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Relativity - Pion

  1. Feb 22, 2017 #1
    1. The problem statement, all variables and given/known data
    After being produced in a collision between elementary particles, a positive pion (π+) must travel down a 1.00 km -long tube to reach an experimental area. A π+ particle has an average lifetime (measured in its rest frame) of 2.60×10−8s; the π+ we are considering has this lifetime.
    How fast must the π+ travel if it is not to decay before it reaches the end of the tube? (Since u will be very close to c, write u=(1−Δ)c and give your answer in terms of Δ rather than u.)
    The π+ has a rest energy of 139.6 MeV. What is the total energy of the π+ at the speed calculated in part A?

    2. Relevant equations
    Δ t = Δt0 / sqrt(1-u^2/c^2)

    E^2 = (mc^2)^2 + (pc)^2

    3. The attempt at a solution
    I got the correct answer for speed, the first part of the question. It's the second part I can't get to work. I used the total energy equation and my speed, which worked out to give me E = 197.4 MeV but this wasn't right. I'm not sure where I'm going wrong?
     
  2. jcsd
  3. Feb 22, 2017 #2

    Orodruin

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    We will not be able to tell you this unless you actually show us what you did, not just try to describe it in words.
     
  4. Feb 23, 2017 #3
    E^2 = (mc^2)^2 + (pc)^2
    I used mc^2 = 139.6 MeV
    I put p = mv so the pc = mvc but m = 139.6/c^2 and v = (1-Δ)c = (1-(3.04*10-5))c so pc = 139.6 MeV
    So then E = sqrt(139.6^2 + 139.6^2) = 197.4 MeV
     
  5. Feb 23, 2017 #4

    Orodruin

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    This is not the relativistic momentum. This relation is only valid at non-relativistic speeds.
     
  6. Feb 23, 2017 #5
    Yes, that makes sense. I forgot to include gamma. I got the correct answer now, thanks.
     
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