In the figure below, the hanging object has a mass of m_1 = 0.405 kg; the slidin

Question

In the figure below, the hanging object has a mass of m_1 = 0.405 kg; the sliding block has a mass of m_2 = 0.775 kg; and the pulley is a hollow cylinder with a mass of M = 0.350 kg, an inner radius of R_1 = 0.020 0 m, and an outer radius of R_2 = 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 v_i = 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

energy decrease of mass m1= energy increase of m2 and pulley

enengy increase of m2= (1/2)*m2*(vf^2-vi^2)=0.3875(vf^2-vi^2)

enengy increase of pulley = (1/2)*Ip*(wf^2-wi^2) =(1/4)*mp*(R2^2+R1^2)*(vf^2-vi^2)/(1/R2^2) =0.284(vf^2-vi^2)

m1*g*h=0.6715(vf^2-vi^2)

2.7783 =0.6715 (vf^2-vi^2)

(vf^2-vi^2)=4.1374

vf=2.19 m/s

b) angular velocity of the pulley= 2.19/0.03=73 rad/s

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