If a 200 pound cable is 100 feet long and hangs vertically from the top of a tall building, how much work is required to lift the cable to the top of the building?

Question

Charles Anctil · Accepted Answer

Since the density of the cable is

#{200}/{100}=2# lb/ft,

the small piece of the cable of length #dx# pulls down with the force

#2dx# lb.

Let #x# be the distance of the piece of the cable from the top of the building. To lift this piece up to the top, it requires the force of

#dW=2dx cdot x=2xdx# ft#cdot#lb .

Since the cable is #100# ft long,

#W=int_0^{100}2xdx=[x^2]_0^{100}=10000# ft#cdot#lb

I hope that this was helpful.

Isabella Ackerman · Answer

undefined The work required to lift the cable to the top of the building is calculated using the formula for work done against gravity:

Work = Force × Distance

In this scenario:
- The force exerted by the cable is its weight, which is 200 pounds.
- The distance the cable needs to be lifted is the height of the building, which is not provided in the question.

To calculate the work required, you need to know the height of the building. Once you have the height, you can multiply the force (200 pounds) by the distance (height of the building in feet) to find the work required.