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Homework Help: Elastic Collision (Urgent)

  1. Oct 23, 2012 #1
    A cart with a mass of 340 g moving on a frictionless linear air
    track at an initial speed of 1.2 m/s undergoes an elastic collision with an
    initially stationary cart of unknown mass. After the collision, the rst cart
    continues in the same direction at 0.66 m/s. (a) What is the mass of the
    second cart? (b) What is its speed after the collision?

    I have two equations: Conservation of Momentum and Conservation of KE (since this is elastic).

    m1vi = m1v1 + m2v2

    .5m1vi2 = .5m1v12 + .5m2v22

    I've solved for v2 using the equation for Conservation of Momentum, and plugged that into the equation for Conservation of KE and my answer is wrong (used up about a page of algebra, please don't expect me to type it out all on here). The correct answer can be found using the method in the PDF below.

    http://www.physics.ucc.ie/py1052_ps6.pdf (problem 8)

    My issue is that they solve for v1f (or as I called it in the equations above, v1) and yet v2f (or v2) is nowhere to be found on the side opposite of their v1f. I don't see how their algebra makes any sense. All I want is someone to explain this to me as this is supposed to be a straightforward question.
    Last edited: Oct 23, 2012
  2. jcsd
  3. Oct 23, 2012 #2


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    You missed a 0.5 there. Is it as simple as that?
    They used the momentum equation to get v2f in terms of the other variables, then substituted that in the KE equation.
  4. Oct 23, 2012 #3
    v2f = [m1vi - m1vf] / m2

    Substitute that into cons. of KE:

    .5m1vi2 = .5m1v12 + .5m2[(m1vi - m1v1) / m2]2

    Which still doesn't look like what they have. This is what I solved and I ended up getting .127 kg. What mistake have I made at this point that I'm not seeing?

    P.S. Eqn. for conservation of KE is fixed.
  5. Oct 23, 2012 #4


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    Work with that some. You should find vi - v1 cancels, getting rid of the quadratic.
  6. Oct 23, 2012 #5
    use this after you get the numbers from momentum equation of:


    (you have the break down of the above correct?)

    Now plug into this


    Now just place you values in the equation and remove things that you dont use for example the spring.
  7. Oct 24, 2012 #6
    Alrighty, thanks. That did it. I appreciate it : D
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