Math CentralQuandaries & Queries


Question from ron, a student:

four men on a boat are using a capstan for hoisting an anchor weighing 2000lbs. The diameter of the barrel of the capstan at the section in use is 8in., and the pull on the chain carrying the anchor and passing around the capstan barrel is assumed to act at a distance of 1in. from the surface of the barrel. If the distance from the axis of the barrel to each point at which effort is applied to a capstan bar is 40in., what force must be applied by each man hoisting the anchor?

Hi Ron.

To hoist the anchor, the torque applied by the men must equal or exceed that of the torque applied by the anchor.

Torque is calculated by multiplying the force by the length of the lever arm (in your case, the distance from the capstan barrel axis to the place the force is applied).

Thus, let H = the human force applied by one man and let A be the force applied by gravity acting on the anchor.

4 x H x 40" = A x (8"/2 + 1")

You can calculate A using F=ma, where the acceleration is that due to gravity. Solve for H.

Stephen La Rocque.

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