[SaxonViolence]

We've all seen Newton's Cradles.

Pull one Ball back, and let it go.

It goes 1-Right, 1-Left; 1-Right, 1-Left.....And so on.

Nothing strange yet.

Take two Balls at one time.

It Goes 2-R, 2-L; 2-R, 2-L.....And so on.

Once again, nothing surprising.

Pull back three Balls at one time.

It goes 3-R, 2-L; 3-R, 2-L; 3-R, 2-L.....

How does the Cradle "Know" or "Remember" when two Balls strike it from the Left, that those two Balls were launched by three Balls?

Why doesn't it go:

3-R, 2-L; 2-R, 2-L; 2-R, 2-L ?

It isn't a matter of force. You can contrive to give two Balls twice or three times their traditional momentum.....

And they still won't kick out three Balls?

It does not work:

2>>R, 3-L; 2-R, 3-L.....

Or any other permutation that you can imagine.

.....Saxon Violence

[phillip1882]

i'm pretty sure on a neuwton cradle if you pull back 3 balls, 3 balls will come out on the other side; ie. 3-R 3-L 3-R 3-L.
if you don't get this; could you post a youtube video of your cradle giving a different result? cause that basically violates the laws of physics.
(momentum in = momentum out)

[SaxonViolence]

Here is a "U" Tube Video:



Most Cradles that I have seen, are much "Deader"--withou nearly so much "Slippage".

Most sets only have Five Balls--so 3-3 would kinda be impossible.


Saxon Violence

[CraigD]

Hi Saxon – welcome to hypography, and thanks for the video, and a physics question I can actually answer!

SaxonViolence, on 10 January 2012 - 11:05 AM, said:

We've all seen Newton's Cradles.
...
Pull back three Balls at one time.

It goes 3-R, 2-L; 3-R, 2-L; 3-R, 2-L.....

No, as Phillip though, and the video shows, it goes 3R, 3L, 3R, 3L ...

or, to ASCII art draw it perhaps more clearly, it goes

OOO-> OO / OO OOO-> / OO <-OOO / <-OOO OO / OOO-> OO / ...

The physics of this cool old desk toy is pretty simple. Because the system is fairly elastic – not much of its kinetic energy is converted into sound, heat, etc. – it must satisfy the 2 equations for conservation of momentum and conservation of energy:



and



Where is a ball i’s mass, it’s velocity, and its speed (the scalar component of its velocity), and P and E constant.

I’ll leave it as an exercise to the reader to prove that only one possible “permutation” is possible for a Newton’s cradle with equal mass balls and no tricky stuff to sick them together, etc. It’s not a hard proof/derivation, and one you need to do whenever you write any sort of physics-based motion simulator with elastic collisions, such as my old “Newtonian bowling” sim, where you can see the solution written in an actual program.

[maddog]

I will add my two cents on this subject as I had such a toy when I was a child.

It behaved exactly as CraigD described in the previous post.

I did in essence your experiment.

When I let go 1 ball, 1 ball came out other side.

When I let go 2 balls together, 2 balls came out other side

When I let go 3 ball together, 3 balls came out other side

When I let go 4 balls together, 4 balls came out other side.

This was the demonstration of the Conservation Laws as CraigD described.

Nothing Magical at all....

maddog