Introduction toIntroduction toFundamental Physics LaboratoryFundamental Physics Laboratory

Lecture ILecture I

Dr. Yongkang LeDr. Yongkang LeMarch 5March 5thth, 2010, 2010

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☺ 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

ContentContent

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

IntroductionIntroduction 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

ArrangementArrangement Each group two students (Registration on web)

Unit 1 Unit 2 Unit 3 Unit 4

1,2 W 3-8 W 9,12-16 W 17 W

2 Lec.

H.W.

Mech.+Ele.

4 Labs+2 Dis.

Th. + Op.+Mod.

4 Labs+2 Dis.Test

Phy.403 GH Bld. GH Bld.+Phy. Bld N/A

Le Le+Su Le+Su Le+Su

PurposePurpose Support the learning and understanding of basi

c physical principles Assist acquirement of basic techniques for han

dling 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

Importance of physics experimentImportance of physics experiment

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 processingNormative calculation and expression

To derive ：Quantitative law and reliable conclusion

Error and UncertaintyError and Uncertainty Error:

Difference between measured value

and true value Origin:

Method—— Error Devices Operator: estimation

Uncertainty

Measuring the length of an object

Left end： 10.00cmRight 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 ExamplesTwo Examples

Uncertainty estimationUncertainty 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

Uncertainty type AUncertainty type AAfter n time same measurement of unknown x:

uA decreases with increasing n

where

Uncertainty type BUncertainty type B From measurement(For single measurement):

From device：

2B

au

c

Best situation

In case

Worst situation

d: smallest deviation

uB2=a/3 : Average distribution, uB2=a/3 : normal distribution, large na: maximum uncertainty of the device, usually given with the device

Combination of Combination of UncertaintyUncertaintySingle measurement：

)()()( 22

21 xuxuxu BB

)()()()( 222

211

21 xuxuxuxu BBB

2 22( ) ( ) ( )A Bu x u x u x

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

Multiple measurements(n>=5)：

Expression of the resultsExpression 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, uL ~ 0.01cm (not specified)

)(xux

%100)(

x

xu

Significant figuresSignificant figuresAll 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 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

5 - rounding for even end

abandon rounding

Rule in calculationRule 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

If the results is calculated:

+ , - : * , / : xn：

General equation: Measured quantities are independ from each other

22)()(

x

xun

y

yunxy

Propagation of UncertaintyPropagation of Uncertainty

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.

D/cm2.014 2.018 2.016 2.020 2.018

2.018 2.020 2.022 2.016 2.020

Uncertainty estimation：For mass：

g015.0g3

02.001.0))(())(()(2

222

21

MuMuMu BB

cm32.15cm)00.432.19(12 HHH

cm029.0cm3

01.002.02)()(2)(2

222

21

HuHuHu BB

cm0184.210

1 10

1

i

iDD

cm00078.0 )110(10

)()(

10

1

2

i

i

A

DDDu

cm0014.0cm3

002.0)00078.0())(())(()(2

222

2

DuDuDu BA

For height：

Average value of the diameter：

3322 cmg639.1

cmg

32.15)0184.2(1416.3

36.8044

HD

M

V

M

222)()(

2)()(

H

Hu

D

Du

M

Muu

2 2 2

0.015 0.0014 0.0292

80.36 2.0184 15.32

33 cmg004.0

cmg639.1%24.0

)()(

u

u

33

3 mkg10)004.0639.1(

cmg)004.0639.1()( u

%24.01058.31092.11048.3 668

Results：

Density ：

Question?Question?

Thank you!Thank you!

Homework: see the webpageHomework: see the webpage