Why do 2 balls bounce in a Newton's Cradle instead of just one?

[Yuc4h]

Hello everyone

There is this device called Newton's Cradle

http://www.heurekashop.fi/files/magneetti/productpics/496picture2Upload.jpg

You lift one ball and let it impact with other balls, the impact is followed by other ball bouncing from the other side.

However, when you lift 2 balls, the impact is followed by 2 other balls bouncing. Why is that? I would initially guess that only one ball bounces, the answer can not be very simple since I actually asked a professor of physics about this and he didn't really know the answer.

 

[TVP45]

The simple answer is that this involves elastic collisions where no deformation occurs. Both kinetic energy and momentum are conserved. When you satisfy both conditions, you get 1 ball = 1 ball, 2 balls = 2 balls, etc as the only possible solution.

 

[Yuc4h]

But also 2 balls = 1 ball would satisfy the conditions if the ball would get twice the momentum and it also would make more sense.

 

[Doc Al]

But also 2 balls = 1 ball would satisfy the conditions if the ball would get twice the momentum and it also would make more sense.

How would that conserve energy? And why would it make more sense?

 

[TVP45]

Both conditions have to be satisfied. If you have 2 balls, each of mass m, moving with velocity v before the collision, the combined momentum is 2mv and the combined kinetic energy is mv^2. After the collision, these must still be true.
If you had only one ball leaving, its momentum would have to be 2 mv. Since its mass is m, its velocity must be 2v. However, that would make the kinetic energy 2mv^2. So, this cannot be a solution.
This is a standard problem in Physics. The solution is well known and accepted. Thousands (millions?) of students have played with Newton's cradles and tried to get a different result. All have failed.
If this solution were not true, it would be impossible to play the game of pool (billiards) as we know it.