Question

Help please! Calc work problem.

A Leaky bucket 10kg bucket is lifted from the ground to 12m at a constant speed with a rope .8kg/m. Initially the bucket contain 36kg of water but leads at a constant rate and finish draining just as the bucket reaches 12 meter level. HOw much work is done?

Answer 1

Steps I would take:
1) Find the time taken to lift the bucket.
2) Find the rate at which the water leaves the bucket
3) Find a function for the weight of the bucket at time t
4) Find a function for the position of the bucket at time t
5) Find a function for the weight of the bucket at position x
*Remember that the weight of the bucket is also the force required to move the bucket at a constant speed.
6) Integrate:
\[W = \int\limits_{a}^{b} F(x) dx\]