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Analyzing Experimental Data: Hyperbola (F as a function of r)

This tutorial explains how to analyze experimental data using a graphing calculator to plot the relationship between force (F) and radius (r) and determine if the relationship follows a hyperbolic shape.

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Analyzing Experimental Data: Hyperbola (F as a function of r)

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  1. Analyzing Experimental Data • Hyperbola • (F as a function of r) Created for CVCA Physics by Dick Heckathorn 30 August 2K+4 page 25 Practice 1 Hyperbola

  2. A. Getting Ready • 1. “On”, “Mode” • Normal, Float, Degree, Func, Connected, Sequential, Full Screen • 2. To Exit: • “2nd”, “Quit”

  3. B. Storing Data 1. “Stat”, “Edit” 2. Clear all columns Cursor over each header, “Clear”, “Down Arrow” 3. With cursor over blank headers: a. “2nd”, “INS”, ‘R’ (one header) b. “2nd”, “INS”, ‘F’ (2nd header)

  4. B. Storing Data 5. Input data into appropriate columns. 6. ‘R’(cm) 1 1.2 1.8 2.4 3.0 ‘F’(N) 10 6.9 3.1 1.7 1.1 Remember to plot ‘F’ as a function of ‘R’

  5. C. Clear Previous Graphs 1. “y=” 2. clear all equations 3. “2nd”, “stat plot” 4. Enter “4” - PlotsOff 5. “Enter”

  6. D. Preparing to Plot 1. “2nd”, “Stat Plot” 2. With cursor at 1, “Enter” 3. a. on b. Type: - select 1st graph c. Xlist to ‘R’: (“2nd”, “List”, “R”) d. Ylist to ‘F’: (“2nd”, “List”, “F”) d. Mark: - select square

  7. E. Graphing The Data 1. “Zoom”, “9:ZoomStat” (This allows all points to be plotted using all of the screen.) 2. “Windows” a. Set Xmin= and Ymin= to zero b. “Graph” (This shows all of 1st quadrant)

  8. F. Analysis Shape of line is? Which indicates? 1. It is a hyperbola (pulled away from y-axis). 2. An inverse power is implicated. 3. So plot ‘F’ vs “1/R” where n = 1.

  9. G. Analysis of F vs 1/R 1. “Stat”, “Edit” 2. Label 3rd column Cursor on top of third column “2nd”, “INS”, ‘InvR’ 3. Move cursor on top of ‘InvR’ 4. Type “1/”, “2nd”, “List”, “R” 5. “Enter”

  10. G. Analysis of F vs 1/R 1. “2nd”, “Stat Plot” 2. With cursor at 1, “Enter” 3. a. on b. Type: - select 1st graph c. Xlist to ‘1/r’: (“2nd”, “List”, ‘INVR’) d. Ylist to ‘F’: (“2nd”, “List”, ‘F’) e. Mark: - select square

  11. G. Analysis of F vs 1/R 1. “Zoom”, “9: ZoomStat” (This allows all points to be plotted using all of the screen.) 2. “Windows” a. Set Xmin= and Ymin= to zero (This shows all of 1st quadrant) b. “Graph”

  12. G. Analysis of F vs 1/R Shape of line is? An upright parabola. Which indicates? A greater power of ‘n’ is implicated. So plot ‘F’ vs ‘1/R2’ where n is 2.

  13. H. Analysis of F vs 1/R2 1. “Stat”, “Edit” 2. Label another blank column Cursor on top of blank column “2nd”, “INS”, ‘IRSQ’ 3. Move cursor on top of ‘IRSQ’ 4. Type: “2nd”, “List”, “InvR”, “^2” 5. “Enter”

  14. H. Analysis of F vs 1/R2 1. “2nd”, “Stat Plot” 2. With cursor at 1, “Enter” 3. a. on b. Type: - select 1st graph c. Xlist to: ‘1/r2’, “2nd”, “List”, ‘IRSQ’ d. Ylist to: “2nd”, “List”, ‘F’ d. Mark: - select square

  15. H. Analysis of F vs 1/R2 1. “Zoom”, “9: ZoomStat” (This allows all points to be plotted using all of the screen.) 2. “Windows” a. Set Xmin= and Ymin= to zero b. “Graph” (This shows all of 1st quadrant)

  16. I. Further Analysis Now that we have found a straight line that fits the data points, we can proceed to find its equation.

  17. J. Finding the Equation 1. “Stat”, “Calc” “4:LinReg(ax+b) 2. “2nd”, “List”, ‘IRSQ’, ‘,’ “2nd”, “List”, ‘F’, “Enter” 3. On screen we see: a. LinReg y=ax+b a=10.003, b=0.017 a = slope, b = y-intercept

  18. J. The Equation is: Using y = ax+b, substitute in the value for ‘a’ and ‘b’ getting: Since b is almost zero, we can say: Replace ‘y’ with ‘F’ and ‘x’ with ‘1/R2

  19. J. The Equation Did you get the equation F = 10 (N.m2) 1/R2 Make sure you know to obtains the units ‘N . m2’

  20. I. Plotting Line of Best Fit 1. “y=”, “VARS”, “4:Statistics...”, “EQ”, “1:RegEq”, “Graph” 2. And there you have it, the equation of the best fit line for the data points plotted. 3. In real life data gathering, all the points will not fall on the line due to normal measurement error.

  21. K. A Thought That’s all there is to it. If the data yields a straight line, analyze it to find the equation. If it is a hyperbola or a parabola, then you must make additional plots until you get a straight line.

  22. K. A Final Thought What do we say is the relationship between F and R? We say the relationship is: ‘F’ is inversely proportional to the square of ‘R’.

  23. K. A Final, Final Thought At this time, write out a brief summary using bullet points outlining what you did. Do not go on unless you have completed the above.

  24. L. A Shortcut 1. Using original data plot ‘F’ as a function of ‘R’. 2. “Stat”, “Calc”, “A:PwrReg”, 3. “2nd”, “List”, ‘R’, ‘,’ 4. “2nd”, “List”, ‘F’, “Enter”

  25. L. A Shortcut -2- 5. Substitute: y=a*xb value of ‘F’ is 9.997 value of ‘R’ is -2.011 6. How does this equation compare to that found earlier?

  26. That’s All Folks

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