Question

A rope is wound round a fixed cylinder of radius r so as to make n complete turns . Show that if one end of the rope is held by a force f, a force f e^2(pi)nu must be applied to the other end to produce slipping,where u is the coeff. of friction between rope and cylinder. Find also the work required to turn the cylinder through one complete turn under these conditions

Answer 1

Now where might this question come from ?

Answer 2

How do you solve it?

Answer 3

this question is of ohysics

Answer 4

May I please know how do you do it?first of all how to prove the first part?

Answer 5

take an element d A where A is the angle around the cylinder
tension T to the left
tension T + dT to the right
then normal force toward center = (T+dT)(dA/2) + T(dA/2)
= T dA for small dA
so friction force = mu T dA
so
dT = mu T dA
dT/T = mu dA
ln T = mu A
T = c e^mu A
at A = 0, T = F
so
T = F e^mu A
A = 2pi * number of turns

Answer 6

Thanks a lot...and how do you find out the work required to turn the cylinder through one complete turn under these conditions?