Introduction / Theory Physics concerns itself with finding functional relationships between physical variable;. In class, each student will study some of the more important relationships that have been found to exist. In the lab, the student will perform experiments in order to confirm these relationships, and graphing is the tool that will be used. A detailed explanation of the theory behind this method is contained in the. Lab Manual3 which can bgu found on the Blackboard. Reference this material before coming in and domg the experiment, as 1t wi help in completing the pre-lab. Additionally, looking at proper graph form will also help. The equation relating the circumference C and diameter d of a circle is 1) C=mnd ( where Tt is a dimensionless constant. From this equation, it can be seen that the functional relationship 1S Coxcd _ : and a plot of C vs. d produces a straight line through the origin with theoretical slope. There is no need to change the format of the equation, e.g. change it to @ = , because there is no clearly defined independent variable in the experiment. The equation relating the distance x an object moves and the time t it takes is 1= X=at 2) ( where a is the (constant) rate of acceleration. Here, assume that the object starts at the origin (X, = 0) with no initial velocity (v, = 0). From this equation, it can be seen that the functional relationship is 2 xoct e s 1 S and a plot of x vs. t* produces a straight line through the origin with theoretical slope Ea . However, it 1s better to rewrite equation 2, since x is the inde pendent variable in the experiment. Therefore, equation 2 becomes equation 3, below. =2 a From this new form, it can be seen that f2ocx ,50 a plot of t* vs. x produces a straight line through the origin with theoretical slope % : Recommended Reading from the Lab Manual posted on Blackboard: * How-To: Graphs Using Excel Graphing: Proper Form Graphing: Sample Graph Graphing: Linear Regression Data Analysis: Percent Error Functional Relationships: Theory Functional Relationships: Examples