Really hard related reates problem

  • Thread starter iRaid
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  • #1
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Homework Statement





Homework Equations





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:

Answers and Replies

  • #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?
 
  • #3
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It means that they're getting smaller, therefore negative right? so that's why dS/dt is negative and not dE/dt?
 
  • #4
Dick
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Does it mean that dS/dt=-.4? Not sure?

If the side walls are getting closer it's the end walls that are getting shorter, right?
 
  • #5
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If the side walls are getting closer it's the end walls that are getting shorter, right?

OH I see, one sec let me retry this.
 
  • #6
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Ended up getting -1/12 = dH/dt is this correct? So therefore the depth of the liquid is decreasing.
 
  • #7
Dick
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Ended up getting -1/12 = dH/dt is this correct? So therefore the depth of the liquid is decreasing.

Well, I got +1/12=dH/dt. One of us made a mistake.
 
  • #8
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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..
 
  • #9
Dick
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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..

What did you use for dS/dt and dE/dt?
 
  • #10
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dS/dt=-.3
dE/dt=+.2
 
  • #11
Dick
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dS/dt=-.3
dE/dt=+.2

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.
 
  • #12
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That's what I thought I did wrong, thanks for all your help.

Much appreciated.
 

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