Chapter 10, Problem 10.60P

The mechanism shown in Fig. P10.60 is used to raise a crate of supplies from a ship’s hold. The crate has total mass 50 kg. A rope is wrapped around a wooden cylinder that turns on a metal axle. The cylinder has radius 0.25 m and moment of inertia I = 2.9 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. When the crank is turned, the end of the handle rotates about the axle in a vertical circle of radius 0.12 m, the cylinder turns, and the crate is raised. What magnitude of the force $\stackrel{\to }{F}$ 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.)

Figure P10.60