[paul.fr]

how does a Newtons cradle work?

[syhprum]

As no replies have yet arrived about the operation of this device which is quite complex I will make an attempt.
When the first ball is dropped onto the stack its kinetic energy is used to compress the next ball, as this ball releases this stored energy it is transfered to the next one and so on, when it reaches the last one it is reconverted to kinetic energy and accelerates the last ball causing it to to rise against gravity .
When it reaches its zenith its stored energy reconverts to kinetic and it comes back and strikes the penultimate ball and the wave of energy propergates back the way it came.
It travels back and forth until inherent losses converts it into heat.

[ukmicky]

Ok now to make it a bit more complex ,why if you drop two balls  are two balls released rather than one

[lyner]

I think the best approach is to look at the momentum.
When two equal masses collide, they 'exchange velocities'.  Momentum is conserved.
So, the falling (first) ball collides with the next (second) ball.
This ball moves off at the same speed and the first ball stays stationary.
The second ball strikes the third ball - which  moves of and leaves the second  ball l stationary. . . .  until the last ball, which moves off, leaving all the others stationary. When the ens ball returns to its rest position, the process is repeated.
If you put two coins on a slippery table top, you can show the effect. Flick one against the other and the one you flicked will  stop and the other will  move  off. Use a row of coins and only the end one will move off. (Coins need to be all the same). You can play for hours on a beer-soaked pub table; it makes a change from flicking beer mats.
This principle is used in some electrical switches, to ensure a clean 'make and break' of the contacts.

[syhprum]

I would like to see a version where the steel balls are replaced by compression springs so that the whole operation is slowed down.
I think the whole secret of operation is the storage of energy in the steel balls as they are compressed.
This modified version could be filmed in slow motion.
How about a version where the mass of the balls varies in an expotentional manner?
Ukmicky has quite defeated me !!!
I would like to build an electrical analog with the balls replaced by resonant LC circuits, but how to simulate the contacts between them?, or perhaps a computer simulation.
I think the two ball situation is the same as using a double mass first ball

[syhprum]

I think we must turn the idea on its head and regard the the chain of steel ball as the mechanical analog of an electrical delay line (a string of LC circuits).
When a pulse of electricity is injected into the delay line it flows down the the string of circuits until it reaches the end were it is normally adsorbed by a terminating resistor, if the resistor is absent (as in the mechanical analog)the pulse is reflected back whence it came.
Just as the string of balls could be replaced by a solid bar (a quasi infinite string) the string of LC circuits can be replaced by a co-axial cable to the same end. I think we should rename it to the Heavyside cradle in honour of the man who first gave us the electrical delay line.
The delay line analogy explains the question asked by Ukmicky "how do you explain what happens when you drop two balls".
When I inject an electrical pulse into my delay line the width of the pulse can be any value I choose (provided it does not exceed the transit time of the delay line) and when it reaches the un-terminated end it is reflected back in inverted form.
In the mechanical version the width of the pulse is quantised and can be generated by an integral number of balls but it behaves in the same manner when it reaches the end it is reflected back the same width in inverted form.
Although a delay line well simulates the wave of compression moving thru the string of steel ball that are in contact let us consider what happens when it reaches the end and the last ball (balls are) airborne this can be simulated by a last section of delay line where the values of inductance and capacitance are much higher giving a much slower speed of propagation.