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Homework Help: Gravitational formula help

  1. Jan 31, 2010 #1
    hi!
    in my book they are trying to derive a formula for how much energy is needed to move an object height h from the earth's surface. so large that:

    dent's total work (W) spent a
    to move a body with mass m from the earth to a point at distance R from the center of the earth:
    [tex]W=c\cdot m\cdot M\cdot (\frac{1}{R_0}-\frac{1}{R})[/tex]
    c = 6.66 * 10 ^ -11, R_0 = 6370
    when R increases approaching the term 1 / R all zero, and work to keep a body from the earth's surface infinitely far into the universe can be calculated by the formula
    [tex]W=c\cdot \frac{m\cdot M}{R_0}[/tex]
    what I can not really understand is that work is defined as force*distance, W=F*s.
    why is [tex]\frac{1}{R_0}-\frac{1}{R}=distance[/tex] and why is [tex]c\cdot m\cdot M=force[/tex]??

    can someone explain to me, thanks

    2) why is [tex]c\cdot m\cdot M [/tex] the same at [tex]m\cdot g\cdot R^2_0[/tex], also
    [tex]c\cdot m\cdot M=m\cdot g\cdot R^2_0[/tex]
     
    Last edited: Jan 31, 2010
  2. jcsd
  3. Jan 31, 2010 #2

    tiny-tim

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    Science Advisor
    Homework Helper

    Hi aloshi! :smile:

    (It's not c, it's G. :wink:)

    Work isn't force*distance unless the force is constant.

    Work is the integral of force wrt distance … W = ∫ F.ds,

    and in this case F = GMm/r2, so W = ∫ GMm/r2 dr = GMm/r + constant. :smile:
     
  4. Jan 31, 2010 #3
    Re: gravitational

    but I can not about Integration, can you explain in a different way? pleas
     
  5. Jan 31, 2010 #4
    Re: gravitational

    unless the force is not constant, way they write the worke sow??

    and i find this:
    [tex]W=\int_{r=R_0}^{R}Fdr=\int_{r=R_0}^{R}\frac{cmM}{r^2}dr=cmM\int_{r=R_0}^{R}\frac{1}{r^2}dr=cmM\[-\frac{1}{r}\]_{R_0}^R=cmM\(\frac{1}{R_0}-\frac{1}{R}\)[/tex]
    but i can not anderstund't
     
    Last edited: Jan 31, 2010
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