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Energy and momentum conservation laws problem

  1. Jun 11, 2007 #1
    1. The problem statement, all variables and given/known data

    Two balls go vis-a-vis (each of them speed is v) and strike. Hit is absolutely elastic. After the hit, one of the balls changes his motion direction 30 degrees. I need to find the direction of the other ball and both ball speeds after the hit.

    3. The attempt at a solution

    This problem is solved in center-of-mass frame of reference.

    In this frame net momentum is zero, and total kinetic energy is conserved. Let Uo and Vo be the velocities of the balls before collision:

    Vo = +v​
    Uo = -v​

    Energy KEo = 1/2 m (Vo² + Uo²) = mv²

    After collison their velocities are V1 and U1. Since net momentum is conserved, and remains zero

    V1 = -U1​

    Energy after collison is

    mv² = KEo = KE1 = 1/2 m (V1² + U2²) = mV1²
    mv² = mV1²
    Vo² = V1²​

    Therefore, despite the velocity vector changed, its absolute value (i.e. speed) remains unchanged.

    Answer:
    both balls' absolute velocities did not change, and both their directions changed by 30 degrees.

    Isn't here made any mistakes in the solution? And is it possible to solve the problem if the masses of the balls are different?

    Thanks in advance.
     
  2. jcsd
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