A uniform spherical shell of mass M = 7.70 kg and radius R = 0.850 m can rotate

Question

A uniform spherical shell of mass M = 7.70 kg and radius R = 0.850 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 I = 0.150 kg middot m^2 and radius r = 0.140 m, and is attached to a small object of mass m = 4.00 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 1.47 m after being released from rest? Use energy considerations. Number Units the tolerance is +/-5%

Explanation / Answer

here,

M = 7.7 kg , R = 0.85 m

I = 0.15 kg.m^2

radius , r = 0.14 m

m = 4 kg

the accelration of the mass , a = net force on the system / effective mass

a = ( m * g) /( 2/3 * M * R^2 /R^2 + I/r^2 + m)

a = ( 4 * 9.8 )/( 2/3 * 7.7 + 0.15/0.14 + 4)

a = 3.84 m/s^2

distance fallen , d = 1.47 m

the speed of object when fallen 1.47 m , v = sqrt( 2 * d * a))

v = sqrt(2 * 1.47 * 3.84) = 3.36 m/s

the speed of mass is 3.36 m/s

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