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Conservation of Momentum of two trolleys

  1. Apr 19, 2015 #1
    1. The problem statement, all variables and given/known data

    There are two trolleys travelling in the same direction which are about to collide.

    Trolley 1 is travelling at 4 metres per second and has a mass of 2kg
    The other, Trolley 2, (which is in front) is moving a 1 metre per second and has a mass of 4kg.

    After the impact, they move off together

    What is the total kinetic energy of the trolleys after the collision:

    1. 1.3J
    2. 12J
    3. 18J
    4. 19J

    2. Relevant equations

    Linear Momentum (kgms^-1) = Mass (kg) * Velocity (ms^-1)

    3. The attempt at a solution

    I could be approaching it completely the wrong way, but I have tried to work out the momentum of each trolley prior to the collision:

    Momentum of Trolley 1 = 2kg * 4 metres per second = 8kgms^-1
    Momentum of Trolley 2 = 4kg * 1 metre per second = 4kgms^-1

    As I understand it, as momentum is conserved, the combined momentum once they have collided is 12kgms^-1

    Any help would be much appreciated
     
  2. jcsd
  3. Apr 19, 2015 #2

    Orodruin

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    Edit: I should read all the post better ...
    Correct.
     
  4. Apr 19, 2015 #3

    Doc Al

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    So far, so good. Now use that to find the speed after the collision.
     
  5. Apr 19, 2015 #4
    Thanks! So using the equation I used earlier:
    Rearranging this equation, Velocity = Momentum/Mass

    Therefore, by my reckoning, velocity = 12/6 = 2 metres per second

    Using this, can I then use Kinetic Energy = 1/2mv^2, to give a Kinetic Energy of 12J (option 2)? Is that correct?
     
  6. Apr 19, 2015 #5

    Orodruin

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    Yes, it is correct. I would like to point out that there is also no need for you to compute the velocity. You could equally well note that, since ##p = mv##, the kinetic energy can also be expressed as ##E_k = p^2/(2m)## (this can also be useful to remember) and you only need to use your computed momentum and the total mass.
     
  7. Apr 19, 2015 #6
    Thank you very much Orodruin! I haven't seen that equation before - will definitely come in handy!
     
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