l Verizon 9:52 PM e capa9.phy.ohio.edu Print into An Interesting Arrangement Due

Question

l Verizon 9:52 PM e capa9.phy.ohio.edu Print into An Interesting Arrangement Due this Friday, Mar 23 at 11:59 pm (EDT) A uniform spherical shell of mass M4.50 kg and radius R 27.0 cm 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 5.00x10-3 kg.m2 and radius r 3.00 cm, 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 4.00 m after being released from rest? Use energy considerations Submit AnswerTries 0/10 Post Discussion Send Feedback

Explanation / Answer

By Conservation of energy

mgh =(1/2)mV2+(1/2)IWpulley2+(1/2)(2/3)MR2*Wsphere2

Since W=V/R

mgh =(1/2)mV2+(1/2)I(V/R)2+(1/3)Mr2*(V/r)2

mgh =(1/2)mV2+(1/3)MV2+(1/2)(I/r2)V2

4*9.81*4 =(1/2)*4*V2+(1/3)*4.5*V2+(1/2)(0.005/0.032)*V2

V=5 m/s

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