Work problem -- raising a chain and load

[Mr Davis 97]

Homework Statement

Consider a 40-foot chain that weighs 4 pounds per foot hanging from a winch 40 feet above ground level. Find the work done by the winch in winding up the entire chain with a 600-pound load attached to it.

Homework Equations

The Attempt at a Solution

$\displaystyle \int_{0}^{40} 600 + 4(40-y) ~dy = 27200$ ft-lbs

Is this the correct answer?

 

[person123]

It looks correct. I get the same answer if I consider the center of mass of the load and chain and find the change in gravitational potential energy of the objects.