A wooden bucket filled with water has a mass of 68 kg and is attached to a rope that is wound around a cylinder with a radius of 0.078 m. A crank with a turning radius of 0.250 m is attached to the end of the cylinder. What minimum force directed perpendicularly to the crank handle is required to raise the bucket

210.2N

Explanation:

Assume a bucket of water with a total mass of 68kg is attached to a rope, which in turn is tied around a 0.078m radius cylinder at the top of a well. A crank with a turning radius of 0.250 m is attached to the end of the cylinder.

the minimum force directed perpendicular to the crank handle required to raise the bucket is

(Assume the rope's mass is negligible, that the cylinder turns on friction-less bearings, and that g = 9.8 m/s2

The crank handle provides a torque T=0.25F where F is the force we are looking for.

A free body diagram will show that the tension in the rope times the cylinder radius R is equal to the torque on the cylinder. But the tension in the rope is just the weight of the bucket

W=mg= 68kg

W(0.078)=T=0.25F

F=0.312W=0.312(68kg)=21.216kg= 210.2N

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