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Particle decay: Relativistic or classical?

  1. Nov 3, 2016 #1
    IMG_0819.JPG This question was asked in an competitive exam in India.

    The relevant equations are momentum conservation in the classical sense and the 4 momentum conservation.

    My attempt: Classical momentum conservation would seem inaccurate since the kinetic energies are high. However, a straightforward application of it yields option (a). I think it is wrong since we end up with more energy than we started with. Initial energy is 3GJ, but final energy is 10 GJ since C has 8GJ of energy.

    I wanted to know how to solve it using special relativity. It looks like information about the masses is missing.(I know that I cannot use conservation of masses.) So I am wondering whether it is possible to solve this problem with relativistic corrections and whether the answer still remains 30 degrees.

    Thanks,
     
    Last edited: Nov 3, 2016
  2. jcsd
  3. Nov 3, 2016 #2

    PeroK

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    It's got nothing to do with Relativity. The piece that went off at right angles should have ##1 GJ## not ##2 GJ##.
     
  4. Nov 3, 2016 #3
    How did you know that it is a classical momentum problem apriori?

    The energies of the two pieces are 8GJ and 2GJ.

    I have updated my original post.

     
  5. Nov 3, 2016 #4

    PeroK

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    If it was a SR problem, it would have said "relativistic velocity", not "high velocity".
     
  6. Nov 3, 2016 #5

    vela

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    1 GJ might sound like a lot, but if you calculate the equivalent amount of mass, you find ##m = \frac{10^9}{(3\times10^8)^2}= 1.1\times 10^{-8}\text{ kg}.## The mass of the missile is many orders of magnitude above that.
     
  7. Nov 3, 2016 #6

    PeroK

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    Or, if the missile had a mass of ##1 kg## then its velocity would be less than ##8 \times 10^4 m/s##
     
  8. Nov 3, 2016 #7
    Thanks for that clarification.

    If it is classical, how has the total energy increased?
     
  9. Nov 3, 2016 #8

    PeroK

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    That would be a mistake in the question, as pointed out in post #2.
     
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