Experimental Physics Fall 2024 Lecture Notes PDF

Experimental Physics Fall-2024 Dr. William C. Mahone Experimentation Experimentation is the process of carrying out objective tests to ascertain facts about phenomena. There are 2 primary objective reasons for experimentation. Testing of a prediction based on an hypo...

Experimental Physics Fall-2024 Dr. William C. Mahone Experimentation Experimentation is the process of carrying out objective tests to ascertain facts about phenomena. There are 2 primary objective reasons for experimentation. Testing of a prediction based on an hypothesis. Generation of a data base on which to form an hypothesis Steps to Experimantation Formulate an Objective Formulate an approach Formulate a detailed set of procedures Raw Data Generation Process Data Present Results {Key Data; Data that will be used to make conclusions) Raw data and processed data go in the Appendix. Discuss data and make conclusions Experimental Data Three kinds of numbers are generated during an experiment. Indefinite: Numbers generated by a measurement. Definite: Numbers generated by a theoretical calculation or a commonly accepted experimental number. Given: A chosen experimental quantity. Also definite. Indefinite numbers have an uncertainty zone around an average number. Definite numbers and givens are exact. No uncertainty. Results(1) ; Data Processing Organize raw data tables, Use raw data to perform all necessary calculations. Generate averages, average uncertainty, and percent differences. Generate uncertainty zones. Results (2); Data Analysis. Compare data and notice data trends Compare experimental data and theoretical predictions. Using percent difference. Specify Quality of data using uncertainty zones and percent deviations. Results and Discussion What does data mean? How does data answer the objective? Integrity of experiment i.e. was it good? What are possible sources of error ? How does error affect data and conclusions? Grading Lab Reports Your Lab Report Grade will depend on several factors. How well do you understand the subject. (Introduction) How well do you understand the relationship between the data and the objective.(the approach) Your ability to identify key data. Your ability to make conclusions about the objective based on the data. Most important is readability. I.e. Anyone reading your report should be able to understand what you are trying to communicate. Example of data processing Let “A” be a measured number, “B” be a given, and “C” a theoretical number that can be calculated from “A” and “B” Let C = 5 x A/B, the theoretical value for C is 2 For “B” = 10 measure “A” 5 times A1 = 3.7, A2 = 4.1, A3 = 3.9, A4= 4.2, A5 = 3.8 Example of data processing C = 5 x A/B, the theoretical value for C is 2 For “B” = 10 measure “A” 5 times A1 = 3.7, A2 = 4.1, A3 = 3.9, A4= 4.2, A5 = 3.8, then C1= 5 x 3.7/10, C2 = 5 x 4.1/10, C3 = 5 x 3.9/10, C4= 5 x 4.2/10 And C5 = 5 x 3.8/10 Example of data processing C1= 5 x 3.7/10, C2 = 5 x 4.1/10, C3 = 5 x 3.9/10, C4= 5 x 4.2/10 And C5 = 5 x 3.8/10 thus C1 =  A B C 3.7 10 1.85 4.1 10 2.05 3.9 10 1.95 4.2 10 2.1 3.8 10 1.9 C dev 1.85 0.12 2.05 0.08 1.95 0.02 2.1 0.13 1.9 0.07 avg C = 1.97avg Dev = 0.084 % dev = 4.264 % diff = 1.5 unzone = from 1.89 to 2.05 low 1.886 high 2.054 Key Data Average C +/- Avg Deviation +/- % deviation 1.97 +/- 0.89 +/- 4.3 % Theoretical C = 2 Uncertainty Zone Between 1.89 and 2.05 % Difference (avg C – theo C)/theo C x 100 (1.97 -2)/2 x 100 = 1.5% Conclusions The experiment was well done be cause of the low % deviation 4.5% and the low percent difference 1.5%. This suggests that the data is highly precise and highly accurate. Also note that the theoretical “C” which is 2 is inside the uncertainty zone of 1.89 to 2.05. This also suggests that the experiment is accurate. Because of the high accuracy and low uncertainty suggest that there were no major errors associated with the experiment. Also the high accuracy validates the equation used to calculate “C” A Comparison Between 2 different Measurement Techniques! Often a experiment will require 2 different measurement techniques to validate a theoretical number. When an experiment requires the generation of 2 or more data sets, One may wind up comparing 2 or more numbers each with their own uncertainty zone. When this occurs there will be a variety of ways to compare the 2 data sets. When comparing 2 data sets Identical; When both average values are inside each others uz. Very Similar: When only one of the averages are inside the uz of the other average. Slightly Similar: When both averages are outside the other’s uz but the uz themselves overlap. Different; When the uz do not overlap at all. For the data sets below process the data and identify key data. First for a single data set, then for two data set. Make conclusions for single data set and the 2 data set. Write up analysis and submit via email by dye date. Comparison of theoretical data and single data set. True C = 4.6 set1 A 6.5 c = a x 5/b 6.2 6.8 C = 4.6 7 6.3 B=7 Comparison of two data sets with theoretical True C = 4.6 for both data sets. set1 set2 A B=7 A B= 34 6.5 c = a x 5/b 15.7 c = a x11/b 6.2 15.9 6.8 14.7 Theoretical C = 4.6 7 15 6.3 14.4