Newton's cradle
Why does only one ball fly out?
The question
Drop one ball on a Newton's cradle and one flies out the other end. Why not two balls, at half the speed?
Have a guess, then show the answer
Two at half speed would keep the push (momentum) but carry only half the energy. Only one ball at full speed keeps both.
Play
Try to break the rules
Pick how many balls you pull back, then try making a different number fly out. Watch the two bars.
Both kept. 1 in, 1 out: this is what really happens.
What's happening
- 1
When the balls collide, two things are kept. Momentum, the "push" (mass times speed), and the energy of motion, which grows with speed squared.
- 2
One ball comes in at speed v. Two balls leaving at half that speed have the same momentum, so the first rule allows it.
- 3
But they carry only half the energy, because halving the speed quarters each ball's energy. Energy can't just vanish, so it can't happen.
- 4
One ball at full speed keeps both. Pull two back and two fly out, for the same reason.
- 5
Real steel isn't perfect. Every click loses a little energy as heat, sound and air drag. Later, all five balls end up swinging together with about a fifth of the energy.
The maths
For n balls leaving at speed u after one ball hits at speed v, both rules must hold:
The first rule says u = v ÷ n. Put that into the second and it only works when n = 1.
Simplified, and sources
Real steel balls are nearly, but not perfectly, bouncy, and the line of balls shuffles a little on every hit, so the middle balls aren't perfectly still. The interactive shows the ideal, perfectly bouncy case.