1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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.


    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


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    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?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook