1. Introduction to Fundamental Physics Laboratory Lecture I Dr. Yongkang Le March 5 th, 2010 http://phylab.fudan.edu.cn/doku.php?id=course:fund_phy_exp:start

2. For share ☺ In science, there is only physics. All the rest is stamp collecting. By Ernest Rutherford ☺ Experiments are the only means of knowledge at our disposal. The rest is poetry, imagination. By Max Plank

3. Content  Introduction  Arrangement  Importance of physics experiment  Error and uncertainty  Significance digit  Uncertainty estimation

4. Introduction  Name: Fundamental Physics Laboratory  Course duration: ~3 hours  Credit: 2  Content: 2 lectures, 8 labs, 4 discussion and final test (oral)  Marking: labs and discussions 70% test 30%  Supervisors: Mrs. Weifeng Su and Dr. Le

5. Arrangement  Each group two students (Registration on web) Unit 1Unit 2Unit 3Unit 4 1,2 W3-8 W9,12-16 W17 W 2 Lec. H.W. Mech.+Ele. 4 Labs+2 Dis. Th. + Op.+ Mod. 4 Labs+2 Dis. Test Phy.403GH Bld.GH Bld.+Phy. BldN/A LeLe+Su

6. Purpose  Support the learning and understanding of basic physical principles  Assist acquirement of basic techniques for handling the practical problems  To be familiar with the experimental research on the physical phenomena  How to design an experiment to reach the proposed objective  How to analyze the experimental data and the errors  How to report what you obtain a physical experiment to others

7. Importance of physics experiment  Historical view  Classical Physics  Development of modern physics  Support to other fields  Statistic of Nobel Prize

8.  Real Experiment can not be perfect  Most laws are quantitative relationship F=ma  Criterion and convertion c = (299792.50±0.10) km/s Data processing Normative calculation and expression To derive ： Quantitative law and reliable conclusion

9. Error and Uncertainty  Error: Difference between measured value and true value  Origin:  Method—— Error  Devices  Operator: estimation Uncertainty

10. Measuring the length of an object Left end ： 10.00cm Right end ： 15.25cm Display of a digital ammeter 1. When the display is stable ： 3.888A 2. How about when the display is instable ？ Two Examples

11. Uncertainty estimation  ‘‘Guide to the Expression of Uncertainty in Measurement ISO 1993(E)” from BIPM and ISO etc., issued in 1993  Uncertainty--Distribution property of measured results Important ： too large--waste ； too small--wrong 。  Two Type ： Type A--- Evaluated with statistical methods Type B---Evaluated with other methods

12. Uncertainty type A After n time same measurement of unknown x: u A decreases with increasing n where

13. Uncertainty type B Uncertainty type B  From measurement(For single measurement):  From device ： Best situation  In case Worst situation d: smallest deviation u B2 =a/  3 : Average distribution,  u B2 =a/3: normal distribution, large n a: maximum uncertainty of the device, usually given with the device

14. Combination of Uncertainty Single measurement ： For length measurements, since x=x 2 -x 1, we have: Multiple measurements(n>=5) ：

15. Expression of the results 1 、 Usually ： e.g., L = 1.05±0.02 cm. 2 、 Percentage expression of the uncertainty ： e.g., L =1.05cm ， percentage uncertainty 2%. 3 、 Use significant figures to indicate the uncertainty e.g. L =1.05cm, u L ~ 0.01cm (not specified)

16. Significant figures All digits from first nonzero digit: e.g. 0.35 (2); 3.54 (3); 0.003540 (4); 3.5400 (5) 。 Uncertainty is usually given in one digit(max 2). Results should has the last digit same as the uncertainty. i.e. ： The last digit of the result is uncertain. Rounding ： 4 - abandon 6 - rounding 5 - rounding for even end e.g. ， x=3.54835 or 3.65325 If u x =0.0003, then x=3.5484; 3.6532 If u x =0.002, then x=3.548 ； 3.653 If u x =0.04, then x=3.55; 3.65 If u x =0.1, then x=3.5; 3.7 5 - rounding for even end abandon rounding

17. Rule in calculation +, -: highst digits 57.31 ＋ 0.0156 － 2.24342 （ =55.08218 ） =55.08 *, / : minimum significant figures 57.31×0.0156÷2.24342 （ =0.398514767 ） =0.399

18. If the results is calculated: +, - : *, / : x n ： General equation: Measured quantities are independ from each other Propagation of Uncertainty or

19. Example ： Density of a metal cylinder Mass measured with an electronic balance: M=80.36g, d =0.01g, a =0.02g. Height measure with a ruler:H ＝ H 2 － H 1, where H 1 ＝ 4.00cm, H 2 ＝ 19.32cm ； d =0.1cm ， u B1 =d /5 ； a =0.01cm. Diameter measure with a slide callipers (D data are given in the table); d =0.002cm ； a =0.002cm 。 Please calculate the density and its uncertainty. D/cm 2.0142.0182.0162.0202.018 2.0202.0222.0162.020

20. Uncertainty estimation ： For mass ： For height ： Average value of the diameter ：

21. Results ： Density  ：

22. Question? Thank you! Homework: see the webpage