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Collision Problem

  1. Feb 19, 2007 #1
    1. The problem statement, all variables and given/known data

    An atom (m = 19.0 u) makes a perfectly elastic collision with another atom at rest. After the impact, the atom travels away a
    a 52.9° angle from its original direction and the unknown atom travels away at a −50.0° angle. What is the mass (in u) of th
    unknown atom?

    2. Relevant equations

    Conservation of Momemtum
    Law of Sines

    3. The attempt at a solution

    Atom A is the m_a=19 u...

    m_a*v_a,i=m_a*v_a,f + m_b*v_b,f

    Draw triangle, use law of sines...


    4 eqns (bottom one can be seperated into 3 eqns correct?), 4 unknowns (m_b, v_a,i, v_a,f, and v_b,f)

    Tried to solve in my TI-89 and it did not work (note I'm not in radian mode or anything stupid)
  2. jcsd
  3. Feb 19, 2007 #2
    Use conservation of momentum and conservation of kinetic energy to find the answer.

    (Hint: Write the conservation of momentum expressions in the x- and y-directions. Note that the y-momentum before the collision is 0, so it has to be 0 after.)
  4. Feb 19, 2007 #3
    So like...?


    m_a*v_a = m_a*v_a*cos(52.9) + m_b*v_b*cos(50)

    0.5*m_a*(v_a)^2 = 0.5*m_a*[v_a*cos(52.9)]^2 + 0.5*m_b*[v_b*cos(50)]^2


    0 = m_a*v_a*sin(52.9) + m_b*v_b*(-sin(50))

    Don't need to do KE in y-direction because already have 3 equations for 3 unkowns...
    Does doing the trig fucntions eliminate the need to do the initial and final subscripts on the velocities?
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