Communication is the lifeblood of science. No matter how incredible or revolutionary your results or ideas, if you can’t present them so other people can understand, you have proven nothing but that you don’t know what you’re talking about. The following format has been designed to clearly and succinctly communicate your findings. There may be other ways to report this, there may be better ways. But in this class the format is the way. If you do not follow the format, points will be deducted.

The lab report can be handwritten or printed out. A Lab Report Template in Microsoft Word is provided on all the PC's in the labs. One report per individual is required for each experiment. Write your report as outlined here, unless you are notified otherwise. 

Pay special attention to each numbered item. In grading the lab your TA writes down the number of each criterion that you do not meet to let you know why points are deducted.

Each section in your report is worth the specified point value and

1. must be clearly labeled and presented in the same order as presented here. Up to five points will be deducted if this is not followed.

An annotated example lab report is available here.

Title Page (4 points)

Include on the first page

2. the name of the experiment,
3. your name,
4. your partner's name (you get a zero for the lab if it is not here.),
5. the date of the experiment,
6. your TA's name,
7. the lab section number, and
8. an abstract.
9. Nothing else should be on this page.

An abstract is a concise summing up of the experiment that includes

10. the type of measurements made,
11. the numerical results, and
12. the significance of these results.
13. It is not a parroting of the Purpose stated in the manual.

On occasion you will be calculating many results, in which case it is okay to state a few representative cases. The full report of results will be in the Conclusions section.

14. An abstract should contain no more than four or five sentences . For example:

Abstract: The acceleration of a freely falling mass was measured using the Behr free fall apparatus where a falling metal bob sparked through a tape every ¹ /₆₀ second. The value of 9.73 ± 0.04 m/s² was calculated which agrees with the accepted value the acceleration of gravity of 9.80 m/s².

Title Page example

Data (5 points)

Pay attention to the following items. When you present your raw data sheet to the TA to be signed, it will also be graded immediately.

Make a clear delineation between observation and analysis, between numbers you read off an apparatus and calculated quantities.

15. Do not make simple calculations and present the results as raw data.

The raw data sheet or sheets are filled out during the experiment. Standard, official sheets are passed out by your TA at the beginning of class.

16. The original data sheet that you write as you take data is a part of the report. Do not plan on recopying the data to make it prettier.
17. Write down in permanent ink your measurements as you conduct the experiment. (No pencils!)
18. On each data sheet put your name, your partner's name, and the date (if it's not already there).
19. Each data sheet must be signed or initialized by your TA or Henry or Dr. Bortner.
20. Include an annotated sketch (drawing, schematic) of the experimental apparatus showing how it is used. If more than one configuration of equipment is used, there should be a sketch of each different setup.
21. Define or describe all quantities that you (or the computer) are measuring. This includes the algebraic abbreviation. x is the length of the flag that goes through the photogate
22. Most of the numbers should be in a data table with headings and ruled lines since usually you will be changing one quantity many times and measuring another quantity that changes with it. Make it clear what each number represents and what the quantity's corresponding units are by using the commonly accepted symbol for that variable (m (kg) , for mass).
23. Indicate where the values originated-- reading a meter stick, copying the reading off a voltmeter, counting, whatever.
24. Note the uncertainty of each type of measurement, where appropriate. (Sometimes the uncertainty is statistical in nature and must be calculated, meaning it would not be included here.)

* Always write your data down on a data sheet first. You need a permanent, honest record of your observations. Both partners keep their own independent copy of the data and a sketch of the set up.

* Do not have one person write down the data while the other person copies it down later.

* The experiments in this lab class require manipulation of numbers with a computer. Entering data directly into the computer as you take it is OK as long as it is being done in addition to each partner handwriting data and observations.

* Purported mistakes should be lined out (single line) in case the classification of it being incorrect is itself later found to be wrong.

Fig. 1 is an abbreviated raw data page for a Hooke's Law experiment:

Raw data example

Sample Calculations (5 points)

It may happen that the results of one of your experiments are totally off-base. The instructor needs to determine whether the mistake is in the data acquisition or analysis. 

 25.    To see if it is in the analysis, or calculations, you need to show in your report a typical numerical evaluation of each important derived (calculated) quantity.

There are two types of sample calculations. Since you use Excel to do the actual calculations, you need to show the Excel formula that is used. This is put on your printout in the Data Analysis section and is not graded here. Then there is the standard, or multi-line hand calculation, similar to what you would do for a homework or test problem, which is what you put in this section.

You do not have to show hand calculations of least squares fits or standard deviations or averages.

For the standard sample calculation:

26. Write down the equation using the standard variable letters.
27. Plug in numbers, with units, in the next line.
28. Show what units cancel.
29. Show the result of the calculation, with the proper unit.

For example, suppose you were investigating wave phenomena in light and needed to evaluate the expression asinq, where a is the width of a slit in a glass plate and is the angle subtended by a dark spot a distance y_n from a central bright spot on a screen a distance R from the slit. The numerical sample calculation would be

30. Note that Propagated Errors are calculations and each type must be shown in this section.
31. SET's are also calculations, but you only have to show the details of one in a standard sample calculation.

Sample Calculations example

Error Analysis (6 points)

See Appendix 1 for a detailed discussion of errors and Appendix 2 for a discussion of the propagation of uncertainties.

In general, a stated error quantity should not have more than two significant figures; typically, one is sufficient.

In this section state the

1. measurement uncertainties
2. systematic errors
3. propagated errors.

Measurement Uncertainties

32. Include a list of each type of measurement performed during the experiment, with a numerical estimate of the uncertainty and an explanation of how you came up with this number.Yes, this is usually just restating what you wrote down on your data sheet. Sometimes, though, the error in a measured quantity must be calculated, as with the standard deviation. The final error that you associate with a measurement is what you put here. Examples of measurement errors are:

mass of the bob, m_b = 0.1 g; scale limited error for balance reading,

for the static centripetal force, m = 3 g; minimum mass that moved the bob from the marker,

pendulum length, L = 0.2 cm; estimated error in using a meter stick to measure the distance from the point of support to the pendulum center of mass.

Systematic errors

In order to explain a particular physical occurrence, a mathematical model is drawn up. Many times this model is oversimplified and fails to take a physical quantity into account that affects your results; this is a systematic error.

33. List in this section any such phenomena that would significantly change your final numbers, were they to be considered in the analysis. (Significance means that accounting for the phenomena would change your results by an amount on the order of or larger than the uncertainties.)
34. For full credit, discuss how the lack of inclusion in the treatment makes your result larger or smaller than what it should be.
35. Do not include possible sources of error that do not bias the results one way or the other.
36. Some experiments may not have identifiable systematic errors; make a statement to that effect.

Friction of the falling bob against the sparking wire slowed it down, meaning that the distance intervals that we measured are shorter than what they should have been. Hence the calculated average velocities are consistently smaller and the slope of velocity vs. time, or the acceleration of gravity g, is smaller than actual.

Propagated errors

If you do a calculation that uses one or more experimental quantities, the result will have an uncertainty associated with it. This error in a calculated quantity is called the propagated error. Rules for coming up with an expression for this error, starting from the original calculation, are listed in Appendix 2. Your instructor will give you additional rules as needed.

37. The calculation of the value of the uncertainty is shown in the Sample Calculations (besides the stated exceptions). Restate the results of each type of propagated error here.

Slope of velocity vs. time, g= 0.09 m/s²; as calculated from the least squares fit function LINEST.

Final momentum of the two cars together, DP_f =160 g*cm/s ,

Error Analysis example

Data Analysis (10 points)

38. This section is where you should have a neat tabulation of results and any graphs, where appropriate. The results are the number or numbers relating to the derived physical quantities, with errors, that you were investigating.
39. Where there is a calculated quantity with an associated uncertainty in that quantity, round off the error to one significant figure, or two s.f.’s if the last two digits are between 10 and 20 (look at the number without a decimal point). The decimal places of the error determines the number of decimal places of the quantity.
40. All of this is on a computer printout of an Excel spreadsheet.

The following conventions should always be followed for graphs:

41. Use Excel to produce them.
42. Have a descriptive title.
43. Label axes with the proper variables and units.
44. The size of the chart should be roughly ¼ to ½ a page (sometimes a full page). One side should be about the same size as the other. Any one side should not be more than half again as long as the other.
45. If there is only one data set, do not include a legend. If there is more than one, include a legend that distinguishes each data set.
46. Include error bars (both x and y)-- if they are too small to be viewable, mention it on the printout.
47. There will be a deduction if there are any stray points that do not fall on the line or curve suggested by the other points, as in the first data set of A Spreadsheet Primer. This is one of the reasons you plot points. Double check both partners’ raw data sheets and retake the data point if need be.
48. The sequence of presentation in your report should be the preliminary analysis initialized by your TA, then the final analysis if you need it. The preliminary analysis is the computer printout of the work you do in class, where you have done at least a portion of the calculations and come up with preliminary numbers to see if you are headed in the right direction. If you and the TA are satisfied with the outcome, this sheet or these sheets can also be the final results page(s).

All printouts should have as headings at the top of the page indicating

49. the name of the experiment,
50. the time and date of the printout,
51. your name,
52. and your partner's name.
53. Each page of the printout must have the gridlines and the row and column headings. See A Spreadsheet Primer.

The Excel formula:

54. As mentioned earlier, you must include an example of the Excel formula you use for each type of calculation. 
55. The formula that you show is specific, not general. Make it clear what number (or numbers in the case of LINEST) the particular formula calculates.

The computers in the labs have an icon marked as =F called formula box that copies the formula in a selected cell into a text box placed about one cell to the right and one cell down. Also, all templates have a button or buttons embedded in the spreadsheet that do the same thing. You may want to move or resize the resulting box, or add an arrow (see the last step below)

.

Formula box is a custom macro, not available on off-the-shelf versions of Excel. If you have to include the Excel formulas outside the labs and you don't have a copy of the macro, the procedure to do this is as follows:

• If the Drawing toolbar is not showing (or you're not sure), click on the View menu and choose Toolbars. From this submenu choose Drawing.
• Click on the Text Box icon on the Graphics toolbar.
• Click in the spreadsheet where you want the formula to be. A narrow box appears.
• Click on the cell that contains the formula.
• Highlight all the text in the formula bar and select Copy.
• Click inside the text box and choose Paste .
• The box resizes automatically. You may what to resize it manually or change the position.
• If it is not clear what cell the formula is in, click on the Arrow icon on the Graphics toolbar, then click and drag a line from the box to the cell that contains the formula. You can also use the Elbow Arrow Connector or the Curved Arrow Connector.

In your analysis of the data, you may be calculating, say, 50 velocities.

56. You only have to show one Excel formula for each type of calculation (one LINEST, e.g.)

The exception to this:

57. The formulas of all SET's must be shown in the spreadsheet.

Data Analysis example

Conclusions (10 points)

58. State the pertinent numerical results or observations.
59. Discuss your results and compare with theory or with a more accurate experiment.

These experiments are not designed to uncover new physical laws but to verify existing ones. Nonetheless, you should write as if your results were new. Your job here is to draw conclusions from your data and convince someone with some knowledge of physics and logic who is not cognizant of this particular experiment that your conclusions are correct.

60. Consider and address in your discussion any objections this anonymous someone might have with how the experiment was conducted and how the data was analyzed
61. Any questions posed in the lab manual should be answered here, with adequate justification--if the reasoning is not sound or is absent, a correct answer may have points deducted. The number of points each question is worth will be determined by the instructor.

Possible reasons for poor results outside of those listed in the Error Analysis can be addressed here, as can suggestions for improvement.

Conclusions example

Extra Credit Measurements (8 points)

This part is optional. You get this credit for clever modifications of the original experiment that allow you to learn something new. Doing "more of the same" is just doing the old experiment better and, while laudable, does not count towards extra credit.

You need to

62. come up with a testable hypothesis,
63. take measurements (zero points if no measurements are made), and
64. draw conclusions apart from the purpose of the assigned experiment.