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Introduction to Fundamental Physics Laboratory Lecture I

Introduction to Fundamental Physics Laboratory Lecture I. Dr. Yongkang Le March 5 th , 20 10 http://phylab.fudan.edu.cn/doku.php?id=course:fund_phy_exp:start. For share. In science, there is only physics. All the rest is stamp collecting. By Ernest Rutherford

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Introduction to Fundamental Physics Laboratory Lecture I

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  1. Introduction toFundamental Physics LaboratoryLecture I Dr. Yongkang Le March 5th, 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)

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

  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: uAdecreases with increasing n where

  13. uB2=a/3 : Average distribution,  uB2=a/3 : normal distribution, large n a: maximum uncertainty of the device, usually given with the device Uncertainty type B • From measurement(For single measurement): • From device： Best situation  In case d: smallest deviation Worst situation

  14. Combination of Uncertainty Single measurement： For length measurements, since x=x2-x1, we have: Multiple measurements(n>=5)：

  15. Expression of the results 1、Usually： e.g., L = 1.05±0.02cm. 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, uL ~ 0.01cm (not specified)

  16. abandon rounding 5 - rounding for even end 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 or3.65325 If ux=0.0003, then x=3.5484; 3.6532 If ux=0.002, then x=3.548； 3.653 If ux=0.04, then x=3.55; 3.65 If ux=0.1, then x=3.5; 3.7

  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. Propagation of Uncertainty If the results is calculated: + , - : * , / : xn： General equation: Measured quantities are independ from each other 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＝H2－H1, where H1＝4.00cm, H2＝19.32cm；d =0.1cm，uB1 =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.

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

  21. Density ： Results：

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

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