system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: In Newton’s cradle, when raising two balls, why doesn’t just one ball move from the opposite side with double the velocity of the 2 balls on the other side? Why do 2 balls move? Why can’t the collective momentum from both balls all be transferred to a single ball?
gpt
If all we had to concern ourselves with was conservation of momentum, it could easily do.just what you suggest.  Really it could create many different combinations of balls and speeds.

However in any collision there are two things conserved, momentum and energy.  Specifically in this type of collision all kinetic energy must be the same before and after.  If an equal mass is not sent flying at the end of this collision, then either energy or momentum is not conserved.

Math version for those interested:

KE1=KE2. (Kinetic energy is the same before and after the collision where no deformation occurs)
.5*m*v^2.     You asked what happens Masses if is 2 at the start, and 1 at the end.  Let's choose a speed of 2. And solve for our final speed.


0.5x2x2^2 = 0.5x1xV^2

4 = 0.5xV^2

Sqrt(8)=v

-----------------------

Also p1=p2.  P=m*v

2x2 = 1xV

4=v


If we try this change in mass, we get two different speeds.  Conservation of energy states it is sqrt8, while conservation of momentum requires that the final speed is 4. As both statements must be true, this possibility does not happen.

Now if the collision has some deformation, or another way to store/transfer energy, the energy equation will be a bit different, and you can have a different mass ejected.  But that isn't true for a Newton's cradle.