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One-fourth of length L is hanging down over the edge of a frictionless, table. The rope has an uniform, linear density (mass per unit length), lambda, and the end already on the table is held by a person. a) How much work does the person do when she pulls on the rope to raise the rope and from this the work done. Note that this force is variable because at different times, different amounts of rope are hanging over the edge. b) Suppose the segment of the rope initially hanging over the edge of the table has all of its mass concentrated at its center of mass. Find the work necessary to raise this to table height. You probably find this approach simpler than that of part a). How do the answers compare and why is this so?

Started by Jesse Simpson ( University of Wisconsin-Green Bay )

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a) The work done by the person pulling the rope up is equal to the force exerted by the person multiplied by the distance the rope is pulled up. This force varies because as more and more rope is pulled up, the force required to lift it increases. b) The work necessary to raise a segment of the rope with all its mass concentrated at its center of mass is equal to the mass of that segment multiplied by the distance it is lifted up. The amount of work required in this situation is independent of the varying force since the mass of the rope is the same. This is simpler than the approach in part a) because the mass does not change and the work does not depend on the varying force. The answers for both parts will be equal because the work done is equal to the mass times the distance lifted.

Answered by Theresa

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