Chapter 10, Problem 066 A uniform spherical shell of mass M- 17.0 kg and radius

Question

Chapter 10, Problem 066 A uniform spherical shell of mass M- 17.0 kg and radius R 0.630 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 0.160 kg-m2 and radius r - 0.130 m, and is attached to a small object of mass m- 4.50 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 1.43 m after being released from rest? Use energy considerations. M, R Number Units the tolerance is +/-296

Explanation / Answer

initial energy Ei = m*g*h

linear speed of mass m = v

angular speed of sphere ws = v/R

angular speed of pulley wp = v/r

after falling a distance h

final energy Ef = (1/2)*Ispere*ws^2 + (1/2)*Ipulley*wp^2 + (1/2)*m*v^2

Isphere = (2/3)*M*R^2 = (2/3)*17*0.63^2 = 4.5 kg m^2

Ipulley = 0.16 kg m^2

Ef = (1/2)*(4.5)*(v/0.63)^2 + (1/2)*0.16*(v/0.13)^2 + (1/2)*4.5*v^2

from enegy conservation Ef = Ei

(1/2)*(4.5)*(v/0.63)^2 + (1/2)*0.16*(v/0.13)^2 + (1/2)*4.5*v^2 = 4.5*9.8*1.43

speed v = 2.23 m/s <<<<-------ANSWER

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