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Work emptying a bowl

  1. Mar 20, 2007 #1
    1. The problem statement, all variables and given/known data

    A hemispherical bowl with radius 8-inches is filled with punch (weighing .04 pound/in^3) to within 2-inches of the top. How much work is done emptying the bowl if the contents are pumped just high enough to get over the rim?

    2. Relevant equations


    3. The attempt at a solution

    Work = Force(weight)* displacement.

    i said displacement was "x"
    and for the weight:
    r = sqrt(64- x^2)
    weight = (.04) (pi * r^2)dx

    and so, work to lift weight at a given "x"
    is weight*displacement

    so i get total work is

    integration from 2 to 8 of

    (.04pi)(x)(64 - x^2)dx

    Is this the right way to approach this problem?
     
  2. jcsd
  3. Mar 20, 2007 #2
    Is it being pumped from underneath so that there is free space between the liquid and the bowl?
     
  4. Mar 21, 2007 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Yes, that is exactly right!
     
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