anonymous
  • anonymous
a circular swimming pool has diameter of 24ft, sides are 5 ft high, and the depth of the water is 4 ft. How much work is required to pump all of the water out over the side? water weighs 62.5 lb per cubic foot
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
dW = ρgAx dx
anonymous
  • anonymous
..... ρ∙g given as 62.5 lb/ft³ ..... A = πr²
anonymous
  • anonymous
so we are doing Force* distance = work. we are going to move cross sectional slabs of water with radius 12, pi*12^2, each slab has a different height to cover. for example the slab on the bottom has to cover 4 feet and then another foot. this is the x part. and all the slabs need to cover one foot so x + 1

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anonymous
  • anonymous
the 1 foot extra on top
anonymous
  • anonymous
so 62.5 * pi *12^2 integral ( x+1) from 0 to 4 is your work
anonymous
  • anonymous
whats important is that the force is given as pounds. dont worry about the pg part. im not so sure about that
anonymous
  • anonymous
well g is gravitational constant, and weight is mass * g , and you have density in there as well. but it all works out
anonymous
  • anonymous
you there?
anonymous
  • anonymous
yes just trying to make sense of it all. im still not understanding the x+1 since the bottom has to clear 5 ft not 1 ft
anonymous
  • anonymous
well it clears 4 feet, then +1 foot for the top . the next slab say has to clear 3 feet then +1 foot for top, so on and so forth. the toppest slab has to clear just +1 foot. but each slab has that extra +1 foot to clear
anonymous
  • anonymous
ah ok i see, thank you for clarifying

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