Statement of a problem № 41307


The mechanism shown in Fig. 10.53 is used to raise a crate of supplies from a ship s hold. The crate has total mass 50 kg. A rope is wrapped I around a wooden cylinder that turns on a metal axle. The cylinder has radius 0.25 m and moment of inertia I = 2.9 kg • m2 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. What magnitude of the force F applied tangentially to the rotating crank is required to raise the crate with an acceleration of 0.80 m/s2? (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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