Final answer:
The monkey has done 480 ft-lbs of work.
Step-by-step explanation:
To calculate the work done by the monkey, we need to consider the work done against the force of gravity. The monkey must balance its own weight and the weight of the rope in order to climb the rope. The total weight is the sum of the monkey's weight and the weight of the rope.
Weight of the monkey = 10 lbs
Weight of the rope = (length of rope) x (weight per unit length)
In this case, the weight of the rope is (30 ft) x (0.2 lb/ft) = 6 lbs
So, the total weight is 10 lbs + 6 lbs = 16 lbs
The work done is given by the equation:
Work = Force x Distance
Since the work is done against the force of gravity, we use the weight as the force:
Work = Weight x Distance
Work = 16 lbs x 30 ft = 480 ft-lbs