Practice Problem: Work of Lifting

A cable weighs 3 lb/ft and is unwinding from a cylindrical drum. If 50 feet are already unwound, find the work done by gravity as 250 feet more unwind.

Solution

Start with the general equation for work:

We need an equation for F(x).

F(x) = 3lb/in(50ft) + 3lb/in x = 150 + 3x

Now put this into the equation for work and solve:

Here’s another way to work this problem, by using a different measurement of x and then setting up your limits differently: