A uniform spherical shell of mass M = 11.0 kg and radius R = 0.520 m can rotate

Question

A uniform spherical shell of mass M = 11.0 kg and radius R = 0.520 m can rotate about a vertical axis on frictionless bearings (Fig. 10-44). A massless cord passes around the equator of the shell, over a pulley of rotational inertia I = 0.0800 kg·m2 and radius r = 0.0820 m, and is attached to a small object of mass m = 2.50 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 when it has fallen a distance 0.975 m after being released from rest? Use energy considerations.

Explanation / Answer

K_m = (1/2)mv^2 K_sphere = (1/3)Mv^2 K_pulley = (1/2)(I/r^2)*v^2 So, mgh = (1/2)mv^2 + (1/3)Mv^2 + (1/2)(I/r^2)*v^2 v = SQRT((6gh)/(3m+2M+(3I/r^2))) = SQRT((6*9.8*.975)/(3*2.50+2*11+(3*.0800/.0820))) v = 1.3 m/s please rate!

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