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 39 kg . A rope is wrapped around a wooden cylinder that turns on a metal axle. The cylinder has radius 0.32 m and a moment of inertia I = 2.0 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.

Part A

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.)

Express your answer using two significant figures.

Explanation / Answer

Apply equilibrium condition of torques:

F*R - m(g + a)*r = I = I*a/r

F*0.12m - 39kg*(9.8 + 1.4)m/s² * 0.12m = 2.0kg·m² * 1.4m/s² / 0.12m

F = 631 N

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