Understanding Tension Forces in a Slowly Rising System

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SUMMARY

The discussion centers on the mechanics of tension forces in a system where a person and a bucket have a combined mass of 75 kg. The conclusion drawn is that to raise herself slowly at a constant speed, the individual must exert a downward force equal to half her weight, leading to the equation W=2T. This is attributed to the presence of two tension forces acting on the rope, which effectively divides the weight between them. The tension in the rope remains W/2 due to the system's equilibrium.

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Homework Statement


GIANCOLI.ch04.p32.jpg
How hard must she pull downward to raise herself slowly at constant speed? The mass of the person plus the bucket is 75 kg .

The Attempt at a Solution


Hey everyone, so I've answered this question and it equals too half her weight. W=2T, but i just want to intuitively understand it better because it still confuses me. Why is the force exerted only half if its usually the whole weight required? is it because she's holding the rope? Also I've read that people say its because there's two tension forces on both sides, but wouldn't that be the case if it was just another regular force pulling down? Thank you
 
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Ask yourself if the end of the rope were attached to the bucket what the tension in each part of the rope would be. Obviously W/2. Since the girl is effectively part of the bucket her holding it does not change the situation so the tension on the end remains W/2.
 

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