Linear mass density and dangling rope.

[Timothy S]

A rope of mass M and length of L is dangling from a branch. The only force acting on it is gravity. The question is how do you find the tension of the rope at any position on the rope.

My proposed equation is this: F(r) = (Mg/L)(r) where r is any position on the rope. Is this equation correct? If it is incorrect what equation would be able to describe what I am asking?

 

[Chestermiller]

A rope of mass M and length of L is dangling from a branch. The only force acting on it is gravity. The question is how do you find the tension of the rope at any position on the rope.

My proposed equation is this: F(r) = (Mg/L)(r) where r is any position on the rope. Is this equation correct? If it is incorrect what equation would be able to describe what I am asking?

It is correct if r is the distance measured upward from the bottom of the rope.

Chet