Problem

A winch drawing 9 hp powers a pulley system lifting a 600 lb crate C with a constant speed...

A winch drawing 9 hp powers a pulley system lifting a 600 lb crate C with a constant speed vc. The pulleys are all identical and have a radius rp = 1.25 ft. The cord is inextensible and does not slip relative to the pulleys. For each pulley, the friction at the pulley bearings produces a moment about the pulley’s center with magnitude k|ωp | opposing the rotation of the pulley, where k = 1.5 lb·ft·s and |ωp | is the angular speed of the pulley. Neglecting the inertia of the pulleys and of the cord, and treating segments of cord that do not touch the pulleys as being vertical, determine vc if the motor’s efficiency is ϵ = 0.87. Hint: Adapt to this problem the solution in Part (a) of Example 4.16, observing that friction at the pulley bearings causes the tension in the cord on the two sides of a pulley to be different.