You are visiting your friend Fabio\'s house. You find that, as a joke, he filled
ID: 2858301 • Letter: Y
Question
You are visiting your friend Fabio's house. You find that, as a joke, he filled his swimming pool with Kool-Aid, which dissolved perfectly into the water. However, now that you want to swim, you must remove all of the Kool-Aid contaminated water. The swimming pool is round, with a 13 foot radius. It is 7.5 feet tall and has 3 feet of water in it. How much work is required to remove all of the water by pumping it over the side? Use the physical definition of work, and the fact that the density of the Kool-Aid contaminated water is =63lbs/ft3
Explanation / Answer
area =pi r2=pi(13)2=169pi
volume of thin strip =169pi dx
weight of thin stip =63*169pi dx
distance moved by thin stip =7.5-x
work done w= [0 tp 3]63*169pi (7.5-x)dx
work done w= [0 tp 3]63*169pi (7.5x-0.5x2)
work done w= 63*169pi (7.5*3-0.5*32) -0
work done w=602073.6lb ft
work required to remove all of the water by pumping it over the side =602073.6lb ft
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