Question

A 10 lb. monkey is attached to the end of a 30 ft. hanging rope that weighs 0.2 lb./ft. The monkey climbs the rope to the top. How much work has it done? (Hint: The monkey needs to balance its own weight and the weight of the rope in order to be able to climb the rope.)

Answer 1

The work done by the monkey is 480 ft.lb.

Step-by-step explanation:

In order for the monkey to climb the rope, it needs to balance its own weight and the weight of the rope. The total weight that needs to be balanced is the weight of the monkey plus the weight of the rope. The weight of the monkey is 10 lb. The weight of the rope can be calculated by multiplying the weight per unit length by the length of the rope. The weight per unit length is 0.2 lb./ft. and the length of the rope is 30 ft. Using these values, the weight of the rope is 0.2 lb./ft. * 30 ft. = 6 lb.

The total weight that needs to be balanced is 10 lb. + 6 lb. = 16 lb.

The work done by the monkey can be calculated using the formula:

Work = Force * Distance

The force is the total weight that needs to be balanced, which is 16 lb. The distance is the length of the rope, which is 30 ft. Substituting these values into the formula:

Work = 16 lb. * 30 ft. = 480 ft.lb. (foot-pounds).

Answer 2

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