The mechanism shown in the figure (Figure 1) is used to raise a crate of supplie

Question

The mechanism shown in the figure (Figure 1) is used to raise a crate of supplies from a ship's hold. The crate has total mass 53 kg . A rope is wrapped around a wooden cylinder that turns on a metal axle. The cylinder has radius 0.24 m and a moment of inertia I = 2.8 kgm2 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 1.40 m/s2 ? (You can ignore the mass of the rope as well as the moments of inertia of the axle and the crank.)

Explanation / Answer

Tension T = mg + ma = 53*[9.8+1.4] = 593.6 N

now torque = i alpha where alpha = a/R = 1.40/0.24 = 5.833

F*r - T*R = 2.8 *5.833

F*0.12 - 593.6*0.24 = 2.8 *5.833

F = [ 2.8 *5.833 +593.6*0.24]/0.12

= 1323.3 N answer

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