Sunday 29 November 2015

Newton's Cradle

Newton's cradle is a popular 'executive toy' that demonstrates conservation of momentum/energy. The steel (usually) balls that it is made with are quite elastic and do not lose much of the kinetic energy of the balls when they hit each other.



(For various things you can do with Newton's cradle, see this link and play the video. It also notes why Mythbusters' large-sized example didn't work as planned.)

When you pull back one steel ball and release it, it hits the other four and the last ball moves off with (almost) the same speed as the first one that hit the four. And interestingly, if you pull back two of the balls and release them, when those two hit the remaining three balls it is almost as if they 'know' that you pulled back two balls, since now the last two balls move off.

But how could it 'know' that you pulled back two balls? Of course, you can go through the equations (fairly straightforward) but the explanation at wikipedia is pretty good for a simplified situation:

"...when two balls are dropped to strike three stationary balls in a cradle, there is an unnoticed but crucial small distance between the two dropped balls and the action is as follows: The first moving ball that strikes the first stationary ball (the 2nd ball striking the 3rd ball) transfers all its velocity to the 3rd ball and stops. The 3rd ball then transfers the velocity to the 4th ball and stops, and then the 4th to the 5th ball. Right behind this sequence is the 1st ball transferring its velocity to the 2nd ball that had just been stopped, and the sequence repeats immediately and imperceptibly behind the first sequence, ejecting the 4th ball right behind the 5th ball with the same small separation that was between the two initial striking balls."

Seems like you only need a few micrometers separation for this to be true, so I'll have to look at that first photo a bit more closely!