The Falling Body

The Falling Body Physics Experiment 2 Lab Report Purpose/Goal: The purpose of this experiment is to apply the least squares fit method and statistical analysis methods from Experiment 1 to interpret data of a falling bob. Its position will be measured at specific time intervals, which will allow for construction of a velocity versus time graph of the falling bob. A best fit line will be created to best represent the data and finally gravitational acceleration will be experimentally calculated and compared to the accepted value of gravitational acceleration, 9.81 m/s2. Procedure: 1) Analyze the image of ticker tape to read the positions of the falling bob at each time recorded and copy the image to lab report. 2) Make note of how marks are spread out and what it means. 3) Make an Excel spreadsheet, make room for 31 rows, and label the first five columns Mark #, Time (s), Meter Stick Reading (cm), Fall Distance (cm), and Velocity (cm/s). 4) Using the image of the ticker tape, measure the position of each mark and record it in the table. 5) Enter the time that each mark was created into its column. 6) Calculate the distance that the bob fell, and put these results in the spreadsheet 7) Calculate the velocity of the bob at each point and record these results in the spreadsheet. 8) Create a graph of the bob position versus time. 9) Create a graph of the velocity of the bob versus time. 10) Create a trendline for the velocity versus time graph, including the equation for the line and the R2 value. 11) Determine acceleration of the falling bob. 12) With the LINEST function, obtain least squares analysis of the velocity versus time data. 13) Determine the acceleration with the most probable error of the falling bob using the LINEST values. 14) Calculate percent error of the experimental value if it isn’t within probable error of the accepted value of gravitational acceleration (9.81 m/s2) Figure 1: ticker tape with position markers of the falling bob Data: Graphs: Questions: 3) The marks start out somewhat clumped at the beginning of the ticker tape but gradually start spreading out as each 1/60 of a second passes. The distance between the marks gets larger and larger for each passing 1/60 second. It falls with increasing speed. 12) The line of best fit matches the data points very well, as an R2 value very close to 1 indicates a very strong data correlation. 13) Based on the Velocity versus Time graph of the falling bob, the (experimental) acceleration of gravity is 9.73 m/s2. 16) No, the experimental value found for g with probable error does not include the accepted value of g in its range. Results: The calculated slope and intercept were (972 +/- 4) cm/s2, and (5 +/- 1) cm/s2, respectively. These measurements can be converted in to meters to obtain the experimental g value, as follows: (9.72 +/- 0.04) m/s2. Since my experimental g value doesn’t include the accepted g value in its probable error range, percent error calculations will be necessary. (9.81-9.72)/9.81 x 100% = 0.92% error Conclusion: My experimental value of g obtained for this lab is 9.73 m/s2. From my results, I can conclude that my experiment was conducted and analyzed very well, since the R2 value for the velocity versus time graph is extremely close to 1. Although the experimental g value doesn’t include the accepted g value in its probable error range, the percent error is extremely low (0.9%) which shows the validity and accuracy of this experiment. The objectives were successfully met and the results stand for themselves in support of this. Discuss your overall conclusions of the experiment, what conclusions can you draw from your results? Think back to your stated purpose, discuss whether your objectives were met and if the lab was successful. Support your claim. Error Analysis: The main source of error in this experiment would be systematic error. Systematic error would be introduced as I read and interpret the dots on the ticker tape because there are exact values but my possible consistent bias in reading them would somewhat skew the values. It’s also not terribly helpful that the ticker tape image is somewhat blurry, which introduces even more systematic error. If each of my readings were off by same amount from the actual values, the calculated acceleration wouldn’t change. Because that’s not likely, though, the calculated acceleration and velocity will be higher or lower than the accepted values depending on how the measurements differed from the actual values. This would result in a R2 value that is far from 1, meaning that the data isn’t very well correlated.