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Assuming the length of a chain to be L and cofficient of static friction mu calculate the maximum length of the chain which can be held outside a table without sliding?

Assuming the length of a chain to be L and cofficient of static friction mu calculate the maximum length of the chain which can be held outside a table without sliding?
 

Grade:11

1 Answers

Arun
25750 Points
5 years ago
Let x be the length of chain that is hanging outside the table as shown in figure. Let λ be the mass per unit length of chain.
various forces acting on the chain are shown in figure. weight of hanging part of chain pulls the part of the chain resting on the table.
Friction force acting against the pull experienced by the resting part of the chain.
 
hence,  if x is the length of the chain just long enough to hang outside, then we have  xλg = μN =  μ(L-x)λg ............(1)
 
from eqn.(1) we get
 
x = μL / (1+μ)

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