- #1
Mr Davis 97
- 1,462
- 44
Homework Statement
A device called a capstan is used aboard ships in order to control a rope which is under great tension. The rope is wrapped around a fixed drum. The load on the rope pulls it with a force ##T_A## and the sailor holds it with a much smaller force ##T_B##. Show that ##T_A = T_B e^{\mu \theta}##, where ##\mu## is the coefficient of friction, and ##\theta## is the total angle subtended by the rope on the drum.
Homework Equations
Newton's second law
The Attempt at a Solution
So I think that I can get a solution. That is, I think that I can look at an infinitesimal section of the rope, apply Newton's second law in the horizontal and vertical directions, take the limit as ##\theta## goes to zero, and then integrate. However, I have some questions about which forces will be acting on the rope. My first question is, is the rope massless? If so, how would friction and a normal force be acting on the rope? Also, if the rope is massless, wouldn't the tension in the rope be uniform?