You are visiting your friend Fabio\'s house. You find that, as a joke, he filled

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 12.5 foot radius. It is 8 feet tall and has 5.5 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 weight of the Kool-Aid contaminated water is 63.5 lbs/ft^3 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 12.5 foot radius. It is 8 feet tall and has 5.5 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 weight of the Kool-Aid contaminated water is 63.5 lbs/ft^3

Explanation / Answer

area of cross section of pool =pi *(12.5)2=156.25 pi

let length of thin strip =dx

volume of thin strip =156.25 pi dx

weight of thin strip=63.5*156.25 pi dx

distance of thin strip from bottom of pool =x

distance thin stip moved =8-x

work done =[0 to 5.5]63.5*156.25 pi (8-x)dx

work done =63.5*156.25*pi[0 to 5.5] (8-x)dx

work done =63.5*156.25*pi[0 to 5.5] (8x-(1/2)x2)

work done =63.5*156.25*pi(8*5.5-(1/2)5.52) -0

work done =900048 lbs-ft

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