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Momentum Questions

  1. May 10, 2008 #1
    1. The problem statement, all variables and given/known data

    Two heavy frictionless carts are at rest. They are held together by a loop of string. A
    light spring is compressed between them. When the string is burned, the spring expands
    from 2 cm to 3 cm, and the carts move apart from one another. Both hit the bumpers
    fixed to the table at the same instant, but cart A moved 0.45 metre while cart B moved
    0.87 metre.
    What is the ratio of :
    A. The speed of A to the of B after the interaction?
    B. Their masses?
    C. The impulses applied to the carts?
    D. The accelerations of the carts while the spring pushes them apart?

    2. Relevant equations

    This is an Explosion, therefore momentum before is going to be 0.
    0 = m1v1 + m2v2.
    The impulse will also equal 0
    Ft = 0.

    3. The attempt at a solution

    Well I wish I knew where to being, right now the only that I can think about is the displacement of the respective carts, and that they hit at an instant. But I cannot figure out much on the ratio and the solution. Any help would be appreciated.

    Thank You.
  2. jcsd
  3. May 10, 2008 #2
    Alright I can help you with the masses: Thinking back to the units that make up momentum p=(kg times m)/s So this can be broken down further to be p=(mass times distance)/time. Time is the same for both so. m1d1=m2d2. m1/m2=.87/.45 so I hope that helps.
  4. May 10, 2008 #3
    I would say the impulses are the same based on the fact that they are moving at different velocities... and have different masses. Impluse if based on change in momentum so I believe the an equal impulse is given to each cart in an opposite direction (so they do cancel out). So there are parts B and C. :)
  5. May 10, 2008 #4
    Thank you for the quick reply. Well to figure out the velocity ratio, this is what I derived.

    Because of you I was able to figure out the velocity ratio.

    va/vb = da/t * t/db (*Note: the velocities are just equal to their respective d/t equations, where time will cancel out, therefore you are just left with the ratio of displacements.)

    va/vb = .45m/.87m = .51

    I just want to know how exactly I could prove the impulse, and acceleration, but I will keep working at it.
    Last edited: May 10, 2008
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