Chapter 10, Problem 066 Your answer is partially correct. Try again. A uniform s

Question

Chapter 10, Problem 066 Your answer is partially correct. Try again. A uniform spherical shell of mass M 18.0 kg and radius R 0.320 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 0.140 kg.m2 and radius r 0.0580 m, and is attached to a small object of mass m = 3.80 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 0.510 m after being released from rest? Use energy considerations. M, R I, T ini Number T1.44 UnitsT m/s

Explanation / Answer

here,

M = 18 kg

R = 0.32 m

I = 0.14 kg.m^2

r = 0.058 m

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

a = ( m * g) /( m + I/r^2 + ( 0.67 * M * R^2 /R^2))

a = ( 3.8 * 9.81 /( 3.8 + 0.14 /0.058^2 + 0.67 * 18))

a = 0.65 m/s^2

s = 0.51 m

the final speed , v = sqrt(2 * a * s)

v= sqrt(2 * 0.65 * 0.51) m/s

v = 0.81 m/s

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