I can't teach myself to how to solve problems involving work. I've watched many videos, tutorials, and read my textbook many times. I can't get the information to click.
Here is the problem I am working on:
A bucket that weighs 4 lb and a rope of negligible weight are used to draw water from a well that is 80 ft deep. The bucket is filled with 40 lb of water and is pulled up at a rate of 2 ft/s, but water leaks out of a hole in the bucket at a rate of 0.2 lb/s. Find the work done in pulling the bucket to the top of the well.
I don't know how/where to start.
What I have done:
Total weight = 44 lb
Total distance is 80 ft and we are suppose to integrate from 0 to 80
F = (44 - 0.2x)?
then integrate f fomr 0 to 80?