Question

The mass of a bucket full of water is 15 Kg. It is being pulled up from a 15m deep well. Due to a hole in bucket 6 Kg of water flows out. Find the work done in pulling it out of the well.

Answer 1

**Assuming** the bucket is not accelerating and that the leakage is at a uniform rate per time (and thus distance)

you can say that the mass of the buckets as it rises from distance z = 0 [bottom of well] to z = 15 [top of well] is \(m(z) = 15 - \frac{2}{5}z\). Check, z = 15, \(m(z) = 15 - \frac{2}{5}15 = 9 \ \checkmark \)

from definition of work, \(W = \int F dz\)
\(F = m(z) . g\)

\(W = g \ \int_{z=0}^{15} 15 - \frac{2}{5}z \ dz \)