In physics classes, even at the university level, students spend a large amount of time making graphs and deriving equations for lines. Not that this isn't important, but once students know how to perform such tasks it's a waste of time to make him or her keep at it when computers can do the task more rapidly and accurately.
Physics students, especially physics education students, should be able to readily recognize a number of graphs that typically appear in introductory physics teaching. Click here to examine a PDF resource that will help you to become able to do so. You'll want to use your "Back" key on your Web browser to return to this page.
Vernier Software of Portland, Oregon, has recognized the futility of requiring students to manually analyze data in the computer age. David Vernier has created an application called "Graphical Analysis" which allows lab students to learn physics without having to wade through all the time-consuming mathematics associated with graphing.
1. Following your initial introduction to the Graphical Analysis 3.0 application by your instructor, you might read pages 1 - 18 of the user's manual.
2. The application "Graphical Analysis" is already stored on the Mac computers' hard drives in Moulton 307-B. Start up the application and familiarize your self with its basic operation, using the teacher's manual as necessary.
3. Turn to the "Sample Data Files" section (page 25) of the Graphical Analysis teacher's guide. Introduce yourself to the various capabilities of Graphical Analysis by working through some of the more interesting data sets. Practice regression routines, linearization techniques, and curve-fitting techniques. Once you have become familiar with the program, continue on to the following three introductory lab exercises.
4. Measure the circumferences and diameters of a set of aluminum disks provided you by the instructor. Create a data set using all disks provided. Input this data set into graphical analysis package and generate a graph. Plot the circumferences on the y-axis; plot the diameters on the x-axis. Use point protectors to assure identity of data points on the graph. Fit the data points with a regression line. Generate slope, y-intercept, and correlation coefficient and show on graph. Print a copy of this graph. Give the following as part of your lab report.
As part of your graphical analysis, provide the following graphs and relationships:
As part of your error analysis, provide the following given the fact that PI = 3.14159:
Write a separate lab report following the general format given in #7 below.
5. Measure the lengths and widths of a set of Plexiglas rectangles provided you by the instructor. Create a data set using all rectangles provided. Input data set into graphical analysis package and generate a graph. Plot the length on the y-axis; plot the width on the x-axis. Use point savers to assure identity of data points on the graph. Print this graph with lines connecting the data points. (This is not normally done, but to show the non-linearity of the graph it helps.) Linearize the plot by the techniques you've learned. Plot this graph. Fit the linearized data points with a regression line. Generate slope, y-intercept, and correlation coefficient and show on graph. Print the graph. Write a separate lab report using the bulleted points above as a guideline for graphical and error analysis. In addition, follow the general format given in #7 below.
6. Years ago an astronomer working at Yerkes Observatory happened to notice that crickets appeared to chirp more rapidly during warm evenings and more slowly during cool evenings. He thought that there might be a relationship between the rate of chirping and the temperature Fahrenheit. He counted the number of chirps crickets made in 60 seconds each evening, and then divided that number by 4 to get the rate for 15 second. He also recorded the air temperature. After a week he ended up with the following data:
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Use graphical analysis to find the mathematical relationship between these two variables, and give an approximate verbal rule for how to find the temperature from listening to crickets using 60-second counts. Generate the graph and perform an automatic curve fit using a linear mode. Explain the possible reasons why the data points don't fit precisely on the regression line in the Graphical Analysis text screen. To print all, use the File/Print Screen command. Using the Analyze/Interpolate command, determine the temperature when the 15-second chirp rates are as follows: 11, 20, 35. Include the results in your lab write up. Write a separate lab report following the general format given in #7 below.
7. Prepare a lab write-up reporting your findings. Use the format provided here.
Your work on this project will be evaluated through a brief
presentation of the application to, and a discussion with, the
course instructor. The graphs and lab report produced as indicated
in sections 4 - 7 above are also part of the evaluation.