made by an anonymous reviewer on an earlier draft of this paper.

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The author declares that no funds, grants, or other support were received during the preparation of this manuscript.

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  1. Department of Engineering, University of Southern Maine, Gorham, ME, 04038, USA

    Mehrdaad Ghorashi

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  1. Mehrdaad Ghorashi
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Correspondence to Mehrdaad Ghorashi.

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Ghorashi, M. New insights on the falling ladder problem. Meccanica 57, 2281–2292 (2022). https://doi.org/10.1007/s11012-022-01552-2

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  • DOI: https://doi.org/10.1007/s11012-022-01552-2

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