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Elastic Collisions (Kinetic energy)

  1. Oct 11, 2009 #1
    1. The problem statement, all variables and given/known data

    A nuclear fusion reaction occurs when a deuterium nucleus, mass 2m, and a tritium nucleus, mass 3m, combine (each with velocity v in opposite directions). Most of the energy released in the fusion is carried away in the kinetic energy of the product neutron, mass m, and velocity 5v. The other product is a helium nucleus, mass 4m, and velocity v.

    (a) Show in terms of m and v that momentum is conserved in the process.
    I've done this part, I don't need help with it. I'm just posting it incase it's a sub-step for the next part. The answer is -mv=-mv

    (b) Calculate the kinetic energy released in the fusion in terms of m and v.

    I'm stuck with part b. For part a I had to use all the data in the question, I'm guessing that for part b I only have to use the masses and velocities before the collision.

    2. Relevant equations

    Ek = 0.5mv2

    3. The attempt at a solution

    This is what I've done so far:
    Ek = 0.5mv2

    v1 = 1v
    m1 = 2m
    v2 = 1v
    m2 = 3m

    Ek1 = 0.5m1v12
    Ek1 = 0.5x2m1v2
    Ek1 = mv2

    Ek2 = 0.5m2v22
    Ek1 = 0.5x3m1v2
    Ek1 = 1.5mv2

    EkT = Ek1+Ek2
    EkT = (mv2)+(1.5mv2)

    But the answer in the book is EkT = 12mv2...

    I think I may have messed up in the algebra, or maybe I need to use the data after the collision too.
     
  2. jcsd
  3. Oct 11, 2009 #2

    tiny-tim

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    Welcome to PF!

    Hi Magma828! Welcome to PF! :wink:
    No, the total KE after is greater than the total KE before …

    the difference in energy must have come from somewhere, and it comes from the "nuclear energy" released.

    Try again. :smile:
     
  4. Oct 11, 2009 #3
    Re: Welcome to PF!

    Ahh of course. I'd just spent the previous hour doing part a using the principle of conservation of momentum and decided to invent the principle of conservation of kinetic energy :tongue:

    So it's the exact same method but just with the after-collision velocities?
     
  5. Oct 11, 2009 #4

    tiny-tim

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    It's the exact same method with all the velocities. :wink:
     
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