Fooling Newton's Cradle

A Ceroppi marble based 7 ball Newton's cradle that was picked up at the bin store and very tangled up got me to wondering.
It took about 15 hours of hard work to untangle the knots but for $12 it was a bargain that sells on Amazon for $60.
Anyway the mystery is why does only one ball fly out of the end when one collides with the opposite end, or two and two and so on. Why can't one ball collide and two balls fly out the opposite end.
It sort of reminded me of a fun trick with an electrified wire fence at a dairy farm. About 5 people formed a chain by holding hands and one person touched the wire. No one felt the shock except the person at the end of the chain who wasn't touching the fence.
Stay tuned:)

[@sunnierfish1952]

Idk how but you motivated me to learn ASL

[@johnfitzgerald8879]

The system is then modelled by one larger weight on the left side which has twice the weight of an individual ball. The left two can be simply substituted for that one larger ball. What is happening is that the left balls velocity at impact is half that of the ball on the right. The momentum being conserved and P=mv then the left balls being 2m, then it's velocity V is P=MV or P=2mV or V=P/2m. Now do the same with the kinetic energy of K.E.=(1/2)mv^2 and the fact that at the top of the swing, the kinetic energy goes to zero as the potential energy becomes P.E.= = mgh, when g is the gravitational constant and h is the height it reaches. Using m and M=2m as well as h and H for the right and left balls, the final heights can be calculated. The summary is that conservation of energy and momentum, being conserved, are expressed as different initial velocities and heights for the beginning and ends of swings of the respective balls.
The modelling that allows the aforementioned to be true is based on the assumption of perfectly elastic collisions. The issue with Newton's Pendulum or Newton's Cradle is in the marginal inelasticity and why it settles on the mass on each end being equivalent rather than one ball causing three on the other side to swing. Elastic collisions result in perfect transfer of momentum and energy between the two colliding objects. Perfectly inelastic collisions result in the two masses combing into a single body. Between these two extremes, there is energy loss in the vibrations. Even the two tapped balls has energy loss as the tape vibrates and stretches.
Without a deep dive into how this energy loss varies, my best sense of it is that the reason that one ball bounces one, two balls bounce two, and so on is that energy conservation is absolute. The balance of energy between the two sides is such that it must also account for a balance of energy losses through the system. On closer examination, it is clear that, in fact, the pair of balls separate slightly, the balls at the bottom swing a bit, and all through the system there is a sum of small losses. The system as a whole finds that balance and markedly tends towards bouncing equal balls on both side unless forced to, in which case that imbalance is absorbed by variation in the internal heat generated.

[@johntrainor7851]

So on one level the tape makes the collision inelastic and kinetic energy is not conserved but if you look carefully it is the same as if the two taped together balls were just one ball with twice the mass. But I guess what I am getting at here is that mass is defined in terms of force and force in terms of mass which is circular. In ordinary experience it doesn't matter because we might define force as a push or a pull and we have a built in intuition about it. But if your going to base a science on such a circular definition you really aught to do better. To put it another way you might ask just what is energy? Because if the balls in the middle don't move and energy is defined in terms of motion then how on Earth is energy transferred from one ball to another without moving it? Just some food for thought.

[@magneticpropulsion2507]

There's a video on "The Action Lab" channel that says it's a shock wave that makes the number of balls that fly off equal to the number that impact the opposite end.

[@johnfitzgerald8879]

@@magneticpropulsion2507 Right. And that shockwave dissipates as it goes. The tape changes the nature of that shock wave as well.