Graphical Analysis

Objectives:

1. To gain experience in drawing graphs and in using graphing software.

Materials:

1. Windows based computer with Graphical Analysis software
2. LabPro interface
3. LoggerPro software
4. Motion detector
5. Rubber ball
6. Wire basket

Procedure:

Part I:

1. Gather the required materials and then proceed to turn on the computer. Once started, access the PhysicsApps folder by double-clicking on the folder icon. Subsequently, load the Graphical Analysis software within the folder by double-clicking on its respective icon.
2. Once the program is operational, open the file functionplot by clicking on File (located at the top left-hand corner of the screen), Open, then double-click the Physics folder. If properly executed, it should show a graph of a function and the data used to create the graph. Read the instructions that appear in the text window to see how to enter your own function.
3. Decide upon and choose a mathematical function of your liking to plot. Make sure that the function has the following components:
• a title
• x and y axis labels
• units
4. Make sure that the graph you created has the appearance that you want. Obtain a printout of the graph for each member of your group (excluding data table) by selecting File, then Print.

Part II:

1. Connect the lab pro to the computer and the motion detector to the DIG/SONIC2 port on the LabPro. Load the LoggerPro software in the PhysicsApps folder. Click on File, then Open, and open the mechanics folder. Within that folder, open the graphlab file. Take a position vs. time graph for a falling ball with the motion sensor.
2. When you finally achieve a nice curve, select the appropriate data range and perform a fit to the data. Confirm that the distance fallen adheres to the following relationship: d*α*g*t^n where g = 9.8 m/s2, is the acceleration due to gravity. Obtain a printout of your graph (with the fit) for each member of your group (without the data table).
3. Use dimensional analysis and unit analysis to verify the equation.

Results:


Figure 1



Figure 2

Dimensional Analysis:

d α gt²

v=(dx)/(dt)

g=(dv)/(dt)
therefore:

 v=m/t

 g=m/t^2

 d=g*t^2=[m/t^2]*t^2=m

Unit Analysis:

v=m/t

g=m/t^2

d=[m/t^2]*t^2]=m

Conclusions:

     During the lab, I learned how to use the LoggerPro software in order to capture the velocity of a falling object, accurately detect the acceleration of gravity to be roughly around -9.8 m/s^2, and to analyze a graph to estimate values for velocity through curve fitting a linear fit around a parabolic position vs. time graph (the slope is equal to the velocity).