In Figure 10.43 the sliding block has a mass of 0.860 kg, the counterweight has

Question

In Figure 10.43 the sliding block has a mass of 0.860 kg, the counterweight has a mass of 0.350 kg, and the pulley is a hollow cylinder with a mass of 0.350 kg, an inner radius of 0.020 m, and an outer radius of 0.030 m. The coefficient of kinetic friction between the block and the horizontal surface is 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 0.820 m/s toward the pulley when it passes through a photogate.

(a) Use energy methods to predict its speed after it has moved to a second photogate, 0.700 m away.

__________ m/s

(b) Find the angular speed of the pulley at the same moment.

__________ rad/s

Explanation / Answer

m1 =0.86 kg , m2 =0.35 kg, M =0.35 kg , R1 =0.02m

R2 =0.03 m , uk = 0.25, vi =0.82 m/s

a) Moment of inertia = (1/2)M (R1^2+R2^2)

from conservation of energy

(1/2)(m1+m2)(vf^2 - vi^2) +(1/2)I(wf^2 -wi^2) = m1gh - ukm2g

(1/2)(m1+m2)(vf^2 - vi^2) +(1/2)(1/2)M(R1^2+R2^2)(wf^2 -wi^2) = m1gh - ukm2g

vf = (vi^2 +((m1gh - ukm2g)/((1/2)(m1+m2)+(1/2)M(1+(R1^2/R2^2))))^0.5

vf^2 = (0.82)^2 +(((0.86*9.8*0.914) - (0.25*0.35*9.8))/((0.5*1.21)+(0.5*0.35(1+(0.02^2/0.03^2)))))

vf = 2.94 m/s

(b) the angular speed of the pulley

wf = vf/R2 = 2.94/0.03

wf = 98 rad/s

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