# Homework Help: Work Integration problem

1. Feb 26, 2010

### Precursor

1. The problem statement, all variables and given/known data
A leaky 12 lb bucket is lifted from the bottom of a 10 ft well to the top at
a constant speed with a rope that weighs 0.6 lb/ft. Initially the bucket contains 60 lb
of water but the water leaks at a constant rate and finishes draining just as the bucket
reaches the top of the well. How much work is done?

2. Relevant equations
$$w = \int_{a}^{b} [F(x)]dx$$

3. The attempt at a solution
$$w = \int_{a}^{b} [F(x)]dx$$

$$w = \int_{0}^{10} [0.6(10 - x) + 6(10 - x)]dx$$

$$w = 330$$ lb-ft

Is this correct?

2. Feb 26, 2010

### LCKurtz

Don't forget the weight of the bucket.