1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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

    User Avatar
    Science Advisor
    Homework Helper

    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

    User Avatar
    Science Advisor
    Homework Helper

    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

    User Avatar
    Science Advisor
    Homework Helper

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

    lose the square-root! :wink:
    (and i'm going to bed :zzz: g'night!)​
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook