1. The problem statement, all variables and given/known data
If one ball of a newtons cradle is released at any velocity, why can't two balls on the other side be moved with half of the velocity of that ball.

2. Relevant equations
Law of consrvation of Energy and Low of conservation of Momentum

3. The attempt at a solution
Don't know where to start.
 Mentor Well, suppose this does happen and set up equations of conservation of kinetic energy and conservation of momentum. We have the situation in which one ball moves with velocity v before the collision, with two at rest, then two balls move with velocity v/2 after the collision, with the first at rest. Try setting up the equations.
 Show how it violates Conservation of Energy

 Blog Entries: 1 Recognitions: Gold Member Science Advisor Staff Emeritus Taking the expression for kinetic energy, note we are ignoring gravitational potential energy here since we are considering the velocity of the balls just after and before collision; $$\underbrace{\frac{1}{2}mv^2}_{\text{First Ball}} = \underbrace{\frac{1}{2}mv'^2}_{\text{Second Ball}}+\underbrace{\frac{1}{2}mv'^2}_{\text{Third BallBall}}$$ Now, all you need to do is plug in the value for $v'$, which is the velocity of the second two balls, and check the equality.