A well studied problem in elementary mechanics is the location of the release point of a particle that slides on the surface of a frictionless sphere when it is released from rest at the top. We generalize this problem to include the effects of sliding friction and solve it by a perturbation expansion in the coefficient of sliding friction and by an exact integration of the equation of motion. A comparison of the two solutions identifies a parameter range where the perturbation series accurately represents the motion of the particle and another range where the perturbative solution fails qualitatively to describe the motion of the particle.
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PAPERS| May 01 2007
A block slipping on a sphere with friction: Exact and perturbative solutions
Tom Prior, E. J. Mele; A block slipping on a sphere with friction: Exact and perturbative solutions. Am. J. Phys. 1 May 2007; 75 (5): 423–426. https://doi.org/10.1119/1.2410018
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