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Work problem

  • Thread starter Precursor
  • Start date
  • #1
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Homework Statement
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?
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
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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:)
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.)

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

Is this correct/complete?
No, that's the correct formulal for a cylinder (Area-of-slice = πr2).

Try again! :smile:
 
  • #3
222
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So is the area of the slice actually π(1 - x²)?
 
  • #4
tiny-tim
Science Advisor
Homework Helper
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So is the area of the slice actually π(1 - x²)?
Nooo (btw, it might be easier if you measured x from the top instead of from the bottom :wink:)
 
  • #5
222
0
Is it π√(R² - x²)?
 
  • #6
tiny-tim
Science Advisor
Homework Helper
25,832
249
Is it π√(R² - x²)?
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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