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Some Technical Details for the Scientifically Inclined

The Collision

The balls in this exhibit are hardened steel ball bearings 3.75 inches in diameter. They are too hard to drill holes into them by conventional means. They weigh about eight pounds apiece. If only two balls were involved instead of five, the analysis of this exhibit would be relatively simple. Treating kinetic energy as a conserved quantity and combining this with conservation of momentum determines the outcome precisely: the incoming ball stops completely and gives its velocity entirely to the outgoing ball. If both balls are moving before the collision and they are approaching one another, then they exchange velocities in the collision. If you know the formulas for kinetic energy and for momentum this is a simple physics exercise. But for five balls the problem is more complicated. The simplest way to understand the observations is as a series of two ball collisions: Imagine that the balls hang very close together but do not actually touch. The incoming 1st ball collides with the 2nd ball and transfers all of its velocity to that ball. This 2nd ball only moves a tiny fraction of an inch before it hits the 3rd ball and transfers all of its velocity to that ball. This repeats again with the 3rd ball hitting the 4th ball and the 4th ball hitting the 5th ball which flies away as was observed. But why does this still happen if all the balls are touching at the moment of impact? There is no simple answer. It has to do with the dynamics that occur within a ball when it is struck by another ball. One approach has been to analyze the ball as an extremely stiff nonlinear spring that compresses very slightly when impacted by another ball. This analysis does lead to some small variations from the simple picture - the balls that appear approximately motionless after the collision actually do move very slightly. In this exhibit it may be hard to tell if the balls are actually touching at the moment of impact or not.


The Pendulum

The pendulum-like motion of the balls enables the collision to repeat. Energy is initially transferred to one or more of the balls in the form of gravitational energy when they are pulled back by the claw arm. This is converted to kinetic energy as they move downwards towards the collision site. Gravity pulling downwards on a ball also gives it downward momentum. Force from the cable, which is perpendicular to the direction of the ball's motion, effectively rotates the momentum from downwards to horizontal but has no effect on the kinetic energy. Note that because the exhibit is attached to the earth, momentum is being transferred back and forth between the balls and the earth itself. Because the earth is extremely massive, it can easily absorb momentum from the exhibit with no measurable change in its own velocity. This transfer of momentum occurs during the overall pendulum swing, and does not affect the impact itself which is essentially instantaneous. The energy however remains essentially confined to the balls after they are released by the claw arm. The gradual slowing down of the motion as the balls swing back and forth is mainly caused by the conversion of kinetic energy to thermal energy and the balls will actually heat up very slightly. A small amount escapes as sound waves (acoustic energy).


Angular Momentum

There is another conservation law which has many important applications but doesn't play much of a role here. This is conservation of angular momentum, which is a measure of mass in rotational motion. The balls in the exhibit acquire a small amount of angular momentum because they follow a curved path as they swing back and forth. This further complicates the collision since this is also transferred from the incoming balls to the outgoing balls. But it has little observable effects. The earth has an enormous amount of angular momentum because it rotates on it's axis. Inventors who didn't consider the conservation of angular momentum have actually tried to find ways to extract energy from the rotation of the earth. This would seem to give access to a truly vast amount of energy without violating conservation of energy. What they didn't realize was that extracting rotational energy from the earth would slow it down which in turn would reduce its angular momentum in violation the conservation of angular momentum.