A small mass m hangs at rest from a vertical rope of length l that is fixed to the ceiling. A force F then pushes on the mass, perpendicular to the taut rope at all times, until the rope is oriented at an angle (theta)=(theta)0 and the mass has been raised by a vertical distance h . Assume the force's magnitude F is adjusted so that the mass moves at constant speed along its curved trajectory.

Question

A small mass m hangs at rest from a vertical rope of length l that is fixed to the ceiling. A force F then pushes on the mass, perpendicular to the taut rope at all times, until the rope is oriented at an angle (theta)=(theta)0 and the mass has been raised by a vertical distance h . Assume the force's magnitude F is adjusted so that the mass moves at constant speed along its curved trajectory.
Find the work done by  during this process. [Hint: When the angle is increased by d(theta) (in radians), the mass moves along an arc length ds=ld(theta)

Elena · Answer

W=mgh =mgL(1-cosφ)