A solid sphere of mass and radius is projected along a rough horizontal surface with…

PHYSICS · Single correct · AP · Physics 1: Algebra-based · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems

Problem

A solid sphere of mass MM and radius rr is projected along a rough horizontal surface with speed v0v_0 and no initial rotation. Kinetic friction acts until the sphere rolls without slipping. What fraction of the sphere’s initial mechanical energy is converted into thermal energy during this process? (The sphere’s moment of inertia about its center is 25Mr2\tfrac{2}{5}Mr^2.) (a) 57\dfrac{5}{7} (b) 27\dfrac{2}{7} (c) 2449\dfrac{24}{49} (d) 13\dfrac{1}{3}

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