A uniform spherical shell of mass M = 5.0 kg and radius R = 13.0 cm rotates abou

Question

A uniform spherical shell of mass M = 5.0 kg and radius R = 13.0 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 = 3.78x10^-3 kg m^2 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 = 1.3 m from rest: Use work - energy considerations.

Explanation / Answer

From Work enegy theorem

(1/2)IsphereWsphere2+(1/2)IWpulley2+(1/2)mV2=mgh

Since Moment of inertia of sphere

I=(2/3)MR2

and W=V/r

=>(1/2)(2MR2/3)(V/R)2+(1/2)Ipulley(V/r)2+(1/2)mV2=mgh

2mgh =(2/3)MV2+Ipulley(V/R)2+mV2

2*1*9.8*1.3 =(2/3)*5*V2+(3.78*10-3)V2/0.062+1*V2

5.38V2=25.48

V=2.18 m/s

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