Experiment - Acceleration of Gravity and Error Analysis

EVALUATION OF DATA

1. How do you account for the fact that the values of the slope were nearly the same, whereas the values of the intercept were much more variable?

2. It is highly unlikely that you obtained identical values of the slope of the best-fit line to the velocity vs. time graph for each of your trials. How might you best report a single value for the acceleration due to gravity, g, based on your results? Perform the necessary calculation.

3. How does your experimental value compare to the generally accepted value (from a text or other source)? One way to respond to this question is to determine the percent difference between the value you reported and the generally accepted value. Note that if you simplify your units of slope, they will match those of the reported values of g.

4. Your determination of the percent difference does little to answer such questions as, "Is my average value for g close enough to the accepted value?" or "How do I decide if a given value is too far from the accepted value?" A more thorough understanding of error in measurement is needed. Every time you make a measurement, there is some random error due to limitations in your equipment, variations in your technique, and uncertainty in the best-fit line to your data. Errors in technique or in the calibration of your equipment could also produce systematic error. We'll address this later in the experiment. In order to better understand random error in measurement, you must return to your experimental apparatus to collect more data.

5. Begin the data-collection program as you did before and drop the picket fence through the photogate another 35 times, bringing the total number of trials to 35. Since you are now investigating the variation in the values of g AND v0, you need only record the value of the slope and intercept of the best-fit line to the velocity-time graph for each trial.

6. Close Logger Pro file. Disconnect the photogate from the interface. Open a blank file (double click the Logger Pro shortcut.) The program should open with a table of X and Y columns. Paste the 35 trials into the Y column. To facilitate the evaluation of the data you have obtained for the 35 trials you have performed, and enter your values of slope into a new Logger Pro file.

7. Determine the average value of g for all 35 trials. How does this compare with the value you obtained for the first 5 trials? In which average do you have greater confidence? Why?