A small mass m hangs at rest from a vertical rope oflength
Chapter 7, Problem 7.91(choose chapter or problem)
A small mass m hangs at rest from a vertical rope oflength that is fixed to the ceiling. A force F then pushes onthe mass, perpendicular to the taut rope at all times, untilthe rope is oriented at an angle 6 = 0O and the mass hasbeen raised by a vertical distance h (Fig. 7-34). Assume theforces magnitude F is adjusted so that the mass moves atconstant speed along its curved trajectory. Show that thework done by F during this process equals mgh, which isequivalent to the amount of work it takes to slowly lift amass m straight up by a height h. [Hint: When the angle isincreased by dd (in radians), the mass moves along an arclength ds = d6.\
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