Asmall mass m hangs at rest from a vertical rope of length ℓ that is xed 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. 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 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 = ℓ dθ.]