Tension in a hanging massive rope

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To find the force exerted on a hanging massive rope by the ceiling, one must consider the weight distribution along the rope. The weight of the rope below point P is calculated as (W/l)*y, while the tension at point P is determined by the weight above it, given by (W/l)*(l-y). The total weight of the rope can be expressed as lzg, which is equivalent to Mg. Understanding these relationships is crucial for analyzing tension in the rope. The discussion emphasizes the importance of correctly applying these formulas to determine the forces involved.
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How do I find the direction and magnitude of the force exerted on the massive rope by the ceiling? And what is the tension at point P in the rope? Thanks in advance,
 
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Let W=the weight of the rope.
So the weight of the rope below point p will be (W/l)*y.
The upper part will be just (W/l)*(l-y). This will be the tension at P.
 
Thank you so much, CartooKid. You're the man. :smile:
 
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Yes. For the whole rope, it would be lzg which is same as Mg.
 

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