In the figure below, the hanging object has a mass of m10.460 kg; the sliding bl

Question

In the figure below, the hanging object has a mass of m10.460 kg; the sliding block has a mass of m20.870 kg; and the pulley is a hollow cylinder with a mass of M 0.350 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 ?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 vi = 0.820 m/s toward the pulley when it passes a reference point on the table. 81 mig (a) Use energy methods to predict its speed after it has moved to a second point, 0.700 m away. m/s (b) Find the angular speed of the pulley at the same moment. rad/s

Explanation / Answer

Moment of inertia of pulley

I=(1/2)M(R12+R22) =(1/2)*0.35*(0.022+0.032) =2.275*10-4 Kg-m2

INitial angular velocity

Wi=Vi/R =0.82/0.03 =27.33 rad/s

By Conservation of energy

(1/2)m1V1i2+(1/2)m2V2i2+(1/2)IWi2 +m1gx-ukm2gx =(1/2)m1Vf2+(1/2)m2Vf2+(1/2)I(Vf/R2)2

(1/2)(0.46+0.87)(0.82)2+(1/2)(2.275*10-4)(27.33)2+0.46*9.81*0.7-0.25*0.87*9.81*0.7 =(1/2)(0.46+0.87)Vf2+(1/2)(2.275*10-4)(Vf/0.03)2

Vf=1.67 m/s

b)

Wf=1.67/0.03 =55.54 rad/s

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