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Special Relativity- momentum and energy

  1. Apr 10, 2009 #1

    C.E

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    1. a. An electron of rest mass (0.511Mev) is accelerated in a linear accelerator so it has a total energy of 40 Gev.
    i).What fraction of the total energy is kinetic energy?
    ii).what is the reletivistic linear momentum of the electron?
    iii).What is its relativistic mass?
    b.A particle of rest mass m travels so that its total energy is twice its rest mass energy. It collides with a particle of rest mass m and forms a composite particle.
    i). What is the momentum of each of the initial particles?
    ii).What is the momentum of the new particle produced in the collision.
    iii).What is the rest mass of the new particle

    3. Here is my attempt at part a, there are a few things I am unsure on firstly, in answering this question I have assumed potential energy is negligeable, i.e. there is only kinetic and rest mass energy, is that ok? Secondly I am a bit worried by the fact I keep getting 40 as an answer and finally, I was unsure on units, what are the units of gamma?

    a. (i). (40 x 10^9 - 0.511 x 10^6)/40 x 10^9 =0.99999.
    ii) E^2=p^2c^2 +m^2c^4

    so p=40Gev/c

    iii).E=gmc^2 where g is gamma.
    Therefore g= (40x 10^9)/ 0.511 x 10^6) =78278.
    Hence relativistic mass= 78278 x 0.511 x 10^-3= 40 Gev/c^2.

    Here is part b.
    b. (i). stationary particle: 0.
    moving particle:mc^2sqrt(3) using the same equation as in aii.
    (ii) sqrt(3)mc^2 by conservation laws.
    (iii)Total energy mc^2 + 2mc^2 =3mc^2
    rest energy=sqrt(total energy^2-(momentumxc)^2)
    =sqrt(6m^2c^4)=mc^2sqrt(6)

    Have I done this question right?
     
  2. jcsd
  3. Apr 10, 2009 #2

    tiny-tim

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    Hi C.E! :smile:

    (what happened to that γ I gave you before? :wink:)
    Nope … start again …

    if energy/rest-mass = 40G/.511M, what is γ? :smile:

    (and yes, there is only kinetic and rest mass energy)
     
  4. Apr 11, 2009 #3

    C.E

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    Sorry the 0.511Mev is rest mass energy, (not rest mass), doesa that make a difference to your last post?
     
  5. Apr 11, 2009 #4

    tiny-tim

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    Nooo … that was obvious from the question.
     
  6. Apr 12, 2009 #5

    C.E

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    Ok, here is my new attempt (finding gamma first)
    Energy= gamma x rest energy
    Hence gamma=78278
    Kinetic energy= (gamma -1) x rest mass energy = 78277
    Giving: kinetic energy / total energy = 78277/78278 =0.99999.
    I still get the same answer, what is wrong with the above?
     
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