[Coda]

You already know enough about Newtonian physics to derive that result yourself, actually.

In the absence of friction, a perfectly rigid object in motion that strikes another perfectly rigid object at rest will transfer 100% of its kinetic energy. (Equivalently: in the absence of friction, two perfectly rigid objects exchange their kinetic energy when they collide. You can see this is equivalent by choosing different frames of reference for the same interaction.)

But because real objects aren't perfectly rigid (this would imply an infinite speed of sound in that material), the transfer of energy happens through a finite impulse, and because most experiments you can run don't take place in outer space, there's going to be friction. There are also additional forces acting on the system that you might not be thinking about.

Let's think of hockey pucks on a flat surface with low but nonzero friction. Why hockey pucks? Because balls roll, and spinning introduces angular momentum, which is conserved just like linear momentum is.

In order for puck #1 to make puck #2 move, it has to exert enough force to overcome the friction keeping puck #2 where it is. That force is obviously going to apply an acceleration to puck #2, and the reaction force will apply a deceleration to puck #1.

This means that the two pucks will be sliding together for some distance, remaining in contact with each other until puck #2's velocity exceeds puck #1's.

In the case where puck #1 stops and puck #2 moves away at full speed, this means that the contact time was long enough for that impulse to transfer all of the momentum. In the case where puck #1 slows down but keeps going, that means that only some of the momentum was transferred before puck #2 was moving too fast to keep them in contact.

The only remaining scenario to consider is bouncing back.

I actually don't think this is possible in a sliding-only interaction in the absence of friction if the two objects are of equal mass. Without rolling or friction, bouncing back means that puck #2 would have to have more mass than puck #1, so that the reaction force would accelerate #1 backwards faster than #2 gets accelerated forward.

The force of friction, though, shifts the balance. Static friction is greater than kinetic friction. So the reaction force has less resistance to pushing puck #1 backwards than the action force has to pushing puck #2 forwards. Over the span of the impulse, this could mean that puck #1 is accelerated enough faster than puck #2 to bounce back instead of stopping or proceeding forward.