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

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To find the coefficient of friction (μ) for a cat pulling on a rope wrapped around a fixed cylinder, the relationship involves the belt friction equation. The tension on the cat's side of the rope is greater than on the mice's side due to static friction. This relationship can be derived by applying static equilibrium conditions to a small element of the rope and integrating over the contact angle of π/3. The solution indicates that μ is expressed as a function of the forces F and f, confirming that it is indeed an exponential function. Understanding these principles is essential for solving the problem effectively.
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WOULD SOME1 HELP ME WITH THIS ANNOYING PROBLEM I CANT SOLVE :
a cat is wrapped around a fixed cylinder .theres 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
 
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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. :smile:
 
Super_Leunam said:
a cat is wrapped around a fixed cylinder.

Poor thing!

I like cats :frown:
 

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