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Gravitation field strength/Potential - Mid point between two equal masses.

  1. Jun 17, 2011 #1
    1. The problem statement, all variables and given/known data

    attachment.php?attachmentid=105341.png

    2. Relevant equations

    g = GM/r^2

    V = (-)GM/r

    3. The attempt at a solution

    I know the field strength at the mid point between two masses cancels out but I cant really get my head around the potential.
    My instinct is telling me that it would also cancel out but I just want to check with somebody who knows more than me and could explain it :)
     
  2. jcsd
  3. Jun 17, 2011 #2

    tiny-tim

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    Welcome to PF!

    Hi RSG_9! Welcome to PF! :smile:
    Let's work it out …

    as you know, both gravitational field strength and gravitational potential are additive

    (gravitational potential, of course, is gravitational https://www.physicsforums.com/library.php?do=view_item&itemid=269" per mass).

    So why should gravitational field strengths cancel when they add?

    And why should gravitational potentials cancel when they add? :wink:
     
    Last edited by a moderator: Apr 26, 2017
  4. Jun 17, 2011 #3
    Re: Welcome to PF!

    The forces are equal but in opposite directions to one another?

    (Also, you're welcome, I stalk around here a little bit only just decided to join)
     
    Last edited by a moderator: Apr 26, 2017
  5. Jun 17, 2011 #4

    tiny-tim

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    Yes :smile:, but does that apply to one or both cases? :wink:
     
  6. Jun 17, 2011 #5
    Ahhhh I think I have it?

    V from each mass is equal to -2GM/r

    V1 + V2 = -2GM/r + -2GM/r
    =-4GM/r
     
  7. Jun 17, 2011 #6

    tiny-tim

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    yees :smile:

    but why? :rolleyes:

    why do they cancel for the field strengths, but not for the potentials? :wink:
     
  8. Jun 17, 2011 #7
    Because field strength, Nkg^-1... i.e force so relatively act against each other where as potentials Jkg^-1 is energy so act 'with' each other?


    (btw you're very helpful, usually people just give you the answer and think it's okay where as i like to understand things not just have to remember them :smile:)
     
  9. Jun 17, 2011 #8

    tiny-tim

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    oooh, very woolly …

    official reason: fields are vectors, so they obey the vector law of addition, and so they can cancel even if they have the same strength (ie magnitude)

    but potentials (and potential energy) are scalars, which in the gravitational (though not electric) case are all the same sign :wink:
    (btw, it's partly because i like being awkward!! :biggrin:)
     
  10. Jun 17, 2011 #9
    Ahh yeah, I understand that. Thank you very much for you help.
     
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