7:30 session.masteringphysics.com Problem 9.80 MasteringPhysics Pulley Cylinder

Question

7:30 session.masteringphysics.com Problem 9.80 MasteringPhysics Pulley Cylinder Box Tap image to zoom the cylinder and pulley turn without friction about stationary horizontal axles that pass through their centers. A light rope is wrapped around the cylinder, passes over the pulley, and has a 3.00-kg box suspended from its free end There is no slipping between the rope and the pulley surface. The uniform cylinder has mass 5.00 kg and radius 40.0 cm, The pulley is a uniform disk with mass 2.00 kg and radius 20.0 cm. The box is released from rest and descends as the rope unwraps from the cylinder. Part A Find the speed of the box when it has fallen 2.50 m U= 115.5 m/s SubmitRe Request Answer

Explanation / Answer

By of conservation of energy

Ui +Ki = Uf + KF

Mbgh= (1/2)(Mb v2 + IC WC2 + IpWP2)

Since

Wc = v/Rc ; Wp = v/Rp

The moment of inertia of the cylinder

Ic = (1/2)Mc Rc2

the moment of inertia of the pulley

Ip = (1/2)Mp Rp2
=> Mbgh=(1/2)(Mb +Mc/2 +Mp/2) v2

3*9.81*2.5 =(1/2)(3+5/2 +2/2)v2

v=4.758 m/s

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