Find Coefficient of Friction (μ) on Cylinder with Rope and Cat/Mice Forces

[Super_Leunam]

WOULD SOME1 HELP ME WITH THIS ANNOYING PROBLEM I CANT SOLVE :
a cat is wrapped around a fixed cylinder .there's friction between the rope and da cylinder with a coefficient of friction (mu) , the angle covered by the rope on the cylinder is (pi)/3 .assume a really thin rope. A cat is pulling on one end of the rope with a force F while 10 mice can just barely prevent from sliding by applying a total force of f . Find (mu) in function of F, f and the angle


i know the answer is has to do with an exponential


thanks

Manuel

 

[Doc Al]

belt friction equation

Due to static friction with the cylinder, the tension on the cat end of the rope will be greater than on the mouse end. The relationship between the two tensions, the angle of contact, and mu is given by the so-called "belt friction equation". You can derive it by consider a small element of rope and applying static equilibrium conditions. Then integrate this over the full angle of contact.

Yes, it is an exponential function.

 

[Galileo]

a cat is wrapped around a fixed cylinder.

Poor thing!

I like cats