Simple Solution
The conservation of momentum (mass x velocity) and kinetic energy (0.5 x mass x velocity^2) can be used to find the resulting velocities for two colliding elastic balls. For three or more balls, the velocities can be calculated in the same way if the collisions are a sequence of separate collisions between pairs. In Newton's cradle, all the balls weigh the same, so the solution for a colliding pair is that the "moving" ball stops relative to the "stationary" one, and the stationary one picks up all the other's velocity (and therefore all the momentum and energy). If both are moving, one is picked to be the "stationary" frame of reference. This effect from two identical elastic colliding spheres is the basis of the cradle and gives an approximate solution to all its action without needing to use math to solve the momentum and energy equations. For example, when two balls separated by a very small distance are dropped and strike three stationary balls, the action is as follows: The first ball to strike (the second ball in the cradle) transfers its velocity to the third ball and stops. The third ball then transfers the velocity to the fourth ball and stops, and then the fourth to the fifth ball. Right behind this sequence is the first ball transferring its velocity to the second ball that had just been stopped, and the sequence repeats immediately and imperceptibly behind the first sequence, ejecting the fourth ball right behind the fifth ball with the same microscopic separation that was between the two initial striking balls. If the two initial balls had been microscopically welded together, the initial strike would be the same as one ball having twice the weight and this results in only the last ball moving away much faster than the others in both theory and practice, so the initial separation is important.
When the simple solution applies, the balls more efficiently transfer the velocity from one ball to the next, maintaining the effect. So the effects are more noticeable when the balls are not touching and therefore more closely follow independent collisions.
Read more about this topic: Newton's Cradle, Physics Explanation
Famous quotes containing the words simple and/or solution:
“Religion is the dream of the human mind. But even in dreams we do not find ourselves in emptiness or in heaven, but on earth, in the realm of reality; we only see real things in the entrancing splendor of imagination and caprice, instead of in the simple daylight of reality and necessity.”
—Ludwig Feuerbach (1804–1872)
“What is history? Its beginning is that of the centuries of systematic work devoted to the solution of the enigma of death, so that death itself may eventually be overcome. That is why people write symphonies, and why they discover mathematical infinity and electromagnetic waves.”
—Boris Pasternak (1890–1960)