n the figure below, the hanging object has a mass of m1 = 0.395 kg; the sliding

Question

n the figure below, the hanging object has a mass of m1 = 0.395 kg; the sliding block has a mass of m2 = 0.840 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. (a) Use energy methods to predict its speed after it has moved to a second point, 0.700 m away. Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. m/s (b) Find the angular speed of the pulley at the same moment.

Explanation / Answer

(a)

I(cylinder) = 0.5*0.35*(0.02^2+0.03^2) =2.275*10^-4

By conservation of energy:

initial KE = 0.5*0.84*0.82^2+0.5*0.395*0.82^2-0.25*0.84*9.8*0.7+0.5*2.275*10^-4*(0.82/0.03)^2

= -0.94041

Final KE = 0.5*0.84*V^2+0.5*0.395*V^2-0.395*9.8*0.7+0.5*2.275*10^-4*(V/0.03)^2

=0.74389V^2-2.7097

Thus:

0.74389V^2-2.7097 =  -0.94041

V=1.3374 m/s

(b)

w = 1.3374/ sqrt(.02^2 + .03^2)

=37.0929 rad/s

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