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 45kg . A rope is wrapped around a wooden cylinder that turns on a metal axle. The cylinder has radius 0.25m and a moment of inertia = 2.3 kg * m^2 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 the crate is raised.

Explanation / Answer

The handle radius is rather small .. smaller than the winding cylinder !! btw .. the link diagram doesn't show the set-up described .. anyway, here we go .. Force required to accelerate the crate, Fc = weight (mg) + accel. force (ma) Fc = 57kg x (9.80 + 1.40)m/s = 638.40N Torque at cylinder due to crate, Tc = Fc x r = 638.4N x 0.27m = 172.37 Nm Torque required to accel. cylinder, T' = I.? .. (MoI x ang.accel. .. equivalent to F = ma) T' = 2.60kg.m x (1.40 / 0.27) = 13.48 Nm .. (v = r??dv/dt = r.d?/dt? a = r.??? = a/r) Total torque required = Tc + T' = (172.37 + 13.48) = 185.85 Nm Torque at handle, Fh x 0.12m = 185.85 Nm .. .. Fh = 185.85 / 0.12 .. .. ?Fh = 1549 N

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