Question

A rope lies on a table such that a part of it hangs down the table. when the length of hanging part is 1/3 of entire length the rope just begins to slide. the cofficient of friction between the rope and the table is

Answer 1

The coefficient of friction between the table and the rope is 1/3.

Let suppose the mass of the rope is m, which is uniformly distributed over the entire length of the rope.

the friction force which oppose the motion of the rope is given as

$F_{friction}$=μmg

When the 1/3 or the rope hangs around the table, than the force applied by the gravity on the rope is calculated as

F=(1/3)mg

This force must be equal to the force of friction

μmg=(1/3)mg

μ=1/3

Hence, the force of friction between the table and the rope is 1/3

Answer 2

The question is incomplete.

However,

Given:  

Length of hanging rope = (1/3) of entire length the rope

Mass of hanging rope = (1/3) of the length of the rope * mass of the rope

Length of the rope on the table = (2/3) Length of hanging rope

Mass of the rope on the table = (2/3) Length of hanging rope * mass of the rope

To find:  

The coefficient of friction between the rope and table.

Solution:

Consider,

x as the coefficient of friction

By law,

The weight of rope on the table = The weight of hanging rope

x * (2/3) Length of hanging rope × mass of the rope * gravity  = (1/3)  Length of hanging rope × mass of the rope * gravity

x = 1/2

We get,

x = 0.5

Hence, the required coefficient of friction between the rope and table is 0.5.

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