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Relativity problem

  1. Mar 9, 2012 #1
    1. The problem statement, all variables and given/known data
    Formulate an expression linking the change in time (dT) and the particle's velocity (v) with it's length (l) occurring at relativistic speeds

    2. Relevant equations
    γ = 1/√1-(v^2/c^2)
    T = γT
    l = γl

    3. The attempt at a solution
    Not really sure what it's after...
     
  2. jcsd
  3. Mar 9, 2012 #2

    HallsofIvy

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    You have "dT" but no other "d". You must have either "dl" or "dv". Which is it?
     
  4. Mar 10, 2012 #3
    I think it implies dL
     
  5. Mar 10, 2012 #4
    Just been looking at this question again and knowing that provided that v is a constant in the Lorentz Length Contraction:

    [itex]L_{0}=L\sqrt{1-\frac{v^{2}}{c^{2}}}[/itex]

    Then shouldn't we be able to rearrange this for [itex]\sqrt{1-\frac{v^{2}}{c^{2}}}[/itex] to make

    [itex]\sqrt{1-\frac{v^{2}}{c^{2}}}=\frac{L_{0}}{L}[/itex]

    and then feed this into the equation for Δt perhaps? So that

    [itex]\delta T=\frac{\delta T_{0}}{\sqrt{1-\frac{v^{2}}{c^{2}}}}[/itex]

    becomes

    [itex]\delta T=\frac{\delta T_{0}L}{L_{0}}[/itex]

    It's just an idea...
     
  6. Mar 11, 2012 #5
    Does anyone have any pointers? Perhaps try this under a different sub-forum maybe?
     
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