Answer
$W=650,000 ft-lb$
Work Step by Step
We are given a rope with weight/length ratio of $2 \frac{lb}{ft}$, an initial mass of $800lb$, and a height of $500ft$ being lifted.
We first need to find the force done
$F=800+(2(500-x))$
We then evaluate the integral of work from the starting point to the height lifted
$W=\int^{500}_{0}(800+(2(500-x)))dx$
W=$650,000$ ft-lb
