The physics behind newtons cradle balance balls
Newtons cradle balance balls demonstrates the laws of conservation of energy and momentum.
The Law of Conservation of Energy states: "Although energy can be converted from one form to another, it can neither be created nor destroyed". On the other hand, the law of conservation of momentum asserts that the momentum of an isolated system is conserved/constant, i.e., when two bodies collide, the momentum before and after the collision remains the same.
Going back to Newton's pendulum, at rest, the balls have zero potential energy because they can't move further down (potential energy = mgh, h = 0 at rest), and zero kinetic energy because they don't move (motion) energy = 1/2 mv ^2, v = 0 at rest). Also, the ball has no momentum (momentum = mv, v = 0 at rest).
However, when the first ball is lifted and left, it gains gravitational potential energy as it increases in height, while the kinetic energy remains the same, zero. After release, the potential energy is converted into kinetic energy as the height of the sphere decreases. All potential energy is converted to kinetic energy at the bottom position. Also, the ball gains momentum as it swings down, and gets the most momentum in the bottom position.
On impact with the next ball, the first ball loses all kinetic energy (and therefore, all momentum) and goes to a dead end. However, energy and momentum are not lost, so it must be transferred to the ball it hits. The force exerted by the first ball upon impact causes the second ball to deform slightly in compression. Compression is a symbol of the transfer of energy in the form of potential energy. When the second ball tries to keep its original shape, the potential energy is converted into kinetic energy and passed to the next ball at the same time. The subsequent compression-decompression chain and thus energy transfer continues to the last sphere.
The last sphere after decompression cannot find subsequent spheres to compress and transfer energy to it. Since transferring energy is not a viable option, the final ball pushes the penultimate ball back and out. Every action has an equal and opposite reaction, right?
Since no energy is lost during the transfer, the final ball shoots out at the same speed as the first ball is falling, thus showing momentum is preserved!
Likewise, the last ball of newtons cradle balance balls rises to a level equal to the height of the first fall, indicating that all energy is also preserved!