analyzing experimental data lazy parabola b as a function of a

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Analyzing Experimental Data Lazy Parabola

B as a function of A

Created for CVCA Physicsby

Dick Heckathorn30 August 2K+4

page 26 Practice 3 Lazy Parabola

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A. Getting Ready

1. “On”, “Mode” Normal, Float, Degree,

Func, Connected, Sequential, Full Screen

2. To Exit: “2nd” “Quit”

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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”, ‘A’ (one header)

b. “2nd”, “Ins”, ‘B’ (2nd header)

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B. Storing Data

4. Input data into appropriate column.

5. ‘A’ 100 64 49 36 2516

‘B’ 1.99 1.59 1.39 1.19 1.000.80

[note...‘B’ is a function of ‘A’]

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C. Clear Previous Graphs

1. “y=”

2. clear any equations

3. “2nd”, “stat plot”

4. Enter “4” - PlotsOff

5. “Enter”

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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 ‘A’: (“2nd”, “List”, “A”)

d. Ylist to ‘B’: (“2nd”, “List”, “B”)

e. Mark: select square

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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 zero

b. “Graph”

(All of 1st quadrant shown)

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F. AnalysisShape of line is?

which indicates

a lazy parabola

‘n’ has a power greater than ‘0’

but less than ‘1’.

1 n 0A B So plot ‘B’ vs ‘ An ’ where n = 0.5 .

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G. Analysis of B vs A.5

1. “Stat”, “Edit”

2. Cursor at top of blank column

“2nd”, “INS”, ‘AHALF’

3. Move cursor on top of ‘AHALF’

4. Type: “2nd”, “”, “2nd”, “list”, ‘A’

5. “Enter”

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G. Analysis of B vs A.5

1.“2nd”, “Stat Plot”

2. With cursor at 1, “Enter”

3.a. on

b. Type: select 1st graph

c. Xlist to ‘A’: (“2nd”, “List”, “AHALF”)

d. Ylist to ‘B’: (“2nd”, “List”, “B”)

e. Mark: select square

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G. Analysis of B vs A.5

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)

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G. Analysis of B vs A.5

Shape of line is

We can now….

a straight line.

Find the equation of the straight line.

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H. Finding the Equation

1. “Stat”, “Calc” “4:LinReg(ax+b)

2. “2nd”, “list”, ‘AHALF’, ‘,’

3. “2nd”, “list”, ‘B’, “Enter”

4. On screen we see:

a. LinReg

y = ax+b a = .20 b = .01

[a = slope, b = y-intercept]

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H. The Equation is:Using y = mx+b concept where the

calculator uses y = ax+b, substitute in the value for ‘a’ and ‘b’ and one gets:

0.01 x 20.0 0.5 y

Since b is very close to 0, we can ignore it.

A20.0 B 0.5

Replace ‘y’ with ‘B’ and ‘x’ with ‘A’

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I. Thought

What do we say is the relationship between ‘B’ and ‘A’ ?

We say the relationship is:

‘B’ is directly proportional to the square root of ‘A’.

A20.0 B 0.5

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J. Plotting Line of Best Fit

1. “y=”, “VARS”, “5:Statistics...”, “EQ”, “1:RegEq”, “Graph”

2. And there you have it, the line 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.

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K. Summary

That’s all there is to it. If the data yields a straight line, find the equation of the straight line.

If it is a hyperbola or a parabola, then you must make additional

plots until you get a straight line.

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K. 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.

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L. A Shortcut

1. Using original data plot ‘B’ as a function of ‘A’.

2. “Stat”, “Calc”, “A:PwrReg”, 3. “2nd”, “List”, ‘A, ‘,’4. “2nd”, “List”, ‘B’5. “Enter”

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L. A Shortcut -2-

6. On the screen we see:

a. PwrReg

y = a*x^b

a = .20

b = .50

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L. A Shortcut -3-

7. Substituting:

0.20 for ‘a’ and 0.50 for ‘b’

50.0x20.0y

8. Substituting: ‘B’ for ‘y’ and ‘A’ for ‘x’

50.0A20.0B

y = a*x^b

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M. A Summary

9. How does this equation compare to that found earlier?

They should be the same.

50.0A20.0B

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That’s all folks!