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    A problem on rotational dynamics

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    The mechanism shown in the figure (see attachment) is used to raise a crate of supplies from a ship's hold. The crate has total mass 56 kg . A rope is wrapped around a wooden cylinder that turns on a metal axle. The cylinder has radius 0.310 m and a moment of inertia = 2.40 kgm^2 about the axle. The crate is suspended from the free end of the rope. One end of the axle pivots on frictionless bearings; a crank handle is attached to the other end. When the crank is turned, the end of the handle rotates about the axle in a vertical circle of radius 0.12 m, the cylinder turns, and the crate is raised.

    (See attached file for diagram and figures)

    What magnitude of the force applied tangentially to the rotating crank is required to raise the crate with an acceleration of 0.75 m/s^2 ? (You can ignore the mass of the rope as well as the moments of inertia of the axle and the crank.)

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    Solution Summary

    This problem is solved by application of Newton's second law of motion to the rotational motion.