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Question Number 57400 by ajfour last updated on 03/Apr/19

Commented by ajfour last updated on 04/Apr/19

A small block of mass m at the top of a solid sphere is given a gentle tap to initiate motion. Find angle α till where block remains in contact with sphere. Assume no friction between block and sphere, while enough friction on ground such that sphere rolls. Find also the speed of sphere when the small block loses contact with sphere.

$$\mathrm{A}\:\mathrm{small}\:\mathrm{block}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{m}\:\mathrm{at}\:\mathrm{the}\:\mathrm{top} \\ $$$$\mathrm{of}\:\mathrm{a}\:\mathrm{solid}\:\mathrm{sphere}\:\mathrm{is}\:\mathrm{given}\:\mathrm{a}\:\mathrm{gentle} \\ $$$$\mathrm{tap}\:\mathrm{to}\:\mathrm{initiate}\:\mathrm{motion}.\:\mathrm{Find}\:\mathrm{angle} \\ $$$$\alpha\:\mathrm{till}\:\mathrm{where}\:\mathrm{block}\:\mathrm{remains}\:\mathrm{in}\:\mathrm{contact} \\ $$$$\mathrm{with}\:\mathrm{sphere}.\:\mathrm{Assume}\:\mathrm{no}\:\mathrm{friction} \\ $$$$\mathrm{between}\:\mathrm{block}\:\mathrm{and}\:\mathrm{sphere},\:\mathrm{while} \\ $$$$\mathrm{enough}\:\mathrm{friction}\:\mathrm{on}\:\mathrm{ground}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{sphere}\:\mathrm{rolls}.\:\mathrm{Find}\:\mathrm{also}\:\mathrm{the}\:\mathrm{speed}\:\mathrm{of} \\ $$$$\mathrm{sphere}\:\mathrm{when}\:\mathrm{the}\:\mathrm{small}\:\mathrm{block}\:\mathrm{loses} \\ $$$$\mathrm{contact}\:\mathrm{with}\:\mathrm{sphere}.\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$

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