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Homework Help: 2D momentum (need help in understanding, but have the answer)

  1. Nov 15, 2008 #1
    1. The problem statement, all variables and given/known data
    Assume an elastic collision (ignoring friction
    and rotational motion).
    A queue ball initially moving at 3.6 m/s strikes a stationary eight ball of the same size
    and mass. After the collision, the queue ball’s
    final speed is 1.9 m/s .

    Find the queue ball’s angle θ with respect
    to its original line of motion. Answer in units
    of ◦.


    2. Relevant equations
    p1x + p2x = p1x' + p2x'
    p1y + p2y = p1y' + p2y'
    p = mv

    3. The attempt at a solution
    OK I got the right answer (really I just copied my teacher's work which was too confusing for me to repeat, I only plugged in numbers to get the right answer), which was about 58.14 degrees. Really don't feel like typing out the whole process, but she (the teacher) used the sin^2 theta + cos^2 theta = 1 identity during the process.

    THEN! My friend shows me how she did it, and all she did was arccosine (final speed of ball 1/initial speed of ball 1), which got the exact same answer.

    I don't get the physics behind this. Why did my friend's solution work?
     
  2. jcsd
  3. Nov 15, 2008 #2

    tiny-tim

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    Homework Helper

    Hi Elbobo! :smile:

    (btw, it's a cue ball, not a queue ball!)

    I think her method only works for the special case of equal masses.

    It's a geometry thing …

    Hint: if you draw the vector triangle representing the momentums, you should notice that the energy equation immediately gives you one of the angles of the triangle. :wink:
     
  4. Nov 15, 2008 #3
    Ah I see! Didn't think of using the resulting momentums as the components of the initial momentum in constructing a vector diagram.

    Why wouldn't this method work when the masses are different?
     
  5. Nov 16, 2008 #4

    tiny-tim

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    As a momentum diagram, it will still work fine.

    But if you've tried it, you should have found that the geometry won't work conveniently for the energies. :smile:
     
  6. Nov 16, 2008 #5
    Oh, right, because energy is a scalar quantity.

    (BTW I didn't make up "queue"; I thought that was strange too)
     
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