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 15 foot radius. It is 9.5 feet tall and has 9.5 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 density of the Kool-Aid contaminated water is sigma = 64.5lbs/ft^3. Don't forget to enter the correct units. (You may enter lbf or lb*ft for ft-lb.)

Explanation / Answer

We have been given that:

*g = 62.5 lb/ft³

r = 15 feet

h = 9.5 feet

Work : dW = gA(9.5-x)dx

A = r²

W = 62.5**r2* (9.5-x) dx integrate from [0 to 9.5]

= 62.5**(15)2*(9.5x - x2/2) from [0 to 9.5]

= 1992550.78 ft-lbs is our answer.

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