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Recoil velocity after collision

  1. Mar 19, 2009 #1
    1. The problem statement, all variables and given/known data
    A particle of mass 1.00u travelling at speed v, collides with a stationary Cu nucleus of mass 62.93u, and rebounds in the exact opposite direction with a speed of .9687v. What is the recoil velocity of the Cu atom, in terms of v?


    2. Relevant equations
    F=ma
    P=mv


    3. The attempt at a solution
    If the recoil of the proton is .9687v and the initial velocity was v, then in order to satisfy conservation of momentum, .0313u/v must be transfered to the Cu atom. To solve for velocity of the Cu atom, use p=mv; 0.0313 = 62.93 x v. Therefore v = 0.0005v.

    Am I correct or just going in the completely wrong direction here?
     
  2. jcsd
  3. Mar 19, 2009 #2
    Use conservation of linear momentum, you find that the total linear momentum before collision = v
    Total linear momentum after collision remains the same and the sum equals v.
    Hint : Account for the direction of the particle after collision
     
  4. Mar 19, 2009 #3
    I'm getting the same answer, but still feel like I'm on the wrong track.

    Total linear momentum = v = 1.0(.9687) + 62.93(0.00050v).
     
  5. Mar 19, 2009 #4
    :cool: What would be the direction of velocity of the particle after the collision?
     
  6. Mar 19, 2009 #5
    Wouldn't it be 1.0(.9687 v)? Velocity is a vector, so we have to take into account the direction the body is moving in..
     
  7. Mar 19, 2009 #6
    Negative along x-axis for the proton. Positive for the Cu atom.
     
  8. Mar 19, 2009 #7
    Yes.Correct.
    So wouldn't one take the velocity of the proton to be negative?
    Now, you can write the momentum conservation equation.
     
  9. Mar 19, 2009 #8
    So if the velocity and therefore momentum of the proton is -.9687, the momentum of the Cu particle would have to be... .9687 + .9687 + 0.0313 = 2.2504. Divide by 62.93 = velocity of 0.0357v.

    I'm so far off.
     
  10. Mar 19, 2009 #9
    The momentum conservation equation would be
    v = -0.9687v + 62.93 u
    Express u, the recoil velocity of Cu atom in terms of v. That is the way its found out, I believe.
     
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