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Homework Help: Relating escape velocity equations

  1. May 11, 2010 #1
    1. The problem statement, all variables and given/known data
    I'm having a hard time relating the escape velocity equations, sqrt(2GM/r) to sqrt(2gr)



    3. The attempt at a solution
    I know that both equations mean the same thing, but I can't figure out how to get from the first equation to the second
     
    Last edited: May 11, 2010
  2. jcsd
  3. May 11, 2010 #2

    diazona

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    Do you know the equation for the gravitational force between two objects (in space)?
     
  4. May 12, 2010 #3
    F=-Gm1m2/r^2
     
  5. May 12, 2010 #4

    diazona

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    Yep, and I assume you know the equation for the gravitational force acting on an object on (or near) the surface of the Earth... now, the force should be the same whether you calculate it using one equation or the other. So set the two forces equal to each other and see what you get.
     
  6. May 12, 2010 #5
    err, I think this is where I'm stuck at. if an object is right on the surface of the earth then I guess the gravitational force would look the same as the general equation-ish
    F=-Gm(earth)m(object)/R(earth)^2. I'm not quite sure what I'm looking at when I set them equal to each other.
     
  7. May 12, 2010 #6

    diazona

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    OK, well, that's right... now, when I mentioned the equation for gravitational force on an object near the surface of the Earth, I was trying to get you to think of the equation you used before you learned about [itex]F = -Gm_1m_2/r^2[/itex]. Do you remember?
     
  8. May 12, 2010 #7
    Ah I think I'm starting to get it but I'm making a math error somewhere i think,
    okay so I set f = mg = -Gm1m/r^2, cancel out "m", --> g=-Gm1/r^2.

    now I got to fit that into sqrt(2Gm/R) but that does not get sqrt(2gr)?
    err i think.
     
    Last edited: May 12, 2010
  9. May 12, 2010 #8

    tiny-tim

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    Welcome to PF!

    Hi calfly! Welcome to PF! :smile:

    (have a square-root: √ and try using the X2 tag just above the Reply box :wink:)
    ( diazona :smile: seems to be offline, so …)

    Put g = Gm/r2 into √(2gr). :wink:
     
  10. May 12, 2010 #9

    diazona

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    Just what I was going to say :wink: thanks for jumping in on that, tiny-tim.
     
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