The mechanism shown in the figure is used to raise a crate of supplies from a ship's hold. The crate has total mass 48 kg. A rope is wrapped around a wooden cylinder that turns on a metal axle. The cylinder has radius 0.20 m and a moment of inertia I = 3.0 {rm kg} cdot {rm 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 0.12 m, the cylinder turns, and the crate is raised.
What magnitude of the force vec{F} applied tangentially to the rotating crank is required to raise the crate with an acceleration of 0.80 m/s^2? (You can ignore the mass of the rope as well as the moments of inertia of the axle and the crank.)