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Newton's Cradle
Conservation of Energy and Momentum


Video introduction:


CONTENTS (text and audio versions)
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Some Technical Details For The Scientifically Inclined:



What's Going On

Conservation laws are very helpful tools in understanding how the world works. In this exhibit conservation of energy and conservation of momentum are both involved. When something is conserved, it means that the overall value does not change over time. Energy is a measure of the ability to do work and can change between different forms such as kinetic, thermal, chemical, nuclear, acoustic, radiant and gravitational. The overall energy is precisely conserved. Momentum is a measure of mass in motion and has a direction. Unlike energy, momentum does not have other forms. The overall momentum is precisely conserved. This exhibit is similar to a pendulum except that there is a collision in the middle of the swing. It is made from hardened steel balls which have very elastic collisions. This means that the kinetic energy (or energy of motion) of the outgoing balls is only slightly less than that of the incoming balls. A small amount is converted to heat (or thermal energy). The balls also have momentum and this is transferred from the incoming to the outgoing balls. These two conservation laws impose somewhat different restrictions on the possible outcomes of the collision and are the main reason for the behavior observed, namely that the outgoing balls match the incoming balls in number and velocity.


So What

Energy is the reason you need to eat food. Food contains chemical energy that your body can convert to thermal energy to keep warm and also to kinetic energy to move about and do work. Energy is why it's harder to bike uphill. Going uphill increases your gravitational energy and your body must supply this energy by doing work. Energy is why power plants require an energy source. Some inventors have wasted years of their lives trying to invent "perpetual motion machines" that could produce work without any energy source. They have all failed since such a machine would violate conservation of energy.

Momentum is the reason you need to wear a seatbelt in the car. If the car stops suddenly, your momentum must be reduced either by a sustained force from the seatbelt or from colliding with the windshield. Momentum is why a hammer can drive a nail into a piece of wood. When the hammer hits the nail, the hammer's momentum is reduced to zero by a very intense force over a very short time is it drives the nail further into the wood. In a head on collision between two cars, the combined momentum may actually be zero because they are moving in opposite directions and the individual momentums cancel each other out. Thus after the collision, both cars are at rest. In a rocket ship, any increase in forward momentum must equal the backward momentum of the rocket exhaust. If the fuel runs out, the ship can neither speed up nor slow down.


About Newton

Sir Isaac Newton was born in the year 1642, the same year that Galileo died. He discovered the laws of motion that determine the behavior of this exhibit and many other things. He discovered the law of gravitation which indicates that gravity exists not just between you and the earth but between all objects including between the earth and the sun. Combining gravity with the laws of motion he was able to explain why the earth revolves around the sun and why the moon revolves around the earth. Newton was one of the most important scientists of all time. Newton's laws of motion apply to many engineering problems. They apply to anything that has moving parts (including fluids). They can explain sound waves through air and the vibrations of a guitar string. Newton and Leibniz are both credited with discovering calculus, a very important mathematical tool used in most branches of science and engineering. Newton also discovered that white light from the sun is made up of all the colors of the rainbow mixed together. He did not however invent Newton's cradle. Simon Prebble, an English actor, came up with it in 1967.


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.



Exhibit Version:

What's Going On

Conservation laws help us understand how the world works. In this exhibit, the energy and momentum of the incoming balls is transferred to the outgoing balls. Because the balls are very hard, little of the energy of motion is converted into heat energy. Conservation means that the overall value does not change over time.


So What

Energy is a measure of the ability to do work. Momentum is a measure of mass in motion and has a direction. Both are precisely conserved. Momentum is the reason you wear a seatbelt in the car. Newton discovered the laws of motion that apply here and to many other things like the motion of our planet around the sun.