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Homework Help: Really hard related reates problem

  1. Feb 2, 2012 #1
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    V=20 S=6 E=2 H=20/12 (from V=SEH?)

    [itex]\frac{dS}{dt}=-.2[/itex] <--- + OR -?

    [itex]\frac{dE}{dt}=.3[/itex] <--- + OR -?

    V=SEH

    Product rule for 3 variables:
    [itex]\frac{dV}{dt}=SE\frac{dH}{dt}+EH\frac{dS}{dt}+SH \frac{dE}{dt}[/itex]

    [itex]0=SE\frac{dH}{dt}+EH(-.2)+SH(.3)[/itex]

    [itex]-EH(-.2)-SH(.3)=SE\frac{dH}{dt}[/itex]

    [itex]\frac{-EH(-.2)-SH(.3)}{SE}=\frac{dH}{dt}[/itex]

    [itex]\frac{-(2)(\frac{20}{12})(-.2)-(6)(\frac{20}{12})(.3)}{SE}=\frac{dH}{dt}[/itex]

    [itex]\frac{-7}{36}=\frac{dH}{dt}[/itex]

    Negative, therefore decreasing.
     
    Last edited: Feb 2, 2012
  2. jcsd
  3. Feb 2, 2012 #2

    Dick

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    The method of solution is fine. But picture the problem a little more carefully. It tells you the side walls are moving together at .2 m/s. This doesn't tell you dS/dt=(-.2). What does it tell you?
     
  4. Feb 2, 2012 #3
    It means that they're getting smaller, therefore negative right? so that's why dS/dt is negative and not dE/dt?
     
  5. Feb 2, 2012 #4

    Dick

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    If the side walls are getting closer it's the end walls that are getting shorter, right?
     
  6. Feb 2, 2012 #5
    OH I see, one sec let me retry this.
     
  7. Feb 2, 2012 #6
    Ended up getting -1/12 = dH/dt is this correct? So therefore the depth of the liquid is decreasing.
     
  8. Feb 2, 2012 #7

    Dick

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    Well, I got +1/12=dH/dt. One of us made a mistake.
     
  9. Feb 2, 2012 #8
    Um I think I made the mistake because I said dS/dt is negative, should be positive since the sides are getting bigger and the ends are getting smaller... But I'm not positive..
     
  10. Feb 2, 2012 #9

    Dick

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    What did you use for dS/dt and dE/dt?
     
  11. Feb 2, 2012 #10
    dS/dt=-.3
    dE/dt=+.2
     
  12. Feb 2, 2012 #11

    Dick

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    Now that's not right, is it? If the side walls are getting closer the end walls are getting shorter. So dE/dt should be negative.
     
  13. Feb 2, 2012 #12
    That's what I thought I did wrong, thanks for all your help.

    Much appreciated.
     
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