A 10 ft cable weighs 50 lbs and hangs from the ceiling of a building without touching the floor.

[crosenboom]

A 10 ft cable weighs 50 lbs and hangs from the ceiling of a building without touching the floor. Determine the work that must be done to lift the bottom end of the chain all the way up. I have done this problem with the cable weight 25 lbs instead. Is the process exactly the same just with the different force?

 

[Steven G]

Hi. We get to ask the questions. Is the process exactly the same as the previous just with the different force? Why yes, why no?

 

[MarkFL]

As you lift the free end of the cable upwards, the force increases linearly. The force varies from 0 lbs. to 25 lbs. over a distance of 10 feet. So, I would begin by writing:

[MATH]W=\int_0^{10} F(y)\,dy[/MATH]
where:

[MATH]F(y)=\frac{5}{2}y[/MATH]