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Gravitational Force equation

  1. Feb 24, 2010 #1
    1. The problem statement, all variables and given/known data

    Newton's Law of Gravitation states that two bodies with masses m1 and m2 attract each other with a force:

    [tex]F=\frac{Gm_{1}m_{2}}{r^2}[/tex]

    where r is the distance between the bodies and G is the gravitational constant. If one of the bodies is fixed, find the work needed to move the other from r=a to r=b.

    2. Relevant equations




    3. The attempt at a solution

    [tex]W=F*x[/tex]

    [tex]F=\frac{Gm_{1}m_{2}}{r^2}[/tex]

    [tex]x=r[/tex]

    [tex]W=\frac{Gm_{1}m_{2}}{r^2}r = \frac{Gm_{1}m_{2}}{r}[/tex]

    [tex]r=b-a[/tex]

    [tex]W=Gm_{1}m_{2}(\frac{1}{b-a})[/tex]

    The answer states that [tex]W=Gm_{1}m_{2}(\frac{1}{a}-\frac{1}{b})[/tex]. Did I make a mistake in setting up the problem?
     
  2. jcsd
  3. Feb 24, 2010 #2

    rl.bhat

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    Homework Helper

    Two bodies are attracting each other. If you want to take on body away from the other, then the displacement and the force are in the opposite direction.
    So W = F*x*cos(theta). Here what is theta?
     
  4. Feb 24, 2010 #3
    It seems that you have not learned calculus
    The force here is not a constant,so you can't just use W=F*x
     
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