Why Don't 8 Balls Move after Collision?

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In an elastic collision involving a line of eight balls, the mechanics of force transfer through the balls explain why not all balls move with a velocity of v/4 or why the last ball does not achieve a velocity of 2v. The collision causes the kinetic energy to be conserved, allowing the force from the colliding balls to be transmitted through the stationary balls to the last two balls. This results in only the last two balls being knocked off with the same velocity as the incoming balls, rather than a uniform velocity among all eight. The ideal conditions of the scenario assume no energy loss, which is crucial for the described outcomes. Understanding these principles clarifies the behavior of the balls during the collision.
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Suppose there are 8 balls in line on a horizontal table.
Another 2 balls collide them from left side(both approach together) with velocity v.
The last 2 balls(from right) get knocked off with the same velocity as that of the balls that approached first.Why don't all the 8 balls move with a velocity v/4 or why doesn't only the last ball get knocked off with a velocity 2v?

The collision is elastic.

Something like this:
00 00000000
->
later,
00000000 00
->
 
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This only happens in an ideal case, where there is no loss in kinetic energy. It occurs because of the way the elastic compression of each ball in the pack transfers the force from the colliding balls through the pack of balls to the ejected balls. This was covered in a earlier thread:

https://www.physicsforums.com/showthread.php?t=357358
 
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