(a) To pull the entire rope to the top of the building, we need to overcome the weight of the rope and lift it 120 feet against gravity. The weight of the rope is:
0.5 lb/ft * 50 ft = 25 lb
The work done in lifting the rope is given by:
W = Fd
where W is the work done, F is the force applied, and d is the distance moved in the direction of the force. In this case, the force applied is the weight of the rope, which is 25 lb, and the distance moved is 120 feet. Therefore:
W = 25 lb * 120 ft = 3000 ft-lb
So the work done in pulling the rope to the top of the building is 3000 ft-lb.
(b) To pull half of the rope to the top of the building, we need to overcome the weight of half of the rope and lift it 120 feet against gravity. The weight of half of the rope is:
0.5 lb/ft * 25 ft = 12.5 lb
The work done in lifting half of the rope is:
W = Fd = 12.5 lb * 120 ft = 1500 ft-lb
So the work done in pulling half of the rope to the top of the building is 1500 ft-lb.