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Relativity question

  1. Mar 30, 2009 #1
    1. The problem statement, all variables and given/known data

    http://img140.imageshack.us/img140/1650/25406466.jpg [Broken]

    2. Relevant equations

    [tex]E^{2}= (pc)^{2}+m_{0}^{2}c^{4}[/tex]

    3. The attempt at a solution

    To find the energy I said that in the rest frame of the pion, it has energy 139.6Mev, so this has to equal the sum of the energies of the decay products. I then used conservation of momentum to find an equation for the energy of the muon:

    [tex]E_{1}=\frac{139.6^2+105.7^2}{2*139.6} Mev = 109.8 Mev [/tex].

    And so the energy of the neutrino is

    [tex]E_{2}=139.6-109.8 Mev = 29.8 Mev [/tex].

    I think these are correct. You can the rest energies from these total energies to get the kinetic energies of each:

    [tex]KE_{1} = 109.8-105.7 Mev = 4.1 Mev [/tex]
    [tex]KE_{2} = 29.8 Mev [/tex].

    The momentum can be calculated by rearranging the equation for [tex]E^{2}[/tex] given above, and I found

    [tex]p_{1} = 29.7 Mev/c[/tex]
    [tex]p_{2} = 29.8 Mev/c[/tex] .

    Hopefully those are all okay. I'm unsure as to how to find the speed with respect to c though. If I rearrange the equation for kinetic energy in order to find v, what is this v with respect to?

    Thanks.
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
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