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Digging a Well (Work Problem) 
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#1
Nov2011, 06:16 PM

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1. The problem statement, all variables and given/known data
A well is dug in the shape of a rectangular prism. It is 30ft deep and has a base with area of 40ft^2. Assuming that the soil weighs 150 lbs/ft^3, calculate the work W required to raise the soil to ground level. 2. Relevant equations W = ∫dW dW = ρ(area)(distance)dx 3. The attempt at a solution I had dW = ρ40(30x)dx Then I said W = 150∫[from 0 to 30] 120040x dx Solved to get 2700000ft/lb, which is wrong. I don't really understand what I did wrong here. Isn't this just like pumping water out of a tank or something? 


#2
Nov2011, 10:15 PM

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I get the same answer. I guess we are both assuming "rectangular prism" means the same thing as "rectangular parallelepiped" or "rectangular box".



#3
Nov2111, 02:10 AM

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I think your answer is too large by a factor of 30. Go back to your dW formula to see why. RGV 


#4
Nov2111, 11:24 AM

P: 9

Digging a Well (Work Problem)
I don't understand why it would just be x for the distance rather than 30x. Could someone explain this to me?



#5
Nov2111, 11:31 AM

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It doesn't matter whether you use x or 30  x. I think you are correct and I am puzzled what RGV sees that we don't, since his answers are usually spot on.



#6
Nov2111, 11:46 AM

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But x and 30x give you totally different answers...



#8
Nov2111, 11:57 AM

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RGV 


#9
Nov2111, 12:06 PM

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We are both thinking of a hole shaped by a rectangular box, right? 


#10
Nov2111, 12:08 PM

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Oh, I'm sorry. I see they are the same now, I just don't understand how.



#11
Nov2111, 01:03 PM

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positive up or down. 


#12
Nov2111, 02:12 PM

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No, I was thinking of a wedgeshaped excavation (because of the word "prism" in the original post). In that case I would be wrong anyway, because (my) dW is weight, not work. For a wedgeshaped hole the answer would be
Work = int rho * 40 * x*(1  x/30) dx = 900000 ftlb. RGV 


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