# Science Questions

## How does a Newton’s Cradle work?

Sun, 14th Sep 2008

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### Question

How does a Newton’s Cradle work? In school I was taught that the mass X velocity = mass X velocity. In other words, one ball in means one ball out. The teacher pulled back two balls and let go. The two balls at the other end of the contraption went up about the same distance as the first two balls. Why didn’t just one ball fly off at twice the speed?

Dave -  Newton’s cradle is a whole series of collisions.  You’re taking a really bouncy metal ball, it’s very hard steel ball and bouncing it into a row of them from one end and crashing into it.  In this kind of collision there’s two things which are conserved, which have the same amount at the end that you had at the beginning.  One is energy that you were talking about before.  That’s ˝ x mass x (velocity) squared.  The other one’s something called momentum which is your mass X velocity. You've got one ball dropping into it with a mass and a velocity you will have the same mass and velocity by having one ball coming out with the same energy and the same momentum.  With two balls with the same amount of energy then they’d actually be moving less than half the speed.  So they’d have less than the same amount of momentum you’d put in.  The only solution is to have the same amount of balls coming out as went in.

Chris -  Is it not also that there’s a little tiny delay between one ball hitting and the next ball hitting?  The same when you get two separate collisions throwing off two separate balls.  When you go two balls in you get two balls out because it spits one ball and then the next ball out.

Dave - That would be another way of looking at it.  Physics can be looked at in different ways.

#### Make a comment

Brian asked the Naked Scientists: In high school I was taught that mass times velocity equals mass times velocity. The teacher showed an example by showing us a device with 5 balls hanging from strings in a row. The teacher pulled back 2 balls and let go. The 2 balls at the other end of the contraption went up about the same distance the the first 2 balls. So why didn't one ball fly off at twice the speed? What physics law explains why 2 balls flew up. The equation mv=mv would still work if only one ball flew up at twice the speed. Hope you understand what I mean. thanks What do you think? Brian, Sat, 19th Jul 2008

If you had  started off with all the balls separated by a bit, you could analyse each collision in turn. When identical (ideal) balls strike each other, they 'exchange velocities'  (mv=mv and using a coefficient of restitution of 1 implies their relative speed of parting is the same as the relative speed of approach) so, if balls 1 and 2 are moving, the first collision would be between balls 2 and 3. 3 would go off at the original speed of 2, leaving 2 stationary. Then 1 would strike 2 and 3 would strike 4, leaving 1 and 3 stationary with 2 and 4 moving. This would carry on to the end until, first ball n would leave, then ball n-1 - no ball ever goes faster than the original velocity.
The same thing will happen if the balls are touching, to start with. lyner, Sat, 19th Jul 2008

Brian,
A rather dashing young chap asked two similar questions
http://www.thenakedscientists.com/forum/index.php?topic=11548.0
http://www.thenakedscientists.com/forum/index.php?topic=8225.0 paul.fr, Sat, 19th Jul 2008