1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Science Advisor
    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

    User Avatar
    Science Advisor
    Homework Helper

    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)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?