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Two-particle collision

  1. Jan 19, 2017 #1
    1. The problem statement, all variables and given/known data
    In a two-particle collision the square of the invariant mass is.
    M is total mass of the system (M2 is the square of the total mass)
    m is the mass of each particles
    E is the energy of each particles
    p is momentum vector of eache particles

    2. Relevant equations
    M2 = (E1+E2)2 - (p1+p2)2 = m12+m22+2(E1E2 - p1 ⋅ p2)

    now know the each energy E = mc2, here set the c =1 (Speed of Light),

    3. The attempt at a solution
    But how the momentum have dot product in this equation ? How the dot product p1 ⋅ p2 can derive from (p1+p2)2 ?
     
  2. jcsd
  3. Jan 19, 2017 #2

    Simon Bridge

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    Try doing the algebra... hint: expand the brackets.
     
  4. Jan 20, 2017 #3
    Yeah , i was tried to deriving (p1+p2)2 to the single dot product as above ,but always have the extra term.
    (p1+p2)2
    =p12+p22+2p1p2
    =p12+p22+( p1 ⋅ p2 )
     
  5. Jan 20, 2017 #4

    haruspex

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    What is the relationship between E1 and m1?
     
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