GCSEC'S CONNELL'S COLLISIONS EXHIBIT

Version 1.0 Written November 1998

(This exhibit is based on the suggestion of Mr. Paul Connell, a retired high school teacher.)

This exhibit was fashioned from aluminum angle iron. Each track consists of one straight and two curved ends welded together. The curved ends are pieces (arcs) of a circle. To make the ends, a section of angle iron was bent into a complete circle and then the needed pieces were cut from it.

There are three different sets of balls, all having the same diameter. The metal ones are steel and are very heavy. There are two sets of plastic balls, one slightly darker in color than the other. They are made of delrin and nylon.

Newton's Cradle

The small metal frame between the tracks, with five suspended steel balls, is called Newton's Cradle. It demonstrates transfer of straight line or linear energy and momentum. Pull back one ball and let it go. Then try two or three. Notice that the same number always swing in each direction. Laws of nature require that both energy and momentum must be conserved. In order to satisfy both of these requirements the same number of balls must always leave the group.

(The steel balls in Newton's Cradle are suspended using fishing line, and they can slide sideways on the line. As necessary, adjust them so that the five balls are always in a straight line. If they are out of alignment they will all become hopelessly tangled.)

Potential and Kinetic Energy

Hold any one of the balls at the top of one of the curved ends. The ball is not moving - does it have any energy? When it is released the ball starts moving so it must have had some energy. When the ball was held at the top of the curve it had potential energy. Where did this energy come from? Your muscles provided the energy by lifting the ball against gravity. When the ball starts rolling down the track it is demonstrating kinetic energy or energy of motion. When only part way down the curve some of the ball's potential energy has been converted to kinetic energy but not all of it. Only when the ball reaches the bottom of the curve has all of the potential energy been converted to kinetic energy. And of course as the ball climbs the curve at the other end its kinetic energy is being converted back to potential energy.

Note that each time the ball climbs a curved end it does not rise as high as the time before. The ball is constantly losing energy to air resistance and friction from rolling along the track. This energy is not destroyed - it is warming the air and the track and producing sound. Eventually the ball will stop rolling - all of its previous energy has been given up.

Frame of Reference

The above paragraphs explain how a ball held at the top of the curve had potential energy, and that once the ball stopped rolling it had given up all of its potential energy. That makes sense, since usually we would be discussing the ball in relation to the track.

But what if we were living on the surface of the table. Even though the ball eventually comes to rest on the track, isn't it still elevated above our viewpoint on the surface of the table? Even though the ball is between the sides of the track and not moving, it still has potential energy in relation to the table top.

A more common example of frame of reference is a man riding in a car traveling 35 miles per hour. In relation to a person standing on the sidewalk, the man is moving at 35 miles per hour. In relation to a woman riding in another car traveling in the same direction at 30 miles per hour, the man is moving at 5 miles per hour. And in relation to a couple traveling in the other direction at 25 miles per hour, the man is traveling at fifty miles per hour.

Momentum

Take two balls of the same weight, and hold one at the top of each curved end. The two balls weight the same and are the same distance above the middle of the track, so they have the same potential energy. If they are both released, when the collide they have the same momentum but are traveling in opposite directions. The net result of the equal but opposite momentums is that they essentially stop upon colliding. What would you expect if two balls of equal weight are used, but one is at the top of the curved end and the other starts half way up the curve? What would you expect if you repeated the above with a new set of balls that are identical but weigh much more or much less than the first pair? How can you use this procedure to compare two balls that have very similar but slightly different weights?

Collisions

Place one plastic ball on the middle of the track. Release one of the steel balls from the top of the curve and observe the collision. See if you can predict what will happen if the situation is reversed.

Place a steel ball on the middle of the track. Again, release one of the plastic balls from the top of the curve and observe the collision. Look at this collision as if it were a car that hit a tree. How fast did the "car" come to a stop? Would this depend upon the frame of reference? From the point of view of the "tree" (the steel ball) the "car" was rolling down the track at a high rate of speed and then suddenly stopped.

Now remove the steel ball from the track. Hold a plastic ball at the top of each end and release them. Describe the speeds of the two "cars" just before and just after impact, from the point of view of someone standing alongside the track and from the point of view of each of the "cars". Using a bystander as the frame of reference, the two "cars" are each traveling at the same high rate of speed but in opposite directions just before impact, and both are stationary just after impact. From the point of view of the bystander the change in speed of each car was the same as above when the car hit the tree. But now use one of the drivers' frame of reference. From the point of view of the driver, he or she is stationary and the oncoming car is approaching at twice the speed.

Connell's Collisions Versus Newton's Cradle

When this exhibit was built it was expected to produce the same action as Newton's Cradle. Find four or five balls all of the same material. Hold one at the top of a curved end and place the others together on the middle of the track. Release the ball from the curved end and observe the collision. How does it differ from Newton's Cradle? You probably saw that one ball left from the other side, as in Newton's Cradle, but its speed was much less than the impacting ball. In addition, all of the remaining balls rolled forward slowly. Thus the result does not duplicate Newton's Cradle.

In Newton's Cradle, when a ball is drawn back it has potential energy. When released, all of that potential energy becomes kinetic energy that simply moves the ball from one location to another, called translational kinetic energy. That ball is simply moving through space. Now consider a ball at the top of a curved end of the track. It also has potential energy. When released, it starts rolling down the track. This ball is doing two different things at the same time - it is moving from one location to another (translational energy) at the same time that it is rotating about its center (rotational energy). When this ball collides with the stationary group its translational energy is transferred to the ball at the other end. It leaves the group by starting to roll, so that some of the translational energy of the impacting ball is used to start rotating the departing ball. Therefore the departing ball is not moving at the same speed as the impacting ball. In addition, all of the remaining balls are slowly rolling down the track. The rotational energy of the impacting ball is divided into translational and rotational energy for the remaining balls.

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