Question

3. Sailors use a capstan (shown below) to raise and lower the anchor. It takes two sailors located 1 meter from the center to turn the capstan.
How far from the center would one sailor have to be to turn the capstan by himself?
A 1 meter
B. 2 meters
C.3 meters
D. Both B and C would work

Answer 1

Answer:

B. 2 meters.

Explanation:

To rotate the capstan a certain amount of torque is required, and if each sailor applies a force $F$ at a distance $D$ from the center, then for two sailors the total torque will be

$\tau = 2FD$;

therefore,  for one sailor to apply the same torque it must be that the torque $\tau_2$ he applies must be equal to the torque that the two sailors applied:

$FD_2 =2FD$

which gives

$D_2 = 2D$.

and since $D = 1\:meter$,

$\boxed{D_2 = 2\: meters}$

which is choice B.