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Dimensional analysis universal gravitation

  1. Aug 28, 2005 #1
    Firstly, I admit that my math skills are fairly rusty. I also admit that this is a homework problem. It is not to be turned in for a grade however.
    The problem is to determine the SI units of G in the following equation:

    F = GMm/r^2

    (where F is force (mass * acceleration), M and m are the masses of two objects, and r is a distance)
    which is, of course, Newton's law of universal gravitation.
    I would be greatly appreciative if someone could walk through the steps needed to make this determination.
     
  2. jcsd
  3. Aug 28, 2005 #2

    TD

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    Work it out for G:

    [tex]F = G\frac{{m_1 \cdot m_2 }}{{r^2 }} \Leftrightarrow G = \frac{{F \cdot r^2 }}{{m_1 \cdot m_2 }}[/tex]

    I suppose you now the units of the RHS, LHS has to be equal :smile:
     
  4. Aug 28, 2005 #3
    Thanks for that. The answer in the back of the book is quite different, however. It is given as m^3/kg*s^2. I'm working on it. Do you think you could go into more detail? Again, my skills are a little rusty. Also, how'd you get the math font into your message?
     
  5. Aug 28, 2005 #4

    TD

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    I just worked it out for G. Now you have to replace the right hand side by all their units and simplify to find the unit of G.
     
  6. Aug 28, 2005 #5
    [tex]1N = kg \frac {m}{s^2}[/tex]
    for font (LaTex) read first threads in General Physics forum :smile:

    edit: where 1N is unit of force.
     
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