Newton's Cradle Demonstration

If you've taken a high school physics class, then the odds are pretty good that you've seen one of these gizmos commonly called a "Newton's Cradle", which demonstrates the interaction of kinetic energy and momentum. Essentially the device consists of a small wooden frame with five pinball machine balls suspended from fishing line. As one ball is lifted and then released, it strikes the remaining four balls and causes the energy to be transferred to each successive ball ultimately causing the ball on the other end to fly off.

Take a look at the video below as a demonstration. You are looking at the motion at 1/10th speed or 300 frames per second.

So, what's going on here???

Well, the kinetic energy of the falling ball strikes the first stationary ball of equal mass. Being held in place by the inertia of the other balls, the second stationary ball transfers its energy (and momentum) to the next ball. On down-the-line this goes until the transferred momentum is equal to (or less than) the remaining mass in front of the ball, at which point the energy produces motion (i.e., the end ball, with the same mass as the first ball moves upward with the same amount of energy imparted by the first ball earlier on).

Well sort of... In a perfect world absent of pesky little things like friction and heat, the transfer of energy would be complete (i.e., momentum would be conserved) and we would expect that the first ball would strike with a certain amount of momentum, all intermediary balls would remain motionless, and the last ball would fly off the end up to a height equal to the starting height of the first ball (i.e., conservation of kinetic energy). This is not the case, and even though at a real time speed the process looks pretty good, we can see that when we effectively slow time down by a factor of 10, there is a bit of wobble in the intermediate balls caused by their masses not being exactly equal, frictional losses in the connection points, and the inevitable 'clack' sound as they hit each other converting energy into sound which heats the air. Alas, the motion of our system will decay (and become more chaotic) right in front of your eyes.

So, if the momentum of our system in the above example is, say '1x', what will happen if we drop two balls so that our starting momentum is '2x'? Take a look below.