The double pulley D has mass of mD = 15 kg, center of mass G coinciding with its geometric center, radius of gyration kG = 10 cm, outer radius ro = 15 cm, and inner radius ri = 7.5 cm. It is connected to the pulley P with radius R = (ro − ri )/2 by a cord of negligible mass that unwinds from the inner and outer spools of the double pulley D. The crate C, which has a mass mC = 20 kg, is released from rest. The cord does not slip relative to the pulleys, and the inner and outer pulleys rotate as a single unit.
Assuming that the pulley P has a mass of 1.5 kg and a radius of gyration kA = 3.5 cm, use the impulse-momentum principles to determine the speed of the crate 4 s after release.
Figure P8.102
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