Cofficient of static friction between table and rope

[Mitchlan]

Homework Statement

If the coefficient of static friction between an table and a uniform massive rope is [tex]\mu what fraction of the rope can hang over the edge of the table without the rope sliding?



b]2. Homework Equations [/b]

The Attempt at a Solution

Frictional force keeping it on the table: F[f] = mu (1-f) x m x g

Gravity pulling it off the table: F[g]= f x m x g

then: f x m x g = mu (1-f) x m x g

f= mu - mu x f

therefore the fraction of rope is f = mu / (1 + mu)


Thanks in advance!

 

[issacnewton]

Yes its right. please do search the archives before asking a new question

https://www.physicsforums.com/showthread.php?t=99625

 

[Mitchlan]

Thanks for replying so soon. I did a quick search and couldn't find what I was looking for.

 

[issacnewton]

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[rwisz]

I would like to commend you for your attempt at solving this problem. Your approach is correct, and your final equation for the fraction of rope is also correct. However, I would like to point out that the coefficient of static friction, μ, is a dimensionless quantity and should not have the unit of $$\frac{m}{s}$$. Also, the symbol "f" is usually used for the force of friction, so it might be less confusing to use a different variable for the fraction of rope, such as "x". Keep up the good work!