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The physics of newtons cradle balance balls
Newtons cradle balance balls was first proposed in 1676 by the French physicist Edme Mariotte. When swinging the rightmost ball and colliding with four other balls in close proximity on the swing back, the leftmost ball will be ejected, and only the leftmost ball will be ejected. Newton's pendulum can be approximated as a perfectly elastic collision!
Perfectly elastic collision: In the ideal case, the physical process of a perfectly elastic collision satisfies the conservation of momentum and energy. If the masses of the two colliding balls are equal, the equations of conservation of momentum and conservation of energy can be solved simultaneously: the two balls exchange velocities after collision. If the collided ball was originally stationary, after the collision, the ball has the same speed as the colliding ball, and the colliding ball stops.
A similar analysis can be done when multiple balls collide. In fact, because the collision between the balls is not an ideal elastic collision, and there will be energy loss, the balls still have to stop in the end. This is also the core physical principle of newtons cradle balance balls!