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Gravitation Exercise

  1. Aug 25, 2011 #1
    1. The problem statement, all variables and given/known data

    What is the intensity of the force [itex]F_{g}[/itex] between the ring and a mass 'm', which is at a distance 'x' from the center of the ring?

    http://img52.imageshack.us/img52/6859/ringre.th.jpg [Broken]

    Uploaded with ImageShack.us

    3. The attempt at a solution

    I have got to my own answer, but it is different from the given one. Here's what I did:

    There's a potential energy between 'm' and a dM from the ring, which is given by [itex]dU=-G*m*dM/d [/itex] and [itex]d=\sqrt{r^{2}+x^{2}}[/itex].

    From this, I can find the total potential energy by integrating dU from 0 to M, which gives me [itex]U=-\int^{M}_{0}\frac{G*m*dM}{d}=\frac{-G*m*M}{\sqrt{r^{2}+x^{2}}}[/itex]

    As the variation in the potential energy is equal to the negative of the work done, I did [itex]-\int^{0}_{d}F(d)*dd=\frac{-G*m*M}{\sqrt{r^{2}+x^{2}}}[/itex][itex]\Rightarrow[/itex][itex]F(d)=\frac{2*G*m*M}{(r^{2}+x^{2})^{3/2}}[/itex]

    So, what's wrong? Thanks
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Aug 25, 2011 #2
    I think [itex]-\int^{0}_{d}F(d)*dd[/itex] should be [itex][itex]-\int^{0}_{d}F(d)*cos\theta*dd[/itex], but even this way I didn't get the right answer.
  4. Aug 26, 2011 #3
    Sorry, forgot to post the given answer for the exercise: [itex]F = \frac{GMmx}{(r^2+x^2)^{3/2}}[/itex]
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