In order to be able to make concrete predictions from the physical concepts we are studying we often simplify or idealize the objects and situations being discussed. At first this may seem to imply that the physics you are learning is not applicable to real objects. Luckily this is not true. It is often possible to represent the behavior of complex real objects in one of two ways.

The first is used when the behavior of the object is almost, but not quite, like the idealized stuff from class. In this case, the behavior of the object is modeled (described) as the ideal behavior with one or more small correction factors added in. For instance, the frictional force ideally depends only on the normal, or squeezing, force between the objects. In the case of car tires this is not really correct. Wider tires do generate more frictional force all other things being equal. We could model this real frictional force as ideal physics friction with an additional force (correction factor) that depends on the tire width. We could determine the additional factor by making measurements of the frictional forces generated by a number of tires of differing widths. It might be even more complicated if the actual frictional force also depends on the tire load. This would require another correction factor.

At other times the real object has different types of behavior at different points in the process. Under these circumstances we can say that the object behaves like one idealized object for a while and then, at a identifiable point, changes and acts like a different ideal object. This is a useful technique as long as the transition point between the two types of behavior can be clearly identified. A situation like this that you are familiar with is fluid flow. When water flows through a ditch or pipe below a certain speed it flows smoothly and its velocity is easily predicted. Once the velocity of the water is increased beyond a specific point the flow becomes turbulent and the velocity of the water at a given point becomes difficult to predict. These two types of behavior well understood and are known as laminar and turbulent flow. The transition between them is identified with a flow characteristic called the Reynolds number.

Using these approaches to analyze the behavior of complex system can also help improve our understanding of the system. If the second approach seems more successful then it indicates that there are at least two distinct behavior patterns. We can then look for the causes of the change in behavior. If the first approach is found to be more effective then it suggests that there is only one underlying process at work.

In this lab you will be looking at surgical tube as a real spring which doesn't behave like those ideal springs we talked about in class. However, if you watch it carefully you will see that it goes through two different types of behavior. Each of these stages can be reasonably modeled as an ideal physics spring. This tends to suggest that there are two distinct processes taking place. On the other hand you could model the bungee cords as a single ideal spring with a correction factor based on its length. This second approach would require a greater level of mathematical sophistication to implement. Either approach will work although each has its pros and cons.

You will also be introduced to the idea of normalization of data. This is a general and very valuable data analysis technique which seeks to minimize or eliminate the effect of a single variable in a set of data. In this particular case you will be working with a number of "springs" which are identical except for their length. If we divide our data by the length of the spring in each case we may discover that we can see similarities in the data that might not otherwise be apparent. You do this unconsciously in other parts of your life. When someone says to you that a $2000 bike is a trivial expenditure you may very well divide that $2000 by the speaker's gross annual income and compare it to the same $2000 divided by your gross annual income. These two numbers are likely to make it clear why it seems cheap to that someone but not to you. What you have done is normalize out the effect of your differing incomes to be able to understand the situation more clearly.

The purpose behind all this manipulation of reality is to discover that while we do tend to oversimplify the world in physics the basic ideas are still valid. With more sophisticated math skills we can then modify and adapted these conceptually clear ideas to describe very complex phenomena.