In the figure below, the hanging object has a mass of m1 = 0.370 kg; the sliding

Question

In the figure below, the hanging object has a mass of m1 = 0.370 kg; the sliding block has a mass of m2 = 0.780 kg; and the pulley is a hollow cylinder with a mass of M = 0.50 kg, an inner radius of R1 = 0.020 0 m, and an outer radius of R2 = 0.030 0 m. Assume the mass of the spokes is negligible. The coefficient of kinetic friction between the block and the horizontal surface is mu k = 0.250. The pulley turns without friction on its axle. The light cord does not stretch and does not slip on the pulley. The block has a velocity of v1 = 0.820 m/s toward the pulley when it passes a reference point on the table. Use energy methods to predict its speed after it has moved to a second point, 0.700 m away. m/s Find the angular speed of the pulley at the same moment. rad/s

Explanation / Answer

The total energy in the system is given by


T = 1/2 m2 Vo^2 + 1/2 m1 Vo^2 + 1/2 I wo^2
= 1/2 m2 Vf^2 + 1/2 m1 Vf^2 + 1/2 I wf^2 - m1gd + uk m2g d

where Vo,Vf are the initial and final velocity of the blocks, wo/wf are the initial and finalangular velocityof the pulley, I is the moment of inertia of the pulley. w is related to V as

Vo = R2 wo and Vf = R2 wf.

Also, the moment of inertia is given by

I = 1/2 m (R2^2 + R1^2)

You have all the data now, you can go ahead and solve for Vf in the energy equation above. After that, you can calculate wf.

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