Let's examine our first lab in a bit of detail. The scores ranged from 4/10 to 8/10 with an average score of 6.1. This is a bit lower than it should be, but it was our first lab report. There are a few simple things that will easily boost the scores. Below are excerpts from the "Format of the Report" paragraph of the "Lab Rules" section of the Physics 241 Curriculum page (check it out!), with a few additional comments.
Format of the Report
ITEM #3 - Data (all measurements or information necessary to make calculations). All raw data should be kept in a neat, table format. Calculated quantities are not raw data!
For the acceleration lab, this would be a table of positions and times for your chosen 10 dots on the waxed paper, and a complete table of all times and positions for the runner. Even if you decided to analyze only part of the runner data, show all of it. Then explain why you analyzed only portions. Actually, only a few lab reports were deficient in this area.
ITEM #4 - Sample calculations, include one sample of each type. Do not include all calculations, only one of each type.
The unique sample calculations for this lab should have been something as follows:
1. v1 = (x1 - x0) / (t1 - t0) = (3.1 - 2.4) cm / .0167 s = 42 cm/s
2. a2 = (v2 - v1) / (t2 - t1) = (56 - 42) cm/s / .0167 s = 840 cm/s2
(If you obtained your value of g from the slope of a plot of v vs t, then you would show the slope calculation or make reference to the computer fitted value.)
3. And you would have had similar calculations for the runner section.
ITEM #5 - Results - keep your results in a table format. (Results can be in the same table as the data).
All of the data that you plotted should have been in a table "somewhere". I think it would have been best for the velocities for the freefall torpedo to be in the same table as the positions and times. But there are no hard rules about this. There may be times when a separate table works better. But the results of a repeated calculation should be in a table!
ITEM #6 Conclusions - (What did you prove or disprove?) The conclusion can be short and sweet when appropriate. But it should be meaningful. " ... the acceleration of the runner was not constant and there were some errors." is not much of conclusion. Explain qualitatively how the acceleration change and why that change was or was not expected.
Be sure to proof read your report. There were far too many examples like this " ... and our results showed that the velocity due to gravity was constant."
Often the conclusions reflected what the reporter expected and clearly did not reflect the actual results. There were reports that stated g was a constant, when the results indicated otherwise. Sometimes experiments don't give you what you expect. Double check your work (and come see me for help!), but always write about the actual results. The error in your results should also be in the conclusion, and that's is the final topic.
ITEM #7 Error Analysis.
Finding the difference between your value of g and the book value does not represent the error in your value. It is a difference. Sometimes it is appropriate to compare your calculation to those of others, but it is just a difference, not your error. The error represents the uncertainty in your calculated value that arises from the uncertaintly in your measurements. Let's assume that you are confident of your measurements of the dots to ±.5 mm. And you assumed that WAPA kept a steady beat and the error in time was negligible. For the error in the calculation of the velocity, you would have
v1 = (3.1±.05 - 2.4±.05) cm / .0167 s = (.7±.1) / .0167 = 42 ±6 cm/s
where the ±6 comes from ±.1/.0167. That's right, a whopping ±6 cm/s ! You will have similar error for all the velocities. If you calculated average accelerations (as opposed to using the slope from a v vs t plot at this stage) then you just repeat the process. For example, the next calculation might look like ...
a = (56±7 - 42 ±6 ) cm/s / .0167 s = 14 ±13 cm/s / .0167 s = 840±790 cm/s2
The error is almost the size of your value! Many of you had values such as 1024, 720, 720, 1024, 1450 cm/s2 ...etc. The error analysis would easily have explained this. But the average of all the acceleration values might still have yielded a reasonable result (i.e about 980 cm/s2), since the errors should "average out". Of course, this works very well when you have lots of data and perhaps not so well when you have only a few points. And now for the runner part of the lab.
Assume that you carefully measured the distances so that the error in distance could be ignored. The obvious error was in the timers. There were two approaches for the runners data. First, you could simply look at the range of velocity values you got for all the runs. If the highest value for the first 15 ft was 30 ft/s and the lowest was 22 ft/s, then you could report the average of all the runs with the range for the error as
v1 = 25.6 +4.3/-3.6 ft/s or perhaps 25.6 ±4 ft/s
The error in acceleration would then follow as we did above for the freefall section. You might have also decided to assume a reasonable error in time based upon reflexes. A very typical value often cited in text books is .1 sec. (It would be even better to have actually checked the reaction times of the individual timers and used those values. But that would almost require another lab!) So how does the .1 sec error effect the velocity calculation? You are dividing by t, so you must add % errors. For example,
v1 = (15-0) ft / (.61±.1s) = 15 / (.61±17%) = 24.6 ±17% ft/s (or 24.6 ±4.2 ft/s where 4.2 comes from .17 x 24.6)
The next step would introduce about another 17% error (since you would be dividing by time again) and the % errors would continue to add. If you are not comfortable with the % error method, simply use the "high/low" method.
vhigh = (15-0) ft / (.61-.1s) = 15 / .51 = 29.4 ft/s
vlow = (15-0) ft / (.61+.1s) = 15 / .71 = 21.1 ft/s
for a range of 29.4 - 21.1 = 8.3 and you express the error as 24.6±4.2 ft/s
A final note. The error treatment can be done separately, but it is probably just as efficient to do it with your sample calculations. One final note. It is also often acceptable to find a good average error calculation and use that for all the data. For example, you could take the velocity and acceleration calculations near the middle of the table and find the total error there and use that a good average, since you are going to average all the values in the end.
Our next lab will involve measuring angles on a hill and using the stopwatches. So you'll have significant errors again and you'll get a second chance at error analysis. Come see me if you have any questions or you are not getting the results you expect!