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A rope of length L and mass m is suspended from the ceiling. Find an expression for the tension...

Question:

A rope of length {eq}L {/eq} and mass {eq}m {/eq} is suspended from the ceiling. Find an expression for the tension in the rope at position {eq}y {/eq}, measured upward from the free end of the rope. Express your answer in terms of the variables {eq}m {/eq}, {eq}y {/eq}, {eq}L {/eq}, and appropriate constants.

{eq}T = {/eq} ?

Tension

Tension is a type of force that is commonly exhibited in strings or ropes. Ideally, it is considered massless when attached with a load or mass because the mass of the rope is much smaller than the attached load. However, in this problem we will consider the Tension distribution of a rope attached to the ceiling.

Answer and Explanation:

Firstly, we treat the point of attachment as our origin in the y axis. We equate the force acting in the origin:

{eq}\sum_{i}{} F_i = 0...

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