How do they know? …

I doubt that Newton invented this toy. It seems more like the work of Galileo. But then so much of the western world's discoveries were conscripted from what the Moslems were teaching for centuries.

And it's not as if it were all that secret before them.

What I was wondering… no. Let's have a look at the sketches first:

http://commons.wikimedia.org/wiki/Newton%27s_cradle

Now then, what I was wondering is how the dropping of two balls onto three sends the two balls on the other side out on the swing.

Why not 1 ball twice as far? (Or whatever the equivalent distance is to the mass in the force equation?) Or three balls 2/3rds of the distance?

Here's what I found on it:

Originally posted by Donald Simanek:

The apparatus usually consists of an odd number of identical steel balls suspended from a frame. The balls are carefully aligned along a horizontal line, just touching.

When a ball is lifted and released it hits the next ball. One ball on the other side is knocked away with the same speed as the first ball and all of the other balls remain nearly at rest.

If you pull back two balls and let them strike the others, two balls are knocked from the other end, and all the other balls remain nearly at rest.

Why has this become a standard demonstration that momentum is conserved in collisions? The outcome certainly does illustrate that, but so does every other mechanical interaction you might care to consider.

This particular apparatus, cleverly designed to be nearly elastic, is a special case, and the full generality of conservation of momentum is not demonstrated by it. Some books say that this demo shows that both energy and momentum are conserved in a collision. That's closer to the mark.

"How do the balls "know" that if you have N balls initially moving, that exactly N balls should swing out from the other end?"

Consider three balls:

Balls 2 and 3 are stationary.

Ball 1 hits ball 2 with speed V.

Ball 3 moves away with speed V leaving balls 1 and 2 stationary.

Momentum and energy are both conserved.Why are other results impossible? Consider the hypothetical outcome: Ball 2 and 3 move off with speed V/2, leaving ball 1 stationary. This conserves momentum, but not kinetic energy.

More on here:

http://www.lhup.edu/~dsimanek/scenario/cradle.htm

This has good explanations but the author uses the term "compression". As steel balls, the idea of them compressing when immediate free flow is the apparent option just doesn't sink in. Maybe there is a problem with my grey matter but there must be a simpler explanation.