A small mass m hangs at rest from a vertical rope of length l that is fixed to the ceiling. A force then pushes on the mass, perpendicular to the taut rope at all times, until the rope is oriented at an angle θ=θ0 and the mass has been raised by a vertical distance h (Fig. 2). Assume the force’s magnitude F is adjusted so that the mass moves at constant speed along its curved trajectory. Show that the work done 1 Mm M = + 3 S F ! 2 by during this process equals mgh, which is equivalent to the amount of work it takes to slowly lift a mass m straight up by a height h. [Hint: When the angle is increased by dθ (in radians), the mass moves along an arc length ds=ldθ.]