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!

Homework Help: 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]
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook