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Introduction to Fundamental Physics Laboratory Lecture I

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Introduction toFundamental Physics LaboratoryLecture I

Dr. Yongkang Le

March 5th, 2010

http://phylab.fudan.edu.cn/doku.php?id=course:fund_phy_exp:start

- 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

- Introduction
- Arrangement
- Importance of physics experiment
- Error and uncertainty
- Significance digit
- Uncertainty estimation

- 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

- Each group two students (Registration on web)

- 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

- Historical view
- Classical Physics
- Development of modern physics

- Support to other fields
- Statistic of Nobel Prize

- 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

- Error:
Difference between measured value

and true value

- Origin:
- Method—— Error
- Devices
- Operator: estimation

Uncertainty

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

- ‘‘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

After n time same measurement of unknown x:

uAdecreases with increasing n

where

uB2=a/3 : Average distribution,

uB2=a/3: normal distribution, large n

a: maximum uncertainty of the device, usually

given with the device

- From measurement(For single measurement):
- From device：

Best situation

In case

d: smallest deviation

Worst situation

Single measurement：

For length measurements, since x=x2-x1, we have:

Multiple measurements(n>=5)：

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)

abandon

rounding

5 - rounding for even end

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

+ , -: 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

If the results is calculated:

+ , - :

* , / :

xn：

General equation:

Measured quantities are independ from each other

or

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.

Uncertainty estimation：

For mass：

For height：

Average value of the diameter：

Density ：

Results：