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Work problem

  1. Mar 1, 2010 #1
    The problem statement, all variables and given/known data
    Find the work required to empty a tank in the shape of a hemisphere of radius [tex]R[/tex] meters through an outlet at the top of the tank. The density of water is [tex]p kg/m^{3}[/tex]; the acceleration of a free falling body is [tex]g[/tex]. (Ignore the length of the outlet at the top.)


    The attempt at a solution

    [tex]w = \int_a^b (density)(gravity)(Area-of-slice)(distance)dx
    [/tex]

    [tex]w = \int_0^R (p)(g)(\pi)(R^{2})(R - x)dx
    [/tex]

    Is this correct/complete?
     
  2. jcsd
  3. Mar 1, 2010 #2

    tiny-tim

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    Hi Precursor! :smile:

    (have a pi: π and a rho: ρ and an integral: ∫ and try using the X2 tag just above the Reply box :wink:)
    No, that's the correct formulal for a cylinder (Area-of-slice = πr2).

    Try again! :smile:
     
  4. Mar 1, 2010 #3
    So is the area of the slice actually π(1 - x²)?
     
  5. Mar 1, 2010 #4

    tiny-tim

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    Nooo (btw, it might be easier if you measured x from the top instead of from the bottom :wink:)
     
  6. Mar 1, 2010 #5
    Is it π√(R² - x²)?
     
  7. Mar 1, 2010 #6

    tiny-tim

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    With x is measured from the top, yes :smile: except …

    lose the square-root! :wink:
    (and i'm going to bed :zzz: g'night!)​
     
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