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Analyzing Experimental Data Upright Parabola (D as a function of T)

Analyzing Experimental Data Upright Parabola (D as a function of T). Created for CVCA Physics by Dick Heckathorn 30 August 2K+4. Sample Problem page 26 #3 Upright Parabola. A. Getting Ready. 1. [On] [Mode] Normal, Float, Degree, Func, Connected,

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Analyzing Experimental Data Upright Parabola (D as a function of T)

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  1. Analyzing Experimental Data • Upright Parabola • (D as a function of T) Created for CVCA Physics by Dick Heckathorn 30 August 2K+4 Sample Problem page 26 #3 Upright Parabola

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

  3. B. Storing Data 1. [Stat] [Edit] 2. Clear all columns Cursor over each header, [Clear] [] 3. With cursor over blank headers: a. [2nd] [INS] ‘T’ (one header) b. [2nd] [INS] ‘D’ (2nd header)

  4. B. Storing Data 5. Input data into appropriate columns. 6. T (s) 0 0.8 1.0 1.2 1.4 D (m) 0 12.8 20.0 28.8 39.2 Plot ‘D’ is a function of ‘T’

  5. C. Clear Previous Graphs 1. [y=] 2. clear any equations 3. [2nd] [stat plot] 4. [4:PlotsOff] 5. [Enter]

  6. D. Preparing to Graph 1. [2nd] [Stat Plot] 2. With cursor at 1, [Enter] 3. a. on b. Type: select 1st graph c. Xlist to ‘T’: [2nd] [List] ‘T’ d. Ylist to ‘D’: [2nd] [List] ‘D’ e. 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=] & [Ymin=] to 0 b. [Graph] (This shows all of 1st quadrant)

  8. F. Analysis Shape of line is an upright parabola which indicates? Where ‘n’ must be greater than 1. So lets plot ‘D’ vs ‘T2’

  9. G. Analysis of D vs T2 1. [Stat] [Edit] 2. With cursor on top of a blank column [2nd] [INS] ‘T2’ 3. With cursor on top of ‘T2’ 4. Type: [2nd] [List], ‘T’, ‘^’, ‘2’ 5. [Enter]

  10. G. Analysis of D vs T2 1. [2nd] [Stat Plot] 2. With cursor at 1, [Enter] 3. a. on b. Type: - select 1st graph c. Xlist to ‘T2’: [2nd] [List] ‘T2’ d. Ylist to ‘D’: [2nd] [List] ‘D’ e. Mark: select square

  11. G. Analysis of D vs T2 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)

  12. G. Analysis of D vs T2 Shape of line is a straight line going through the origin. From this we can determine the equation of the straight line.

  13. H. Finding the Equation 1. [Stat] [Calc] [4:LinReg(ax+b)] 2. [2nd] [List] ‘T2’ [,] 3. [2nd] [List] ‘D’ [Enter] 4. On screen we see: a. LinReg y=ax+b a=20, b=0 [a = slope, b = y-intercept]

  14. H. The Equation is: Using y = ax + b substitute in the value for ‘a’ and ‘b’ Replace ‘y’ with ‘D’ and ‘x’ with ‘T’

  15. I. The Relationship What is the relationship between D and T? We say the relationship is: ‘D’ is directly proportional to the square of ‘T’ (‘T’ squared).

  16. J. Plotting Line of Best Fit [y=] [VARS] [5:Statistics…] [EQ] [1:RegEq] [Graph]

  17. K. Summary Did you get the equation Make sure you know how to determine the units.

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

  19. K. Summary Since the first plot was a parabola, we manipulated the ‘x’ variable to a greater power to get a straight line. Once we got a straight line, we determined its equation.

  20. M. A Shortcut 1. Enter original data except for 0, 0 2. Graph it 3. [Stat] [Calc] [A:PwrReg] 4. [2nd] [List] [T] 5. [2nd] [List] [D,] [Enter]

  21. M. Finding the Equation 6. On screen we see: a. PwrReg y = a*x^b a = 20 b = 2

  22. M. The Equation is: y = a*x^b Substituting 20 m/s2 for ‘a’ and ‘2’ for ‘b’. Replacing ‘y’ with ‘D’ and ‘x’ with ‘T’ one gets the equation:

  23. N. A Summary 6. How does this equation compare to that found earlier? They should be the same.

  24. That’s all folks!

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