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Potential energy of a system (gravity)

  1. Apr 18, 2012 #1

    jjr

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    1. The problem statement, all variables and given/known data
    Show that the potential energy of a system which consists of four equal particles, each with mass M, that are placed in different corners of a square with sides of length d, is given by
    ep = - [itex]\frac{G M^2}{d}[/itex]*(4 + √(2))

    2. Relevant equations

    The gravitational force F(r) = - [itex]\frac{G M m}{r^2}[/itex] * ur
    Potential gravitational energy Ep(r) = - [itex]\frac{G M m}{r}[/itex]


    3. The attempt at a solution

    I'm having a hard time achieveing an intuitive comprehension of how one might solve this problem. As far as I can understand, they're asking how much work would be done if all the particles moved in to the center? I'm not sure if I should figure out the work it would take to bring each individual particle in to the center one at a time, all at once, or if I need to approach this in some other way.. Any hints would be greatly appreciated

    Thanks in advance,
    J
     
  2. jcsd
  3. Apr 18, 2012 #2

    ehild

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    Homework Helper
    Gold Member

    The gravitational potential is zero at infinity. You need to calculate the work needed to take the system apart, to move the particles one by one to infinity. The negative of that work is equal to the potential energy of the system.


    ehild
     
  4. Apr 18, 2012 #3

    jjr

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    Of course! Thanks:)
     
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