Question

A sphere of radius R can rotate about a vertical axis on frictionless bearings (see figure below). Let the rotational inertia of the sphere behe.A massless cord passes around the equator of the sphere, overs pulley with rotational inertial and radius r, and is attached to a small object of mass m. There is no friction on the pulley's axle and the cord does not slip on the pulley. Att 0, the mass m has speed Vo The system is subject to the regular force of gravity. (a) Using conservation of energy, derive an expression for the speed of mass m after it has fallen for a distance h. Your expression should depend on whore and (D) For the 3 cases below, evaluate the speed of the falling object in m/s with the following parameters: • Vy = 0, 3.0 kg 1.0 m. • Mass of "sphere": Mr. 5.5 kg. radius of "sphere" - 0.20 m • Mass of pulley: M.1,5 kg. 3. Solid sphere of uniform density b. Pulley is a solid disk of uniform density with radius r = 0.10 m. Case 2: a. "Sphere is a thin spherical shell c Pulley is a solid disk of uniform density with radius r = 0.10 m. a. Solid sphere of uniform density b. Pulley is an annular cylinder (or ring, see figure below) of uniform density, with radia R = 0.10 m and R, = 0.09 m. Annuler cylinder foring about Indera (c) Compare the speeds obtained in Cases 1, 2, and 3 and explain their differences in relation to the moment of inertia for the "sphere and pulley in the various cases,

Answer 1