A solid sphere is pulled forward by a light string wrapped around its equator
PHYSICS · Single correct · AP · Physics 1: Algebra-based · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems
Problem
A solid sphere is pulled forward by a light string wrapped around its equator. As the string unwinds, the sphere rolls without slipping along a horizontal surface. Which of the following best explains why the work done by the tension equals the sum of the sphere’s translational and rotational kinetic energies rather than its translational kinetic energy alone?
(a) Because the tension force acts along a line through the sphere’s center of mass, it can change only translational kinetic energy; the rotational kinetic energy is supplied by static friction.
(b) The point where the string exerts the force moves farther than the center of mass as the string unwinds, so additional energy appears as rotation.
(c) As the string unwraps, the sphere’s center of mass and the point where the string pulls move through the same distance, so the work done by tension equals only the translational kinetic energy.
(d) Static friction does negative work on the sphere; to conserve energy an equal amount of rotational kinetic energy must be added, so the tension’s work equals the sum of the two kinetic energies.