The mechanism shown in the figure is used to raise a crate of supplies from a sh

Question

The mechanism shown in the figure is used to raise a crate of supplies from a ship's hold. The crate has total mass 47 . A rope is wrapped around a wooden cylinder that turns on a metal axle. The cylinder has radius 0.30 and a moment of inertia = 2.7 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 , the cylinder turns, and the crate is raised.


What magnitude of the force applied tangentially to the rotating crank is required to raise the crate with an acceleration of 1.40 ? (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

Force required to accelerate the crate

Fc= weight (mg) + accel. force (ma)

Fc = 51 kg x (9.80 + 1.40)m/s

= 571.2 N

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Torque atcylinderdue to crate,

Tc = Fc x r

= 571.2 N x 0.33m

= 188.49 Nm

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Torque required to accel. cylinder, T' = I.alpha

T' = 3.0 kg.m

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