Problem 10.60 Part A The mechanism shown in the figure (Figure 1) is used to Wha

Question

Problem 10.60 Part A The mechanism shown in the figure (Figure 1) is used to 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.) raise a crate of supplies from a ship's hold. The crate has total mass 52 kg. A rope is wrapped around a wooden cylinder that turns on a metal axle. The cylinder has radius 0.27 m and a moment of inertia 1 = 2.7 kg-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 Express your answer using two significant figures Figure1of 1 kN Submit My Answers Give Up Provide Feedback Continue 0.12 m

Explanation / Answer

Force required to accelerate the crate, Fc = weight (mg) + accel. force (ma)

Fc = 52kg x (9.81 + 1.40)m/s = 582.92 N

Torque at cylinder due to crate, Tc = Fc x r = 582.92 N x 0.27m = 157.388 Nm

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

T' = 2.70 kg.m² x (1.40 / 0.27) = 14 Nm (v = rdv/dt = r.d/dt a = r. = a/r)

Total torque required = Tc + T' = (157.388 + 14) = 171.388 Nm

Torque at handle, Fh x 0.12m = 171.388 Nm

Fh = 171.388 / 0.12

Fh = 1428 N

Fh = 1.428 kN

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