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Collision problem

  1. Sep 18, 2009 #1
    1. The problem statement, all variables and given/known data
    Three particles, A,B,C all of equal mass m,collide at the origin. Prior to the collsion the particles are moving as follows:

    A has speed u in direction (1/sqrt(2))(-i-j)
    B has speed v in direction (sqrt(3)/2)i+(1/2)j
    C has speed w in direction -i

    After the collision all particles remain at the origin.

    find w in terms of u.

    2. Relevant equations



    3. The attempt at a solution

    I know that the momentum of each particle is the mass times the velocity. I know that the momentum of the system of particles at time t is P=0

    I know that from the conservation of linear momentum that the sum of the individual momentums before the collision must also be 0.

    I am probably being a bit thick in my mathematical thinking here because I don't see how to state w in terms of u only.

    I just need a nudge in the right direction. No complete solutions


    Thanks
     
    Last edited: Sep 18, 2009
  2. jcsd
  3. Sep 18, 2009 #2
    wrote the linear momentum as


    [tex]\frac{1}{m} \vec P = \begin{pmatrix} 0 \\ 0 \\ 0 \end{pmatrix} = \frac{1}{\sqrt{2}} \begin{pmatrix} -1 \\ -1 \\ 0 \end{pmatrix} \, u ~ + ~ \frac{1}{2} \begin{pmatrix} \sqrt{3} \\ 1 \\ 0 \end{pmatrix} \, v ~ + ~ \begin{pmatrix} -1 \\ 0 \\ 0 \end{pmatrix} \, w [/tex]​


    so you see that the motion is confined in a plane! So any three vectors in a plane are linearly dependent!



    for more information see : http://en.wikipedia.org/wiki/Linearly_independent



    with best regards
     
    Last edited: Sep 18, 2009
  4. Sep 18, 2009 #3
    Perfect! Thanks
     
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