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 56kg. A rope is wrapped around a wooden cylinder that turns on a metal axle. The cylinder has radius 0.33m and a moment of inertia I = 2.8kg . 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. 0.12m, the cylinder turns, and What magnitude of the force applied tangentially to the rotating crank is required to raise the crate with an acceleration of 1.40m/s2? (Your 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

let force applied be F....so torque on handle is given by F X r where r=12cm

so torque T=0.12F

now this torque acts on cylinder too

we know T-fR=Ia where I is moment of inertia,F is the tension in the string(because F produces opposite torque) and a is angular acceleration

also if a is known then acceleration of crate is given by aR where R is radius.....so acceleration of crate=aR=1.4

so a=4.24 rad/s^2

now writing force equation on crate

f-Mg=M X acceleration

so f=M(g+1.4)

f=627.2N

using this f in T-fR=Ia

we get T=0.12F=639.402

solving we get F=5328.3N

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