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Dimensional Analysis and the mathematical steps throughout a process.

  1. Apr 3, 2012 #1
    One would assume that:

    $$t \propto h^\alpha m^\beta g^\gamma$$

    Where t = time taken for object to fall, h = height dropped from, m = mass, g = acceleration due to gravity.

    By doing some dimensional analysis one can find that:

    $$t \propto h^\frac{1}{2} g^\frac{-1}{2}$$ and that t is independant of the objects mass.

    From this, one can derive that:

    $$t = C \surd\frac{h}{g}$$

    Where C is some unknown constant of proportionality.

    MY QUESTION:

    How does one get from $$t \propto h^\frac{1}{2} g^\frac{-1}{2}$$ to $$t = C \surd\frac{h}{g}$$. I need to know all the mathematical processes and each step in detail.
     
  2. jcsd
  3. Apr 3, 2012 #2

    Integral

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    x-1/2=[itex] \sqrt{ \frac 1 x} [/itex]

    How can you not know this?
     
  4. Apr 3, 2012 #3
    Probably cos I'm 14 and haven't been taught it...
     
  5. Apr 4, 2012 #4
    Besides, that's not even an answer to my question!

    I asked for each mathematical step and all you give me is $$x^-1/2=√\frac{1}{x}$$

    So come on, what's each mathematical step?
     
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