A uniform spherical shell of mass M = 2.0 kg and radius R = 10.0 cm rotates abou

Question

A uniform spherical shell of mass M = 2.0 kg and radius R = 10.0 cm rotates about a vertical axis on frictionless bearings (see the figure). A massless cord passes around the equator of the shell, over a pulley of rotational inertia I = 2.88×10-3 kg m2 and radius r = 6.0 cm, and its attached to a small object of mass m = 1.0 kg. There is no friction on the pulley's axle; the cord does not slip on the pulley. What is the speed of the object after it has fallen a distance h = 1.1 m from rest: Use work - energy considerations.

Explanation / Answer

using conservation of energy

initial Potential energy of hanging mass = kinetic energy of hanging mass + rotational KE of sphere + Rotational KE of pulley

mgh = (0.5) m v2 + (0.5) Is ws2 + (0.5) Ip wp2

Is = moment of inertia of spherical shell = (2/3) MR2 = (2/3) (2) (0.1)2 = 0.013

Ip = moment of inertia of pulley = 0.00288

(1)(9.8) (1.1) = (0.5) (1) v2 + (0.5)(0.013) (V/0.10)2 + (0.5) (0.00288) (V/0.06)2

V = 2.64 m/s

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