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Energy Conservation

  1. Jun 13, 2007 #1
    1. The problem statement, all variables and given/known data
    A car moving with an initial speed v collides with a second lighter stationary car that is 58.3% as massive. After the collision, the two cars stick together and move off in the same direction as before. Calculate the final speed of the two cars after the collision. Give your answer in units of the initial speed (i.e. as a fraction of v).


    2. Relevant equations
    M1V1+M2V2=M1Vf1+M2Vf2


    3. The attempt at a solution
    M1V1=M1Vf+53.8%M1Vf

    I ended up with V/.538=Vf but it says im wrong, any1 know what im doing wrong?
     
  2. jcsd
  3. Jun 13, 2007 #2
    The final answer you have reported says the final velocity is greater than the initial velocity. Intuitively, you should know this is wrong.

    You have M1V1=M1Vf+53.8%M1Vf

    This setup is correct, so I think your error lies in your algebra. Try reworking the simple cleanup steps and see what happens.

    PS: Your title is misleading, because your question is more concerned with the conservation of momentum, rather than the conservation of energy.

     
    Last edited: Jun 13, 2007
  4. Jun 13, 2007 #3
    k, so i got V/1.583=Vf

    is that right? i plugged it in online but it says its wrong...
     
  5. Jun 13, 2007 #4
    That is the answer I came up with.

    Perhaps someone else can chime in?
     
  6. Jun 14, 2007 #5
    mv = (m + .583m)v'
    v/v' = 1.583
    or

    v'/v = .631(7)

    The question asks for Give your answer in units of the initial speed (i.e. as a fraction of v), so you want v'/v not v/v'. In significant units it is .632.
     
  7. Jun 14, 2007 #6
    Oh, and I thought I would mention that your problem doesn't actually concern Energy Conservation, but rather the conservation of momentum. Kinetic Energy is usually not conserved in non-elastic collisions.

    JJ +
     
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