If the coefficient of static friction between a table and a uniform massive rope is μs, what fraction of the rope can hang over the edge of the table without the rope sliding?

Let me give you the procedure like this:
Lets say that F is the fraction of the rope hanging over the table
If its like that then we have to take into account that the friction force keeping on table is given by the following formula:
Ff = u*(1-f)*m*g 
and we need to know aso that gravity force pulling off the table Fg is given by this other formula:
Fg = f*m*g 
What you need to do is Equate the two and solve for f: 

f*m*g = u*(1-f)*m*g 
=> f = u*(1-f) = u - uf 
=> f + uf = u 
=> f = u/(1+u) = fraction of rope
With that you can find the answer

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