Newton's Cradle: Explaining 2-Ball vs. 1-Ball Dynamics

[foyer]

when one ball is pulled out, released, and collides with the other four in Newton's Cradle, one ball will pop out the other side. Likewise, when two balls are pulled back, two balls will pop out the other side. Why doesn't one ball pop out, but with twice the speed?

You are to use the concepts of conservation of momentum and conservation of energy to mathematically show that only two balls may be ejected on the other side when two balls are pulled back instead of one ball with twice the speed.i know that both momentum and energy are both conserved because the collisons are elastic, but i just get stuck there

P initial=P finalany help would be appreciated

 

[Doc Al]

Compare the energy of two balls with speed v to the energy of one ball with speed 2v. Are they the same?