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5. A small mass m starts from rest and slides from the top of a fixed sphere of radius r. (a) If the sphere is frictionless, at what angle θ from the vertical does the mass leave the surface? (b) Suppose there is friction between the mass and the sphere with friction coefficient =0.1. What is the minimum angle θmin at which the mass will start to slide along the sphere? (c) The mass is now placed just past this minimum angle and released. The coefficient of kinetic friction μκ is small but not zero. Does the mass fly off at a larger or a smaller θ than found in part (a)? Assume θ is defined with respect to the top of the sphere. Answer 1 (a) θ-48.2°; (b) θ-5.70; (c) larger.

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