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Two Cars on an Air Track

  1. Mar 16, 2009 #1
    1. The problem statement, all variables and given/known data
    Two carts are set up on an air track with a rubber band connecting them. The carts are pulled just slightly more than the length of the relaxed rubber band. Upon release, mass 1 travels a distance of x1 and mass 2 travels a distance of x2. Show that [tex]\frac{x_1^2}{x_2^2}=\frac{m_2}{m_1}[/tex]


    2. Relevant equations

    [tex]F_s=-kx[/tex]

    [tex]x=x_1+x_2[/tex]

    [tex]p=mv[/tex]


    3. The attempt at a solution
    I'm not exactly sure where the first two equations come in. However, I noticed:
    [tex]m_1 v = m_2 v[/tex]

    [tex]m_1 \frac{x_1}{t} = m_2 \frac{x_2}{t}[/tex]

    [tex]\frac{m_1^2}{x_2^2} = \frac{m_2^2}{x_1^2}[/tex]


    Though that's clearly not the original equation. I'm a bit lost at where I should go from here.

    Thanks!
     
  2. jcsd
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