A heavy rope, 30 ft long, weighs 0.6 lb/ft and hangs over the edge of a building 80 ft high. Approximate the required work by a Riemann sum, then express the work as an integral and evaluate it. Exercise (a) How much work W is done in pulling the rope to the top of the building? Step 1 Since the rope weighs 0.6 lb/ft, the portion of the rope below the top of the building from x ft to (x + Ax) ft weighs_ Ax Ib. Exercise (b) How much work W is done in pulling half the rope to the top of the building?