Water is drawn from a well in a bucket tied to the end of a rope whose other end wraps around a cylinder of mass 50 kg and diameter 25 cm. As you turn this cylinder with a crank, the rope raises the bucket. If the mass of a bucket of water is 20 kg, what torque must you apply to the crank to raise the bucket of water at a constant speed?
A) 24 N · m
B) 2.5 N · m
C) 80 N · m
D) 2.4  103 N · m
E) 49 N · m

Question

Quizplus · Accepted Answer

To raise the bucket at a constant speed, the torque applied must balance the gravitational force on the bucket. The force due to gravity is 20 kg * 9.8 m/s² = 196 N. The radius of the cylinder is 0.125 m (half of the diameter). Torque = Force * Radius = 196 N * 0.125 m = 24.5 N·m, which is closest to 24 N·m.

Water Is Drawn from a Well in a Bucket Tied