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Mass frame.

  1. Oct 24, 2007 #1
    1. The problem statement, all variables and given/known data

    Nucleus A,which has rest mass [tex]m_A[/tex],collides with nucleus B,which has rest mass [tex]m_B[/tex].In the laboratory frame,nucleus A has energy [tex]E>m_Ac^2[/tex]
    abd nucleus B is stationery.Find the total energy of the system in center of mass frame in terms of [tex]m_A,m_B and E[/tex].

    3. The attempt at a solution

    What's the center of mass frame?Is it a frame of nucleus A?
  2. jcsd
  3. Oct 24, 2007 #2


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    Consider the frame in which the total spatial momentum is zero.
  4. Oct 24, 2007 #3
    Is it a center of two nuclei?
  5. Oct 24, 2007 #4
    Then check my solution.
    Velocity of A in labframe is
    velocity of center of mass

    In frame which moves with velocity v_c,nucleus A has velocity

    [tex]v'_A=\frac{v-v_c}{1-\frac{vv_c}{c^2}}[/tex].And nucleus B has velocity [tex]v'_B=v_c[/tex].So the total energy in this frame is

  6. Oct 24, 2007 #5
    I think from the frame moving with velocity v_c,velocities for A and B arer true.But as seems to me [tex]m_Av_A\neq m_Bv_B[/tex] in this frame.
  7. Oct 30, 2007 #6
    Here I tried another solution:

  8. Oct 30, 2007 #7


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    Looks right to me.
  9. Oct 30, 2007 #8
    Thanks very much.

    And ,if after colission reaction occurs [tex]A+B\rightarrowC+D+Q[/tex].[tex]m_A+m_B=m_C+m_D+Q[/tex].Is it

    [tex]E'^2=(m_Cc^2+m_Dc^2+Q)^2[/tex] ? For E minimum
  10. Oct 30, 2007 #9


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    I don't understand. What is the question asking for?
  11. Oct 30, 2007 #10
    Oh,sorry.After collision reaction occurs [tex]A+B\rightarrow C+D[/tex].Suppose that

    [tex]m_A+m_B=m_C+m_D+Q[/tex].Find the minumum E for reaction to occur?And I think that in center of mass frame after reaction total momentum is zero.
  12. Oct 30, 2007 #11


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    sorry. still a little confused. what does Q represent here?
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