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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

    haruspex

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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

    haruspex

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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:

    ƩPi=ƩPf

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


    Now plug into this

    0=ΔKE+ΔPEg+ΔPEspring
    =1/2mv2f-1/2mv2f+mghf-mghi+1/2kx2f-1/2kx2f

    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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