What Happens During a Collision of Three Objects on a Smooth Floor?

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In a collision involving three balls of masses m, m, and 2m on a smooth floor, the scenario assumes elastic collisions. When balls Y and Z are in contact, they will experience different velocities post-collision, as they are treated as one object. To analyze the outcomes, it is suggested to first consider the collision between balls X and Y, followed by Y and Z, and then check for any subsequent collisions. The discussion emphasizes deriving equations for two balls of different masses and velocities to simplify calculations. Understanding the forces at play during the collisions is crucial, as the rigidity of the balls impacts the dynamics of the interactions.
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The floor is smooth. Y and Z are in contact. The mass of the balls are m,m and 2m as stated.
Assume all collision is elastic, what are the velocity of the three balls after all collisions??


Now, Y and Z are reversed in position. At the time of collision, what would happen for the three balls in a mathematical explanation??
If we view Y and Z as one object, then the two will experience same force but different velocity, in the equation, I just can't separate the different velocity out since Y and Z are treated as one!

HELP!
 

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To simplify this, you can pretend that the balls are slightly separated form each other. First see what happens to balls X and Y after X hits Y. Then check what happens to Y and Z after Y hits Z. Then check if Y can now hit X. If so then calculate that collision and check if Y can now hit Z... , it will make things much easier if you first derive the general equation for 2 balls of different masses and velocities coliiding.
 
But they are in contact, are both of them experiencing F respectively at the moment of strike?
 
If the balls are perfectly rigid then yes, but that can never happen.
 

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