1. Introduction to Fundamental Physics Laboratory Lecture I
March 11, 2015

2. Oh, my god, where is my body?!

3. If without the egg white separator …3
图片摘自原媛老师的PPT
If without the egg white separator …

4. So easy! After you accept the fundamental physics experiment training,
you can… 4
So easy!
图片摘自原媛老师的PPT

5. Content: Introduction Arrangement Importance of physics experiments
Error and Uncertainty
Significance digit
Uncertainty estimation

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

7. Arrangement 1,2W Lectures All students Dr., 801 3-5W
Each group two students (Registration on web)
1,2W
Lectures
All students
Dr.,
801
3-5W
Lab I, II, Discussion
Group A, B
Dr. Yuan, 804
Lab III, IV, Discussion
Group C, D
Dr. Su, 805B
6-8W

8. Lab VII, VIII, Discussion
Arrangement
9-11W
Lab V, VI, Discussion
Group A, B
Dr. Yuan, 804
Lab VII, VIII, Discussion
Group C, D
Dr. Su, 801
12-14W
15W
Q&A
All students
801
16W
test

9. Lab List, Lab I Lab II Lab III Lab IV Lab V Lab VI Lab VII Lab VIII
Mechanics laboratory — Target hitting through collision
Lab II
Torsional pendulum
Lab III
Frank-Hertz experiment with Neon
Lab IV
X-ray experiment
Lab V
The latent heat of vaporization of liquid nitrogen
Lab VI
Converging Lens
Lab VII
Wheatstone bridge
Lab VIII
Digital oscilloscope

10. Purpose
Master the basic knowledge, the basic approach and basic skills of physics experiments.
Learn to investigate the physical laws by the experimental method, to deepen understanding and mastery of physical laws, and enhance the ability to raise questions in the experiment, analyze and solve 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 in a physics laboratory to others
Cultivate the scientific attitude

11. Importance of physics experiments
Historical view
Classical Physics
Development of modern physics
Support to other fields
Statistic of Nobel Prize

12. Significant figure is very important.12
Significant figure is very important.
To measure an object’s thickness
2cm
2.0cm
2.00cm
2.000cm
These results are different.

13. Learn to estimate is very important！13
Learn to estimate is very important！
How much hair do you have?
1103
1104
1105
1106

14. Rounding method -- very significant effect on the result.14
Rounding method -- very significant effect on the result.
Where many calculations are done in sequence, the choice of rounding method can have a very significant effect on the result. A famous instance involved a new index set up by the Vancouver Stock Exchange in It was initially set at (three decimal places of accuracy), and after 22 months had fallen to about 520 — whereas stock prices had generally increased in the period. The problem was caused by the index being recalculated thousands of times daily, and always being rounded down to 3 decimal places, in such a way that the rounding errors accumulated. Recalculating with better rounding gave an index value of at the end of the same period.[1]
^ Nicholas J. Higham (2002). Accuracy and stability of numerical algorithms. p. 54. ISBN 
讨论：为什么使用“4舍6入，遇5末偶”的修约规则？
（1. 选取修约规则的原则 – 对大量数据进行修约后，误差能达到相互抵消，而不导致互相迭加而积累；
2.本规则假设最后第二位奇偶几率各半，这样一半几率舍去最后第二位的0.5，一半几率增加最后第二位的0.5）。
A famous instance: a new index the Vancouver Stock Exchange in 1982.
Initially ; after 22 mo. ~ 520
(but stock prices had generally increased)
Problem? rounded down 1000s times daily
rounding errors accumulated.
Recalculating -- with better rounding 
Nicholas J. Higham (2002). Accuracy and stability of numerical algorithms. p. 54. ISBN  , by Wikipedia: Rounding

15. Data processing is very important!15
Data processing is very important!
To investigate on the relationship between resistance and temperature of a resistor,
 / ℃
19.10
25.10
30.10
36.00
40.00
45.10
50.10
R / 
76.30
77.80
79.75
80.80
82.35
83.90
85.10
What is the quantitative relationship of R and  ？

16. Error and Uncertainty Error:
Difference between the measured value and the true value
Origin:
Method — Error
Devices
Operator: estimation
Uncertainty

17. Two Examples Left end: 10.00 cm Right end: 15.25 cm
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: cm
Right end: cm

18. 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

19. Uncertainty type A After n time same measurement of unknown x:
uA decreases with increasing n

20. Uncertainty type B From device：
From measurement(For single measurement):
From device：
uB2=a/3 : average distribution,
uB2=a/3 : normal distribution, large n
a: maximum uncertainty of the device, usually given with the device

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

22. 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 significance digits to indicate the uncertainty
e.g., L =1.05cm, uL ~ 0.01cm (not specified)

23. Significance digit: All digits from first nonzero digit:
e.g (2); 3.54 (3); (4); (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
5 - rounding for even end
abandon
rounding

24. 24
If x1= ; x2=
Uncertainty x1 x2
0.0003
3.5484　
3.6532　
0.002
3.548　
3.653　
0.04
3.55　
3.65
0.3
3.5　
3.7　
Rounding：
4 - abandon
6 - rounding
5 - rounding for even end
Results should has the last digit same as the uncertainty!

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

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

27. 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: d =0.1cm，uB1 =d /5；a =0.01cm.
H＝H2－H1, where H1＝4.00cm, H2＝19.32cm；
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
2.014
2.020
2.016
2.018
2.022

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

29. Density ：
Results：

30. Homework: see the webpage or handouts
Question?
Thank you！
Homework: see the webpage or handouts

31. Learning Goals,
By AAPT