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Physics IAVer. 0.21

Last updated 02.01.02

Data Processing and Presentation Using ICT

Syllabus reference 1.3 Mathematical and Graphical TechniquesAssessment Criteria Data Processing and PresentationDate delivered outDate for handing inAim Show how ICT can be used to make processing and presentation of

data more efficient

Table of Contents

Part 1 – A detailed training example on how to process and present data

1.1 Data presentation and analysis with Excel

1.2 How to transfer a graph on your screen to a Word document

1.3 Data analysis with Graphical Analysis

Part 2 – Two assessed exercises

2.1 Distance travelled for a ball rolling from rest down an inclined plane

2.2 Historical data gathered by Boyle

Part 3 – Optional exercise

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Part 1 – An example on how to process and present data

1.1 Data presentation with Excel1

The speed vs. time data for a freely falling golf ball is shown in figure 1 below:

Fig. 1 Raw data of experiment

Your task is to present these data with uncertainty bars, given that absolute uncertainty in time is 0.03s and absolute uncertainty in velocity is 0.1m/s.

Write first the data into a Excel so that the result is similar to figure 2:

Fig. 2 Raw data in Excel

Select now the region A4:B13 and click the icon for the diagram wizard. In the resulting screen you should choose scattering diagram and select the first subtype:

1 Microsoft Excel ®

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Fig 3. Part 1 of 4 – Diagram Wizard

Selecting “Next” two times, the following picture appears:

Fig 4. Part 3 of 4 – Diagram Wizard with default tab

Choose the title tab and write in title and text along the coordinate axes:

Fig 5. Part 3 of 4 – Diagram Wizard with title tab

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Note the following important points: The title is short and precise, telling what the drawing is all about. Along both the x-axis and y-axis name, symbol, and unit are all given for each

physical quantity.

On the tab for auxiliary lines, cross away the default selection. Thus no lines appears:

Fig 6. Part 3 of 4 – Diagram Wizard with title tab

On the explanation tab cross away the default for explanation. Since you have only one curve in the diagram the title should be good enough to explain what the data are all about. Choose then “Next” and select “New sheet” before you push the “Finish” buttom:

Fig 7. Part 4 of 4 – Diagram Wizard with title tab

The result should then be similar to the following picture:

Fig 8. Resulting diagram after use of the wizard.

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It is rather unusual to use a shaded background for presentation of data. Double-click therefore the shaded background so that the following picture appears:

Fig 9. Formatting box of the background.

In the region “Area” click the white choice and then the “OK” buttom. The background is now white.

Point now on one of the data points and double-click. The result is a collection of tabs where you choose the “x error field” tab:

Fig 9. Formatting series of data.

Choose double uncertainty bar and fixed value 0.03. Quite similar for the “y-error field” tab, a double uncertainty bar of fixed value 0.1 is chosen.

By choosing “OK” the final graph emerges:

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Fig 10. Final graph!

The lower and upper values on the coordinate axes, units etc. may be changed by double-clicking these axes and selecting the “Scale” tab. Change the coordinate axes above so that

The least and the largest value on the x-axis are respectively 0.01 and 0.38. The least and the largest value on the y-axis are respectively 0.50 and 4.30.

1.2 How to transfer a graph on your screen to a Word document

After all this hard work you want to transfer this beautiful art to your lab report in Word.

The idea behind this is very simple: With the graph centered on your screen, push the PrntScrn bottom on your keyboard to make a picture of the screen. Start up Word and push the paste icon. The result is a picture of your screen.

In order to cut away the the part of the picture that does not belong to the graph, choose Show/Work Tools/Picture to get the picture tool bar. Left-click first the picture and then

choose the cut icon .

Point now with the cursor on the middle black square on a boundary of the picture, left-click and hold the mouse and push the mouse towards the center of the picture. This operation may also be done in reverse if you cut too much. Do the same operation for the three other boundaries.

When you are finished, close Word and start up Graphical Analysis in order to do the next section.

1.3 Data analysis with Graphical Analysis

In Graphical Analysis open the file freefall.dat by clicking the open icon. The resulting screen image should be similar to the following:

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Fig 11. Data for the file freefall.dat.

In accordance with the theory for free fall without friction the velocity/time data seem to be along a linear graph. Let us try to find a best fit line:

In the Graph Window select now all the points with the mouse. Choose then Analyze/Analytic Curve Fit on the menue. On the resulting dialog box select the linear function and push the OK bottom:

Fig. 12. Automatic Curve Fitting Dialog Box

On the next screen push the “OK- Keep Fit” bottom. The resulting picture should be

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Fig. 13. Best fit line for the freefall data.

What is the acceleration of gravity according to this analysis? What about initial velocity?

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Part 2 – Two assessed exercises

2.1 Distance traveled for a ball rolling from rest down an inclined plane

The data below represent the distance traveled for a ball rolling from rest down an inclined plane. The timing was done using a waterclock in an attempt to duplicate the work of Galileo. The table was taken from "Project Physics", p. 62, 1970 and converted to metric units.

The uncertainties in time and in distance are respectively 4ml and 0,05m.

a) Make a presentation in Excel of distance versus time.

b) Make a presentation in Excel of distance vs. time square (Hint: Make a new coloumn and use a spreadsheat formula).

c) Use a print-out of the result in b) and a steepest and a least steep line within the uncertainty bars to determine the acceleration with uncertainty.

Remember that the best value is the average of the two extreme values and the absolute uncertainty is half the difference between these two values.

d) Assume that the distance is proportional to a power of time. Make a best fit in Graphical Analysis to determine the exponent and the proportionality factor.

e) Explain why the exponent in d) should be 2.

e) What is the acceleration from the results in d)?

f) Compare the values of the acceleration in c) and e).

2.3 Historical data gathered by Boyle

The following historical data2 were gathered by Boyle in studying the relationship between the volume and pressure of a gas at a constant temperature:

Volume V/cm^3 Pressure p/mm Hg27,94 811,225,4 896,925

22,86 998,525

2 Morris H. Shamos, "Great Experiments in Physics", Dover 1959.

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20,32 1122,3517,78 1277,92515,24 1493,82513,97 1627,17512,7 1795,45

11,43 1978,02510,16 2232,0258,89 2551,17,62 2986,075

Assume that the absolute uncertainty in volume is and that the absolute uncertainty in pressure is 10mm Hg.

a) Present the values of pressure vs. volume (with uncertainties) graphically.

b) Assume the pressure is inverse proportional to volume for a fixed temperature. Determine the constant for this inverse proportionality. (Hint: Use a best fit formula).

Part 3 – Optional Exercise

By dropping a ball from rest towards a Motion Detector (but not hitting!), obtain data of distance versus time for this ball. The Motion Detector has an absolute uncertainty of 1mm and the time values may be considered to be without any uncertainty.

a) Make a plot of distance versus time with uncertainties.

b) Determine the acceleration of gravity with uncertainty.

Possible extensions

1. Use table function in Word to make a Caption to all graphs.2. Make new voloumns in Graphical Analysis.3. More examples.

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