A bucket of water of mass 30 kg is pulled at constant velocity up to a platform 35 m above the ground. This takes 14 minutes, ...

Question

A bucket of water of mass 30 kg is pulled at constant velocity up to a platform 35 m above the ground. This takes 14 minutes, during which time 2 kg of water drips out at a steady rate through a hole in the bottom. Find the work needed to raise the bucket to the platform. (Use g = 9.8 m/s^2.)

Answer 1

Note that the mass is not constant because water drips out at a steady rate. We can express the mass in terms of t since we know it takes 14 minutes to reduce by 2kg. The force due to the mass is mass times acceleration due to gravity. Also v = 35/14 = 2.5m/s which is constant

The displacement at any time is dx = v dt

m = 30 - 2t/14 = 30 -t/7

Work = ∫F dx = mg. v dt = ∫(9.8)[30 -t/7] (2.5) dt = 24.5∫[30 -t/7]dt = 24.5[30t -t²/7]¹⁴_o =(24.5) [420 - 28] = 9604N