Graphing with Microsoft Excel As an AP Physics 1 student, you must be prepared to interpret and construct relationships found in physical laws and experimental data. This exercise is meant to familiarize you with using spreadsheet software, like Excel, to create your own graphs. This will prepare you for the future lab reports you will be assigned and problems that can be found on your AP Physics 1 exam in May. If you are in planning on taking IB Physics next school year, this is especially important since it is embedded in Topic 1 of the IB Physics curriculum. In this exercise, you will: Graph the data using Excel Add important features such as a best-fit line (trendline) and the trendline equation Manipulate the equation to produce a linear relationship Produce a second graph displaying this linear relationship with the trend line and equation Use the slope to determine the acceleration due to gravity, g Calculate percent error Problem: A student wishing to determine experimentally the acceleration due to gravity, g, has an apparatus that holds a small metal sphere above a recording plate, shown to the right. When the sphere is released, the timer automatically begins recording the time of fall. The timer stops when the sphere strikes the recording plate. The student measures the time for fall at various values of distance, D, shown to the right, and records the data. The data is listed below. Data: Distance of Fall (m) Time of Fall (s) 0.10 0.14 0.50 0.32 1.00 0.46 1.70 0.59 2.00 0.63 Note: That a proper data table consists of labels, units and proper significant figures. This table has empty columns that you can fill in later. 1. Using Excel to Graph:
1. Open Excel on a computer 2. Enter your data in two columns on the spread sheet. Make sure that you enter the data for the x-axis in the left hand column, and the data for the y-axis in the right hand column. Excel will automatically put the first variable entered (i.e., the left-hand column) on the x-axis and the second variable entered (i.e., the right-hand column) on the y-axis. Remember independent variables should be plotted on the x-axis and dependent variables should be shown on the y-axis. 3. Highlight both the columns of variables you wish to plot. 4. Click on the tab labeled Insert, and then click on Scatter from the Charts menu. Choose the first plot style from the drop-down menu: 5. Once your scatter plot appears, you ll need to clean it up. First, remove the legend by simply clicking on it and pressing Delete. You only need a legend if there are two or more lines on the graph. 6. Next, add axis titles by clicking anywhere on the scatter plot, selecting the Layout tab in the Chart tools menu at the top and then clicking on Axis Titles. a. For the horizontal title, you want to choose the Title below Axis option.
b. For the vertical (y-axis) title, you want the Rotated Title option. 7. Add the chart title by clicking on Chart Title in the Layout menu. Select the Above Chart option in the drop down menu. Type in your title and press Enter. 8. Right click on any data point and choose Add Trendline. 9. In the menu that appears choose the type of trend line that appears to fit your data best. NOT ALL GRAPHS ARE LINEAR. You will notice that this graph is not. Pick the trendline that best resembles your data points.
10. At the bottom of the same menu, click on the box next to Display equation on chart. 11. Save your file to Your System Folder. Do not save to My documents, or your work will be lost. Click on your chart and print. Example Format for a Complete Graph 0.9000 Graph 3-1 Uniform Motion 0.8000 0.7000 0.6000 Distance (m) 0.5000 0.4000 0.3000 0.2000 0.1000 0.0000 0.00 0.20 0.40 0.60 0.80 1.00 Time (s) (Please Note: Not all graphs are linear. This is an example of format only) Things to notice: 1. Graph is neat and attractive (axis are drawn with a ruler) 2. Graph has a label and a title
3. Both axis are labeled with units displayed 4. Scale matches accuracy of tool used to obtain values. 5. Each axis has a proper and continuous scale (if not done on computer this can only be achieved by using graph paper) 6. Line is BEST FIT (do not connect dots) 7. Graph is created in a reasonable size (not to big, not to small) 2. Linearizing a Curve: Notice that D is not directly proportional to t in the graph you created. Linear relationships offer the clearest information. The graph you made shows that D is exponentially related to t. You will learn how to determine the equation yourself later. For AP Physics, you need to be able to make any equation into a linear relationship (y=mx+b). Given that the equation that represents the data given above is D = 1 2 gt! where D is the distance of the fall in meters, g is the acceleration due to gravity in meters/second 2, and t is the time of the fall in seconds. In order to manipulate the equation so that when graphed it is a straight line, you must change the equation to fit y=mx+b. It is useful to plot an appropriate straight line graph, if possible, so that the slope can be used to find certain values (in this case g). Read the PDF for straigtening a curved graph. If only the variables D and t are used, what quantities should be used in order to produce a linear relationship between the two quantities? Fill in any new quantities used in a modified table (Reproduce the data table given and add the one or two new quantities on either side). Print this table out. Make sure it has all components. Create a second graph in Excel with these quantities that shows the straight line. Make sure it is complete with best fit line and the corresponding equation. Print this graph. 3. Finding the acceleration due to gravity: Having manipulated the equation into y=mx+b form, it is apparent that g, the acceleration due to gravity, is found in the slope. Be careful, the slope is not just equal to g, but ½g. This means that the number given as the slop in the equation of your best fit line is half the value of g. To find g, multiply the slope by 2. Show this calculation below the second graph (line graph) you printed. 4. Calculate percent error: To calculate percent error, you must know the theoretical value for the acceleration due to gravity, 9.81 m/s 2. The experimental value is the value you found with the data. Knowing this, use the formula below to determine the percent error in your findings.
Show this calculation on the same page as the second graph. You will turn both graphs, the modified data table, and both calculations in when school begins. Free free to copy and paste all parts into a single document, but make sure your graphs cover at least ½ page each so they are clear. Show all equations, plugging in of values, and calculations when solving for certain quantities.