Variable mass problem (integration help)

  • Thread starter Liquidxlax
  • Start date
  • #1
Liquidxlax
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Homework Statement



I've pretty much solved it, but i'm unsure of my final integration

A uniform chain of length L and density /rho(kg/m) is initially stationary on a horizontal, frictionless table, with part of the chain (length yo) hanging over the edge. How much time passes before the entire chain has left the table?


Homework Equations



arccosh(x) = log(sqrt(x2-1)+x)


The Attempt at a Solution




I don't think i need to put all the work i've done.


my integral

[tex]\int \sqrt{(y^{2}-y^{2}_{o})g/l}^{-1/2}[/tex]

the answer i get is

[tex]arccosh( \sqrt{l/g}*y/y_{o})[/tex]

or

[tex]\sqrt{l/g}*log(2(\sqrt{y^{2}-y^{2}_{o}}+y))[/tex]

yet on wolfram and other websites they say that l/g should not be square rooted. Yet i don't see why.

thanks
 

Answers and Replies

  • #2
ehild
Homework Helper
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L/g has to be square rooted. If not, the dimension of the time is wrong.

ehild
 
  • #3
Liquidxlax
322
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ah yes, thank you. I should have noticed that
 

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