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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

Introduction toFundamental Physics LaboratoryLecture I

Dr. Yongkang Le

March 5th, 2010

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


For share
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


Content
Content

  • Introduction

  • Arrangement

  • Importance of physics experiment

  • Error and uncertainty

  • Significance digit

  • Uncertainty estimation


Introduction
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


Arrangement
Arrangement

  • Each group two students (Registration on web)


Purpose
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


Importance of physics experiment
Importance of physics experiment

  • Historical view

    • Classical Physics

    • Development of modern physics

  • Support to other fields

  • Statistic of Nobel Prize


  • Data processing

  • Normative calculation and expression

  • To derive:

  • Quantitative law and reliable conclusion


Error and uncertainty
Error and Uncertainty

  • Error:

    Difference between measured value

    and true value

  • Origin:

    • Method—— Error

    • Devices

    • Operator: estimation

Uncertainty


Two examples
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


Uncertainty estimation
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


Uncertainty type a
Uncertainty type A

After n time same measurement of unknown x:

uAdecreases with increasing n

where


Uncertainty type b

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


Combination of uncertainty
Combination of Uncertainty

Single measurement:

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

Multiple measurements(n>=5):


Expression of the results
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)


Significant figures

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


Rule in calculation
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


Propagation of uncertainty
Propagation of Uncertainty

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:


Question thank you homework see the webpage
Question?Thank you!Homework: see the webpage


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