Use the worked example above to help you solve this problem. Two blocks with mas

Question

Use the worked example above to help you solve this problem. Two blocks with masses m1 = 4.73 kg and m2 = 7.38 kg are attached by a string as shown in figure a, over a pulley with mass M = 1.79 kg. The pulley, which turns on a frictionless axle, is a hollow cylinder with radius 0.0590 m over which the string moves without slipping. The horizontal surface has coefficient of kinetic friction 0.351. Find the speed of the system when the block of mass m2 has dropped 2.02 m.
= m/s

EXERCISE HINTS: THIS IS WHAT I REALLY NEED HELP ON!!
Two blocks with masses m1 = 1.90 kg and m2 = 9.30 kg are attached over a pulley with mass M = 3.20 kg hanging straight down as in Atwood's machine (see figure b). The pulley is a solid cylinder with radius 0.0540 m, and there is some friction on the axle. The system is released from rest, and the string moves without slipping over the pulley. If the larger mass is traveling at a speed of 2.04 m/s when it has dropped 1.00 m, how much mechanical energy was lost due to friction in the pulley's axle?
Wnc = J

Hint: This exercise is slightly easier than the associated example because the friction force need not be determined.

Explanation / Answer

the string doesnt move. so that the angular velocity o the cylinder would be w = 2.04/0.054 = 37.8(rad/s). total kinetic energy. (m1+m2)*v^2/2 + I*w^2/2 where v = 2.04, w = 37.8 I = mr^2/2 = 3.2*0.054^2/2 = 4.67e-3(kgm2). so total kinetic energy. K= 26.6(J). --- the change in potential energy. H=9.3*1*9.8 - 1.9*1*9.8 = 72.52(J) so friction work = 72.52 - 26.6 = 45.9(J)

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