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Work emptying a bowl

  • Thread starter teken894
  • Start date
  • #1
25
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Homework Statement



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?

Homework Equations




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?
 

Answers and Replies

  • #2
1,425
1
Is it being pumped from underneath so that there is free space between the liquid and the bowl?
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
41,804
931
Yes, that is exactly right!
 

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