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.

Topics
Phase transitions, Energy conservation, Friction, Rotational dynamics, Computer programming, Integral calculus, Perturbation theory, Series expansion, Energy policy, Public policy and governance
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© 2007 American Association of Physics Teachers.
2007
American Association of Physics Teachers
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