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
Answers
Damon
Now where might this question come from ?
Saraf
How do you solve it?
Saraf
this question is of ohysics
Saraf
May I please know how do you do it?first of all how to prove the first part?
Damon
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
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
Anonymous
Thanks a lot...and how do you find out the work required to turn the cylinder through one complete turn under these conditions?