大学物理实验课程绪论english.ppt

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1、Introduction of Physical ExperimentCenter of Physics ExperimentSeptember,200811.1.Why Must You Have the Class of Physical Experiment?2.Measurement,Error and Uncertainty3.Graph and Method of Least Squares4.How Do Your Best during Class?2 1.1.1.1.Why Must You Have the Class of Why Must You Have the Cl

2、ass of Physical Experiment?Physical Experiment?1.1 Effects of Physical Experiment on Science and Technology 1.2 Purposes of the class of Physical Experiment 3Roles of Physical ExperimentRoles of Physical ExperimentPhysics is a science that has developed out of efforts to describe how and why our phy

3、sical environment behaves as it does.The exciting feature of physics is its capacity for predicting the way nature will behave in one situation on the basis of experimental data obtained in another situation.Such Predictions can have a tremendous impact in our lives,for in this sense physics is at t

4、he heart of modern technology.41997：Laser Cooling and Capturing Neutral Atom Steven Chu Cohen-Tannoudji William D.Phillips 1998：Fractional Quantum Hall Effect Robert B.Laughlin Horst L.Stormer Daniel C.Tsui52001：Bose-Einstein Condensation Eric A.Cornell Wolfgang Ketterle Carl E.Wieman6Purposes of th

5、e Class of Physical Purposes of the Class of Physical ExperimentExperiment Learning of Experimental Knowledge Learning of Experimental Knowledge Training of Experimental Ability Training of Experimental Ability Enhancing of Experimental AccomplishmentEnhancing of Experimental Accomplishment7Learning

6、 of Experimental KnowledgeLearning of Experimental Knowledge How to learn?And learn what?Observe and analyze physical phenomena.Measure physical quantities.Master basic skills of experiment and designing ideas.Have an insight into the frame of physics.8Training of Experimental AbilityTraining of Exp

7、erimental Ability Proper use of instruments by means of textbooks or instructions；Elementary analysis and judgment of phenomena by using laws of physics；Correct record and disposal of data,drawing of plots of curves,rational explanation of results,writing of reports；Proper design of experiments in a

8、ccord with experimental purposes and instruments in hand.9Enhancing of Experimental Enhancing of Experimental AccomplishmentAccomplishment(scientific)Style；(serious and earnest)Attitude(of work)；(exploring)Spirit(of research and innovation；Virtues(of abiding by discipline,cooperating,and taking good

9、 care of facilities).10 Hopefully,all of you pay attention to the course,and really get what you want!112.Measurement,Error and Uncertainty2.1 Measurement and Significant Figures2.1 Measurement and Significant Figures2.2 Error and Basic Knowledge of the Estimate of 2.2 Error and Basic Knowledge of t

10、he Estimate of UncertaintyUncertainty12Measurement and Significant FiguresMeasurement and Significant FiguresMeasurementReadings of Significant FiguresOperation of Significant FiguresRules of Rounding off Significant Figures13Measurement Measurement:with the aid of scientific methods,by using proper

11、 tools or instruments,a characterizing physical quantity(measured quantities)is compared with the selected unit of the same kind of the physical quantity,and the ratio is the value of the measured quantity.14Direct measurement：to directly compare,such as length；Indirect measurement：to calculate the

12、value of the measured quantity,with the help of the known function between the measured quantity and the direct measured ones.Value=reading numbers(significant figures)+unitSignificant figurescredible digitsdoubtable digits15Reading of significant figures15.2mm15.0mm16Operation of significant figure

13、s Addition,subtraction：when numbers are added or subtracted，the last significant figure occurs in the first column(counting from right)containing a number that results from a sum of digits that are all significant.4.178 6.30 +21.3 31.778=31.817Multiplication,division：when numbers are multiplied or d

14、ivided,the final answer has a number of significant figures that equals the smallest number of significant figures in any of the original factors.4.178 10.1 4178 4178 42.1978=42.218Power,extraction:a number of significant figures in the answer are the same as a number of the base。3.253=34.3logarithm

15、:the number of digits of the mantissa has the same number of.lg1.938=0.2973 lg1938=3+lg1.938=3.2973Exponent:the number of significant figures is the same as the digits of the exponent after the decimal point(including the zeros next to the decimal point).106.25=1.8 106 ,100.0035=1.00819Trigonometric

16、 Trigonometric functionfunction:the digits vary with the significant figures of the angle.Sin3000=0.5000 Cos2016=0.9381An exact number is not subject to rules of operation of significant figures.A constant has the same significant figures of the measured quantity that has the smallest ones.20rules o

17、f rounding off significant figuresIf the value of the eliminated part is less than a half unit of the last saved digit，the number in the last digit doesnt change.If the value of the eliminated part is greater than a half unit of the last saved digit，the number in the last digit is added by one.If th

18、e value of the eliminated part equals a half unit of the last saved digit，when the number in the last digit is even,it keeps the same;when odd,it is added by one.4.327494.327 4.327614.328 4.327504.328 4.328504.328Generally speaking：four off six up，five even.21Error and Basic Knowledge of the Estimat

19、e Error and Basic Knowledge of the Estimate of Uncertaintyof UncertaintyErrorDisposal of random errorExpression of uncertainty of a measured resultComposition of uncertainty of indirect measurement22As to a physical quantity x being measuredError dx measurement value x true value True value：the actu

20、al value of a physical quantity under a certain experimentError23 There exist errors in all measurements.An error can be made smaller and smaller,but never zero.Therefore,a measurement without an error is meaningless.Error24Systematic errorDefinition：In the course of measuring a quantity many times，

21、the absolute values and the signs of errors remain unchanged or vary in a fixed way with measuring conditions.Reason：measuring instrument,measuring way,environment,and etc.Classification and disposal：1 quantified systematic error：revision.such as zero position errors of a screw micrometer and multim

22、eter,and errors due to ignoring of inner resistors.2 quantified systematic error：estimate of the range of an error.such as thread interval tolerance.25Random errorDefinition：In the course of measuring a quantity many times，the absolute values and the signs of errors vary in an unpredictable manner.R

23、eason：Fluctuations of experimental conditions and environmental factors.26(1)The probabilities of small errors are greater than those of large ones；(2)The distribution of the error probability is a normal distribution function if times of measurement approach to infinity；(3)Cancellation:the arithmet

24、ic average of measurement values can eliminate or cancel the random error.Characteristic of random error27 Degree of dispersion of measured valuesl28 This probability is called fiducial probability,and the corresponding range is called fiducial range.29If the fiducial range is enlarged,the fiducial

25、probability can increase.30Mean value Suppose that a physical quantity is measured n times,and the measured value is xi(i=1,2，n)The arithmetical average is taken as the optimal measured value.When n approaches to infinity,the result is the true value of the quantity.31 When n is finite,the arithmeti

26、cal average is not equal to the true value,and his deviation is as follows：The meaning of ：the probability of the quantity to be measured in the range is 0.683.32 In physical experiments，the fiducial probability is taken as 0.95,and then the fiducial range of T-type distribution can be written as fo

27、llowing:In general，the measurement time n is taken as six.n345672.481.591.241.050.92633Expression of uncertainty of a measured result Uncertainty is an error limit under a certain fiducial probability,and reflects a range of possible error.In general,Fiducial Probability:0.95!34 Type A :the componen

28、t which can be the component which can be estimated by using statistics estimated by using statistics The type of uncertainty35Type B :the component which cannot the component which cannot be estimated by using statistics,be estimated by using statistics,for example,systematic error.for example,syst

29、ematic error.c is c is fiducialfiducial factor.When the factor.When the fiducialfiducial probability is probability is 0.95,c=1.0536Uncertainty:Relative uncertainty:Result:37Attentions：1.Number of significant figures of the 1.Number of significant figures of the arithmetical average doesnt exceed ar

30、ithmetical average doesnt exceed that of the measured value;that of the measured value;2.Uncertainty and relative uncertainty 2.Uncertainty and relative uncertainty have one or two digits of significant have one or two digits of significant figuresfigures；3.The last digit of uncertainty is even 3.Th

31、e last digit of uncertainty is even with that of the average.with that of the average.38 Example one：measurement of diameter of a wire by using a screw micrometer.d0=+0.004 mm,Instrument tolerance:I=0.004mm123456（mm）0.2490.2500.2470.2510.2530.250 Datum table39 Solution for example one：d0=+0.004 mm,I

32、nstrument tolerance:I=0.004mm 123456(mm)0.2490.2500.2470.2510.2530.250(mm)0.2450.2460.2430.2470.2490.246(mm)0.246(mm)0.0010.0000.003-0.001-0.0030.000 None of abnormal data4041Result:Result:42Calculation of uncertainty of indirect measurementCalculation of uncertainty of indirect measurement The meas

33、ured quantity x as a function of directly measured quantities xi：（1 1 1 1）for addition or subtractionfor addition or subtractionfor addition or subtractionfor addition or subtraction.（2 2 2 2）for multiplication,division,power,or exponentfor multiplication,division,power,or exponentfor multiplication

34、,division,power,or exponentfor multiplication,division,power,or exponent.43Often used formulas 44ExampleAll the sizes of a ring are measured as follows.Please,give the final result of its volume.Resolution：2.Resulting uncertainty1.453.Relative uncertainty4.Final result463.Graph and Method of Least S

35、quares 3.1 Disposal of data by graphic method 3.2 Linear Fitting by method of minimum squares472.Choose proper scales for axes to determine the size of coordinate paper.Data table of voltmeter-ammeter method for resistanceProcedure of disposal of data by the graphic method1.Make a table of data.483.

36、Mark the axes：broadened linebroadened line，arrowarrow，sign,name,and sign,name,and unit.unit.I(mA)U(V)8.004.0020.0016.0012.0018.0014.0010.006.002.000 02.004.006.008.0010.001.003.005.007.009.005.Connect the data points smoothly with a line or curve.4.Symbolize data points.496.Give a legend of the grap

37、h.I(mA)U(V)8.004.0020.0016.0012.0018.0014.0010.006.002.000 02.004.006.008.0010.001.003.005.007.009.007.Give a name of graphA(1.00,2.76)B(7.00,18.58)Volt-ampere characteristicsauthorauthor：xxxx50:Improper figures n(nm)1.6500500.0700.01.67001.66001.70001.69001.6800600.0400.0Dispersion of glass Figure

38、151n(nm)1.6500500.0700.01.67001.66001.70001.69001.6800600.0400.0Dispersion of glassCorrected：52Figure 2I(mA)U(V)0 02.008.004.0020.0016.0012.0018.0014.0010.006.002.001.003.00Volt-ampere characteristics53I(mA)U(V)o o1.002.003.004.008.004.0020.0016.0012.0018.0014.0010.006.002.00Volt-ampere characterist

39、icsCorrected：5402468101214161820220246810121416I/mAU /V 0 30 60 90?XXX?XXXX?05-01-15 55Suppose the quantities x,y abide by the linear relation y=a+b x.xi，yi i=1,.,n当When a sum of square differences between the measured yi and amount of a+b xi is minimum,that is,a and b are fitting parameters.Linear

40、Fitting by method of minimum squaresLinear Fitting by method of minimum squares565758 Correlation coefficient r：Except a and b，r must be calculated.r-1，1,|r|1，linearity between x and y is good;|r|0，there is no linearity between x and y,and the linear fitting is meaningless.In physical experiments,|r

41、|is greater than 0.999.where59 Solutions for a,b,and r：1.Excel;2.Origin or Matlab(ftp:/202.120.52.47/pub/origin);3.Programs written by yourself.Before least square method is used,the abnormal points are removed from data!604.How do your best during the class?PreparationPreparationOperationOperationR

42、eportReport61Preparation Objective，Principle，Precaution。621.Name,objective；2.Sketch（electric or optical），3.Formula；4.Data table（known,given,directly-measured,indirectly-measured quantity,and unit）。Do not copy principlesDo not copy principles！Content of preparation report：63Operation1.Abide by rules；

43、2.Understand usage of instruments；3.Do some tentative operations before formal measurements；4.Look around and anatomize experimental phenomena；5.Faithfully record data and phenomena;6.Record Record data data in in pen pen or or ball ball pen.pen.No No change in original data!change in original data!

44、7.7.7.Tidy instruments，and clean up labs.64Contents of a report1.Name；2.Objective；3.Principle（sketch,formula）；4.Instruments；5.Data,calculation,figure,and result；6.Analysis,error evaluation,brief summary,and discussion.65Cautions1.Be in time;It is absenteeism to be late more than ten minutes.2.Before

45、 you leave lab,the data must be checked and sealed by teacher.3.The report(including preparation one)must be delivered into the mail boxes labeled with teacher numbers on the third floor of Experimental Building within a week after the experiment is done.66Rules of credit1.Two credits for the class

46、with eight experiments2.One credit for the first four experiments;another one for the other four experiments.3.Five grades:A,B,C,D,F;Above D,one credit.A:=90,B:89-80;C:79-70;D:69-60;F=59.4.Final score is an average on the four scores.671.One hundred points.2.Preparation:10;3.Operation:40;4.Integrity of a report:40;5.New ideas(innovation):10.Criterion of score68 Friday:form week 2 to week 14,except week 5 first period：8:00-10:40 second period:12:00-14:40 third period:15:20-18:00Class hour69No Pain,No GainNo Pain,No Gain！70