Physics 30 Example 1: Curve Straightening Coulomb’s Law Given: data of electric forces and charge separation Graph: F g vs r, F g vs. r -2 Analyze: By finding the slope of the line of best fit (allows us to find either k or q 1 q 2 )
Data, worksheets and explanations of curve straightening available at www.ldindustries.ca. www.ldindustries.ca
Graphing using the TI-83/4 1. From the main screen, press STAT, then press ENTER on Edit… 2. This is the list menu. Enter the values of x in L 1 and y in L 2. To clear out a large number of old data points, scroll up to the L 1 or L 2 title, press CLEAR then ENTER. 3. You can now view your graph. Press Y=, clear out any old equations you might have entered in, then scroll up to Plot 1 and press ENTER until it turns black. 4. Use the WINDOW functions as needed to see your graph. The dots should form a rough line.
Graphing using the TI-83/4 5. Press STAT, then scroll one right to CALC, scroll down and press ENTER on LinReg (ax+b). This is the Linear Regression feature. 6. If you have no other data entered into your calculator, you can just press ENTER. If you have other data in the Stat Plot menu, enter in (L 1, L 2 ) behind the LinReg(ax+b) command, then press ENTER. 7. This is your regression equation. The value of “ a ” is the slope, the value of “ b ” is the y-intercept. To see how this equation matches your data, enter it into the Y= menu by hand … 8. … or while in the Y= screen by pressing VARS, scrolling down to Statistics …, pressing ENTER then scrolling right to EQ and hitting ENTER on RegEq. If all went well, the plotted points should match the line.
Physics 30 Example 2: Finding the Index of Refraction of a Medium Given: angles of incidence and refraction of a medium Graph: sin(θ i ) vs sin(θ r ) Analyze: find n by calculating the slope of the graph
Graphing Using Microsoft Excel 1. Open a new document. 2. Enter the data to be graphed. The first column will be the x and the second will be the y. *Note: students can enter in data in degrees and have Excel take the sine of each angle for them.
3. Highlight the two data columns you want to graph. 4. Under “Insert”, choose “scatter graph”. It doesn’t matter much which graph you choose now, because you’re going to change it in a second.
5. Choose the graph format that has the little Fx on it. This one will display the regression equation. 6. Format as needed.
Physics 30 Example 3: Determining the Focal Length of a Convergent Lens Given: distances from the lens to the object and image Graph: 1/di vs 1/do Analyze: find y-intercept to determine focal length.
Graphing Using Google Drive’s Spreadsheet 1. Open a new document. 2. Enter the data to be graphed. The first column will be the x and the second will be the y. *Note: students can enter in data as regular di and do values, then have the spreadsheet reciprocate for them.
3. You can get a graph by clicking “Insert” and “Chart”, but putting on the line of best fit is an ugly process… 4. So you can just use the =INTERCEPT( feature to find the Y-intercept (the program can’t calculate x- intercepts easily either)
Physics 20 Example: Determine Gravitational Field Strength from a Pendulum Given: varying lengths and periods of a pendulum Graph: T vs √L Analyze: find g by rearranging and finding slope.
Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Trial 7 Trial 8 L (m) 0.810.740.530.460.330.230.150.07 L (m 1/2 ) 0.900.860.730.680.570.480.390.26 T (s) 1.761.671.451.311.151.01 0.80 0 0.59 0 These graph nicely in any program, but I like Excel (if you have easy access to it) because you can let the kids do a bit of experimentation.