Explaining Newton's Cradle: The Science Behind the Single Ball Effect

[FulhamFan3]

Everyone here should be familiar with the office toy known as Newton's Cradle where a ball collides with a group of balls and a ball moves out the other side.

What I want to know is when a ball collides with the group why does only one ball come out? Why doesn't two balls come out at half the speed? I mean momentum is conserved in both situations.

 

[krab]

It's because the collision is elastic. So energy has to be conserved as well. The math is really easy for balls of equal mass in 1D.

 

[FulhamFan3]

yeah, I've been thinking about it for days but it's not until i type it in and send it that i realized this. Don't you hate it when that happens.

 

[physfreak]

wait. i have a similar problem. in physics today, we asked the question, "if a person takes 2 balls and pulls back, and releases, why doesn't a single ball on the other side pop out with twice the speed?"
please help!

 

[Vanadium 50]

The answer is the same as it was when this was asked 5 years ago. Please read the above posting.

 

[physfreak]

well how would one solve this problem mathematically?

 

[Vanadium 50]

Read post #2.

 

[rcgldr]

Turns out that there are multiple solutions where both momentum and energy are conserved.

Links to videos and explanations in this thread:

https://www.physicsforums.com/showthread.php?t=357358

 

[Prologue]

Yeah, the real explanation doesn't have anything to do with the conservation of anything for the system, of course those are followed but that isn't why it happens. It happens because one ball whacks another and stops because they have equal mass (just like a billiard ball), then the newly moving ball moves just a tiny bit and whacks the other one, then again, and again. Each ball that did the whacking is stopped because they have equal mass, or it transfers all of it's momentum and energy (just like a billiard ball). If you bring up two balls and let em go then two pop out, then ask, why does that happen? It is because of the same reason, the first ball whacks the other stationary ball, then the second moving ball whacks the newly stationary ball, blah blah, it is as if you dropped them separately, but only a tiny fraction of time apart. This needs a picture but I am too lazy to do it, but think about it.

The reason that the falling ball behaves as if it only hit one ball is because in the real world there is a slight compression of the balls on impact, so there is a delay between when the first stationary ball moves, and the next stationary ball etc.