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Homework Help: Lift to space

  1. Sep 19, 2010 #1
    1. The problem statement, all variables and given/known data

    [PLAIN]http://img194.imageshack.us/img194/2062/57916122.png [Broken]

    2. Relevant equations
    [tex]F_{gravitational}= \frac{MmG}{r^2} [/tex]

    [tex]F_{centrifugal}= \frac{mv^2}{r} [/tex]


    3. The attempt at a solution
    I got this:

    [tex]
    dF_{centr} = dF_{grav} \longrightarrow \frac{dm \cdot v^2}{R+x} = \frac{MdmG}{(R+x)^2}
    [/tex]

    Is this correct?
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Sep 19, 2010 #2

    Delphi51

    User Avatar
    Homework Helper

    The dF's look okay to me. I don't think they would be equal, though. There would be tension in the wire, except perhaps at one value of x.
     
  4. Sep 20, 2010 #3
    Tension? How can I calculate this tension and how does this equation then changes?
     
  5. Sep 20, 2010 #4
    I wouldn't worry about tension or balancing the forces if the question does not ask for it. I think your equations look correct. Here's how I think you should approach the problem.

    From the definition of linear density:
    rho = dm/dx.

    Therefore you could substitute dm in both equations for rho*dx, so that you could actually solve for Fg and Fc as function of x. Then it's just simple calculus to get to a solution.

    dFg = M*rho*G*dx/(R + x)^2
    Fg = -M*rho*G/(R + x)

    dFc = rho*v^2*dx/(R+x)
    Fc = rho*v^2*log(R + x)

    Hope this helps.
     
  6. Sep 20, 2010 #5
    Thanks a lot that helped!
     
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