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Energy conservation in elastic multi-dimenstional collisions

  1. Aug 7, 2011 #1
    Hi everyone. I believe that I'm in the right place for this topic. If not, please excuse me for the misplacement :)

    I am a programmer, not a physicist, so please excuse my lack of knowledge. I currently need help with an energy conservation problem.

    I am currently working on this problem: i have two discs (perfectly round, equal diameter d and equal mass distribution, but different masses m1 and m2) travelling at different translational velocities v, with different angular speeds ω. These two discs collide with each other at a random point in time t1, with a random Θ angle between their velocity vectors.

    From what I remember since highschool, the total kinetic energy is conserved within an isolated system. Thus, I conserve both angular kinetic energy and translational kinetic energy:

    [itex]\frac{1}{2}[/itex]ω1i2m1d2+[itex]\frac{1}{2}[/itex]m1v1i2 + [itex]\frac{1}{2}[/itex]ω2i2m2d2+[itex]\frac{1}{2}[/itex]m2v2i2 = [itex]\frac{1}{2}[/itex]ω1f2m1d2+[itex]\frac{1}{2}[/itex]m1v1f2 + [itex]\frac{1}{2}[/itex]ω2f2m2d2+[itex]\frac{1}{2}[/itex]m2v2f2
    I don't know where to go from here, since i have a single equation with 4 unknown variables.


    But, looking at the problem from another angle, I was trying to conserve the total energy:
    E = Ekin + Epot = constant
    Epot = [itex]\frac{kx^{2}}{2}[/itex]
    -[itex]\frac{\delta E}{\delta x}[/itex] = -kx = F
    And this is what i'm interested in, Fx and Fy on each disc.

    Having the velocity of disc1
    V(r) = [itex]\vdots \stackrel{0,d_{12}>d}{\frac{k(d_{12}-d)^{2}}{2},d_{12}\leq d}[/itex]
    where d12 = distance between centers of discs 1 and 2
    We can derivate
    F1x = -[itex]\frac{\delta v}{\delta x}[/itex] = -[itex]\frac{\delta}{\delta x} [ \frac{k(d_{12}-d)^{2}}{2} ][/itex] = k(r12-d) * [itex]\frac{\delta}{\delta x} ( d_{12}-d )[/itex]

    And so on, typing formulas in here is really time-consuming.

    Am I going in the right place with this? Or am I too off-course, away from my target?
    I just want the final velocities, translation and rotation (or accelerations of some sort).
     
    Last edited: Aug 7, 2011
  2. jcsd
  3. Aug 8, 2011 #2
    Is there anyone you'd recommend me to go to and maybe send a private message to?
     
  4. Aug 8, 2011 #3

    xts

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    1. You should rather say: I conserve sum of angular kinetic energy and translational kinetic energy: Anyway in such collision kinetic energy is not conserved - some must be dissipated on friction
    2. Formulas you used for angular kinetic energy are wrong, but (as 1. was wrong) it doesn't matter
    3. Thus you need 4 (not 3) more equations:
    3.a. two of momentum conservation (only two, as the problem is two-dimensional)
    3.b. Constraint that at the point of collision velocities of points at edges of both discs must be the same
    3.c. Total angular momentum must be conserved.
     
  5. Aug 8, 2011 #4
    Thank you for the reply, I will try to work with a,b,c from here on, I'll post back with the results (if any, since i can hardly remember the highschool physics :D).
     
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