A uniform spherical shell of mass M = 7.20 kg and radius R = 0.780 m can rotate

Question

A uniform spherical shell of mass M = 7.20 kg and radius R = 0.780 m can rotate 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 1 = 0.120 kg-m2 and radius r 0.06 10 m and 1s attached to a small object of mass m 3.60 kg There is no friction on the pulleys a ei the cord does not s pon the pulley. What is the speed of the object when it has fallen a distance 1.11 m after being released from rest? Use energy considerations M, R Number Units

Explanation / Answer

first

The sum of the kinetic energies in the 2 rotating items will equal the loss in PE of the mass - the KE of the mass:

Is = (2/3)* 7.2 * 0.78² = 2.92 kgm²
Ip = 0.120 kgm²

Energy:
0.5 * Is * ws² + 0.5 * Ip * wp² = 3.6 * 9.8 * 1.11 - 0.5 * 3.6 * v²

But ws= v/0.78 and wp = v/0.061, so

0.5 * 2.92 * ( v /0.78) ² + 0.5 * 0.12 * (v / 0.061)² = 3.6 * 9.8 * 1.11 - 0.5 * 3.6 * v²

by solving for v

v = 1.388 m/s

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