A crate of mass 427 kg is being lifted by the mechanism shown in part a of the f

Question

A crate of mass 427 kg is being lifted by the mechanism shown in part a of the figure. The two cables are wrapped around their respective pulleys, which have radii of 0.600 and 0.200 m. The pulleys are fastened together to form a dual pulley and turn as a single unit about the center axle, relative to which the combined moment of inertia is 40.4 kg · m2. The cables roll on the dual pulley without slipping. A tension of magnitude 2510 N is maintained in the cable attached to the motor. Find the angular acceleration of the dual pulley and the tension in the cable attached to the crate. (Enter the magnitudes.) = rad/s2 T2 = N

Explanation / Answer

Tension in the string b/w motor and pulley = 2510N

Corresponding radius = .6m

Torque = 2510 x .6 = 1506 Nm

Torque = I x (alpha)

Thus, alpha = 1506/40.4 = 37.28 rad/s

acceleration provided to the crate = a = r x (alpha) = .2 x (37.28) = 7.4554 m/s2

balancing forces on crate in y direction: T = mg - ma = m x (g - a) = 427 x (9.81 - 7.4554) = 427 x 2.3546 = 1005N

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