Problem 10.68 The mechanism shown in the figure (Figure 1) is used to raise a cr

Question

Problem 10.68 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 42kg . A rope is wrapped around a wooden cylinder that turns on a metal axle. The cylinder has radius 0.24m and a moment of inertia I = 2.4kg 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 O.12rn , the cylinder turns, and the crate is raised. Figure 1 of 1 Part A What magnitude of the force vector F applied tangentially to the rotating crank is required to raise the crate with an acceleration of 1 .40m/s^2 ? (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

F = m*(g+a) = 42*(9.8+1.40) = 470.4 N

angular accelration = a/r = 1.4/0.24 = 5.83 rad/s^2

torque = I*5.83 = 2.4*5.83 = 13.99 N.m

torque applied by crank = 13.99 + 470.4*0.24 = 126.89 N.m

F = 126.89/0.12 = 1057.38 N = 1.057 kN

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