I have one of those Newton’s Cradle games, i.e., the five steel balls suspended in row. You pull one ball back, and it swings forward striking the line of the remaining four balls. The energy travels through three of them, and the fourth one kicks up on the other side. That ball then swings back and the whole process starts again in reverse. It’s a neat demonstration of conservation of momentum.
Obviously the balls don’t keep swinging forever, so that’s one deviation. Energy gets bled off through friction with the air, and a bit to make the clicking sound when the balls strike and various other things. However, the middle three balls also start swinging a bit. Why does that happen? I have in my mind something about inelastic collisions, but I can’t really remember what that means.
I would expect the development of lateral oscillations to be due to inequalities in the lengths of the strings/wires on either side supporting each of the balls (each ball has 2 strings/wires, yes?). This would cause the arc of travel of the end balls to be non-coplanar with the middle three, and the transmission of momentum to occur partly out of the plane defined by the five balls and the local vertical. This would also seem to introduce small rotations in the balls, which are probably the oscillations that you notice.
Well, yes, that’s true. If you look closely, you can see the middle balls wiggle a bit, meaning the end balls are causing some English. Is that what makes them start swinging though? I’m not sure about that.
My mistake - I misunderstood your question to be regarding the wiggles and jiggles (scientific terms ) of the balls, not about how the middle balls start swinging to-fro. So there, I would have to agree that it’s inelastic collisions that cause these oscillations. IMHO, the impacting ball does not transfer 100% of its momentum to the impacted ball; this causes a gradual build-up/imbalance that causes the four balls that should otherwise be stationary after impact to continue swinging. This minor swinging will also go out-of-phase with the lone ball, since it’s only to first order that a pendulum’s period is independent of amplitude (the larger amplitude swings take slightly longer).
I didn’t know it was called Newton’s Cradle, and I didn’t know it was something you could call a game.
But I do know that if the supporting structure, isn’t very solid and stable, the motion of the balls will be transmitted up the strings and cause the entire framework to slowly oscillate lengthwise, much like a tall building in a high wind. Isn’t this what causes the middle balls to start swinging, and eventually dissipate all the energy?
Almost. The key is that not all of the energy is transferred in the colission, some of it being used up in the heat and clacking the OP noted. But the momentum is still conserved, and there’s no way to “hide” momentum like there is for energy. The only resulting solution is that the impacted ball(s) don’t move quite as fast as the original ball, and the original ball keeps moving a little in the same direction.
Thanks - rereading my post, it says the same thing but your is worded much more elegantly. The point that you are making, that momentum is always conserved, causes the imbalance such that the departing ball doesn’t carry all of it (momentum) but that some remains in the should-be stationary other four balls. The inelasticity of the collision is the cause, and that kinetic energy deficit now goes into heat, sound, etc.
) of the balls, not about how the middle balls start swinging to-fro. So there, I would have to agree that it’s inelastic collisions that cause these oscillations. IMHO, the impacting ball does not transfer 100% of its momentum to the impacted ball; this causes a gradual build-up/imbalance that causes the four balls that should otherwise be stationary after impact to continue swinging. This minor swinging will also go out-of-phase with the lone ball, since it’s only to first order that a pendulum’s period is independent of amplitude (the larger amplitude swings take slightly longer).