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Sliding in rough convex bowls

Published online by Cambridge University Press:  23 January 2015

Mark Hennings  and
Jon Ingram
Mark Hennings
Affiliation:
Rugby School, Warwickshire CV22 5EH
Jon Ingram
Affiliation:
Rugby School, Warwickshire CV22 5EH
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Extract

It is an elementary fact that a particle sliding on a rough horizontal table experiences a deceleration of magnitude μg, where μ is the coefficient of friction between the particle and the table. Thus, if the initial speed u of the particle and the braking distance d are both known, then μ can be determined by the formula

The idea of using braking distances to determine the coefficient of friction led the second author to ask the following question:

A particle slides on the interior surface of a rough hemispherical bowl starting from rest. If the starting point of the particle and the point at which it comes to instantaneous rest after its slide are both known, is it possible to determine the coefficient of friction between the particle and the bowl?

Type
Articles
Information
The Mathematical Gazette , Volume 98 , Issue 541 , March 2014 , pp. 8 - 23
Copyright
Copyright © The Mathematical Association 2014

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References

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