Practice Problem

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.


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:

          You can use F(x) = 3x, then:


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