Elastic Collisions
Six identical balls are lined in a straight groove made on a horizontal, frictionless surface, as shown below. Two similar balls each moving with velocity collide with the row of 6 balls from left.
What will happen after the collision, if the collisions are perfectly elastic?
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1 solution
When an elastic ball collides with another identical ball, then their velocities get exchanged. Therefore, if a ball is moving with velocity 'v' hits a stationary ball, then the first will come to rest and the latter will start moving with velocity 'v'.
The situation in problem can be thought of multiple collisions between the balls. The balls can be thought at an infinitely small distance apart. To simplify, consider the situation with four balls.
The balls are numbered. First collision can be taken between ball 2 and ball 3. After the collision ball 2 will come to rest and ball 3 moves with speed 'v'.
Now, the ball 3 and 1 collides with ball 4 and 2, after that ball 1 and 3 comes to rest and ball 4 and 2 start moving with speed 'v'
Now, the ball 2 collides with ball 3 to come to rest and ball 3 moves with speed v. Thus, eventually balls 3 and 4 moves with speed 'v'.
If the situation is extended to 8 balls, still the result will be same last two balls will roll with velocity 'v' each and rest of the balls will come to rest.