## INTRODUCTION

One of the important processes that students and scientists alike engage in is the search for PATTERNS. In Biology, the patterns may be found in such things as symmetry, evolution, genetic coding, etc. In Chemistry, the patterns may lie in similar colors, physical properties or chemical properties.

In Physics, the search is again for patterns, but due to the nature of our subject matter, these patterns are often mathematical relationships between quantities. Some examples include time, speed and distance; mass and weight; force, mass and acceleration; voltage, current and resistance.

These pages are designed to help you to learn various ways in which physicists analyze data to determine the basic mathematical pattern that relates two seemingly different phenomena. Throughout you will find self-check questions. Try these to see if you've cemented down the key ideas.

Most important, though, is the idea that you'll be using these concepts all year in this class, and hopefully a long time into your future. There is a tremendous power wrapped up in these web pages. They will remain on the server and be accessible throughout your year of study in Physics.

There are four basic relationships investigated in this stack. Each has its own pattern, but you will learn to use one or more schemes to unravel which one you have at any given time.

We will use two types of variables and will investigate the relationship between them. The quantity that is controlled by the scientist will be defined as the CONTROL VARIABLE. The quantity that changes as a result of the control variable is called the DEPENDENT VARIABLE.

### Control Variable

In doing an experiment, we deliberately take control of one aspect of a situation or another. Thus we exert CONTROL over what happens.

If you wish to experiment with changing a recipe for a cake, you might make two cakes with more or less sugar. You are controlling the amount of sugar and then judging the end result.

In a Physics experiment we might control the amount of force acting on a car, and then measure the affect that different forces have on the car. In this case, the CONTROL is Force.

### Dependent Variable

In doing an experiment, we control one aspect of a situation while another factor changes depending upon how we change things.

If you wish to experiment with changing a recipe, say for a cake, you might make two cakes with more or less sugar. You control the amount of sugar and then the end result depends upon the amount of sugar you have added.

In a Physics experiment we change the amount of force acting on a car, and then measure its acceleration. In this case, the Acceleration DEPENDS upon the amount of force and is the DEPENDENT variable.

 All data tables will be presented with the first column as the control variable and the next column as the dependent variable. All graphs will be plotted as the dependent variable versus the control variable. [The first variable stated is the vertical axis as shown here.] All ratios will be such that the dependent variable is over the control variable. [Dependent divided by Control.] . Finally, all mathematical operations on a variable will be done on the control variable.
Now we're ready to begin exploring Mathematical Relationships !