Newton's cradle: Glue balls together

[greypilgrim]

Hi.

Assuming only one ball is pulled away and let go, it's fairly easy to show that momentum and/or energy conservation would be violated if this made two balls to bounce off on the other side (if the other ones remain still).

So what happens if we glue the last to balls together or replace them with one ball twice the mass?

 

[BvU]

The physics of Newtons cradle is a lot more complicated than this.

My guess is the ball you pull away and let go bounces back (in addition to the heavy one moving off).

Practice with a row of coins on a smooth table.

 

[greypilgrim]

I know that conservation of energy and momentum allow for more than one solution and you need to take into account the elasticity of the balls to find which solution is realized. So I wonder what happens if we forbid this solution, i.e. by glueing the last two balls together.

If the first ball has velocity v, conservation of energy and momentum are satisfied when the first ball bounces back with -1/3 v and the last two balls bounce off with 2/3 v. I guess this solution will be realized instead.