# Math Help - A Work Problem

1. ## A Work Problem

Elevator weighs 1600 lbs.
It's suspended by 200 ft. of cable.
Cable weighs 10lb./ft.
How much work to raise elevator 30ft.?

I have this so far:

Work of elevator = 1600 x 30 = 48000 ft-lbs.
Work of cable = 10(200-30) x 30 = 51000 ft-lbs.

What do I do from here? Thanks for your time.

2. Originally Posted by kep84
Elevator weighs 1600 lbs.
It's suspended by 200 ft. of cable.
Cable weighs 10lb./ft.
How much work to raise elevator 30ft.?

I have this so far:

Work of elevator = 1600 x 30 = 48000 ft-lbs.
Work of cable = 10(200-30) x 30 = 51000 ft-lbs.

What do I do from here? Thanks for your time.
You are to raise the elevator and 200 ft of cable 30 ft, or are you winding up the cable as the elevator comes up the shaft?

In the first case the work done is equal to the weight of the elevator plus cable multiplied by 30 ft.

In the second case you need to do an integral:
$W = \int_0^{30}(w + 10L)s~ds$
where $L(s) = 30 - s$ is the length of cable left after the elevator has been raised a distance s.

-Dan