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Conservation of Momentum - Collisions

  1. Dec 5, 2012 #1
    1. The problem statement, all variables and given/known data

    A truck (4 000 kg) runs a red light and enters an intersection travelling at 81 km/h [E]. The truck collides with a car (2
    000 kg) that was travelling at 54 km/h [N20oW]. Immediately after the collision the truck was travelling at 60 km/h [N
    30o E]. Determine the velocity vector of the car immediately after the collision.


    2. Relevant equations

    I used the law of conservation of momentum. I used the concept that momentum is conserved in each component direction.

    3. The attempt at a solution

    The answer that I got was a velocity of approx 99 km/h [E32S]. Can anyone confirm this?
     
  2. jcsd
  3. Dec 6, 2012 #2

    mfb

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    This would violate energy conservation, unless the truck or the car have some active system to kick away other vehicles.
    I don't understand the notation for the direction, but I would expect that momentum is not conserved either.
     
  4. Dec 6, 2012 #3
    The notation [N30E] means 30 degrees east of north for example.

    Momentum is conserved in this question, but energy is not
     
  5. Dec 6, 2012 #4

    mfb

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    I agree that kinetic energy does not have to be conserved, but kinetic energy cannot increase in the process.

    Working in units of 1000kg*km/h:
    to east:
    truck initial 4*81=364
    car initial -2*54*sin(20°)
    truck final 4*60*sin(30°)
    car final ~207 or 104 km/h
    Hmm... looks wrong.

    to north:
    truck initial 0
    car initial 2*54*cos(20°)
    truck final 4*60*cos(30°)
    car final -106 or -53km/h

    Total energy initially: 2*81^2+1*54^2=16000 (in 1000kg*(km/h)^2)
    Total energy finally: 2*60^2+1*(104^2+53^2) = 20800
    Clearly this cannot happen in a car accident. The same problem appears with your result of 99km/h total speed as well.
     
    Last edited: Dec 6, 2012
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