Maggie has written an excellent report and received a total grade of 19 outof a possible 20 points for this experiment. The grading commentary below isorganized according to the Grading Breakdown given in the experiment notes. When grading a report, the TA should give feedback both on what was donecorrectly as well as what could use improvement. (Due to time constraints,though, these notes are much more detailed than those your TA will use. Please ask your TA for any necessary clarifications of their own grading notes.)
Maggie's purpose statement is good in that it gives both the goal of theexperiment (to determine the mathematical relationship...)and some indication as to how that goal is to be reached (by studying thegraphs...). Either one of these things alone would have resulted in ascore of 0.5 out of the possible 1 point. If her purpose statement had missedthe point of the experiment she would have recieved a grade of 0 for thissection of the report.
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Maggie's results section is good in that she has both given the equationsfor the best fit lines for each of the three graphs and has stated the correctmathematical relationship between the period of the oscillation and thediameter of the ring. The first two sentences in the results section describethe relevant information about the shapes of the graphs, so the table was notstrictly necessary. It is good, though, to see how she checked the linearityof her graphs.
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One of the four points for the calculation section was assigned to thecalculation of the average period. She recieved only 0.5 out of the possible 1 point for this calculation because, although the equation was correct, she should have shown one calculation of the average period complete with numbers.
Another 1 point for the calculation section was assigned to the calculationof d2 and d1/2. Maggie chose to do these calculations within the spreadsheet. This is OK if you show one example of theeach of the calculations. She does so, but once again it would have beenbetter for her to show one of each of these calculations complete with numbers. She therefore recieved 0.5 out of the possible 1 point for these calculations.
The remaining 2 points for the calculation section were assigned to thedetermination of the best fit lines for the three graphs. 1 point would beawarded for using a ruler to guesstimate the best straight line through thedata. 2 points would be awarded for using the linear regression function inthe spreadsheet to determine the actual best fit line through the data. Maggieused linear regression and has included the regression output for each of thethree graphs. She therefore recieved a full 2 points for this part of thecalculation section.
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Each data point on the graph is clearly marked. Maggie chose good scales for each of her graphs so that the data points fill the entire space rather than being shown in one small section of the graph. The two variables are shown on the appropriate axes. The graph has an appropriate title and each axis is labeled clearly with the name, symbol, and units of the appropriate parameter. The best fit line through the data is plotted on the graph. She could also have included a smooth curve through the data points. Because she used good graphing technique on all three graphs,Maggie recieved a full 4 points for the graphing section of her report.
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In an analysis section it is important to explainwhat conclusions you have drawn from your results AND why youcame to those conclusions. In a good English paper, quotes are used to supportone's analysis of the text. In a good physics lab report, you should givereferences to your data, graphs, etc. to support your conclusions.
The Analysis Notes asked students to discuss the shapes of the three graphsand to explain how the shapes helped them determine the correct mathematicalrelationship. Maggie does this in two ways. In her first paragraph, she discusses the regression output from the best fit lines produced using herspreadsheet program. She explains that she compared the R-squared values sinceR-squared=1 is a perfectly straight line. She the supports her conclusion thatGraph 3 showed the correct mathematical relationship with references to hernumerical results. In her second paragraph, she discusses the visual appearance of the graphs themselves. Even justifies the use of d2 and d1/2 because of the parabolic shape of the T versus d graph. Either one of these two paragraphs would have been a sufficient analysis of her graphs. That she used both is a bit of overkill, but it shows that she truly understands the experiment.
The Analysis Notes also asked students to discuss any experimental error intheir measurements. In her last paragraph, Maggie talks about two places whereexperimental error could have affected her results - the measurements of thediameters and the measurements of the oscillation times. She also explainsthat the error in the diameter measurement was reduced by using larger andlarger rings and that the error in the time was reduced by using the averageover twenty oscillations rather than measuring only one oscillation. She couldhave expanded on this analysis by giving an estimate of the sizes of theseerrors.