1、1,Introduction of Physical Experiment,Center of Physics ExperimentSeptember, 2008,2,1. Why Must You Have the Class of Physical Experiment? 2. Measurement,Error and Uncertainty 3. Graph and Method of Least Squares 4. How Do Your Best during Class?,3,1. Why Must You Have the Class of Physical Experime
2、nt?,1.1 Effects of Physical Experiment on Science and Technology 1.2 Purposes of the class of Physical Experiment,4,Roles of Physical Experiment,Physics is a science that has developed out of efforts to describe how and why our physical environment behaves as it does. The exciting feature of physics
3、 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 the heart of modern technology.,5,1997：Laser Cooling and Capturing
4、Neutral AtomSteven Chu Cohen-Tannoudji William D. Phillips 1998：Fractional Quantum Hall EffectRobert B. Laughlin Horst L. Stormer Daniel C. Tsui,6,2001：Bose-Einstein CondensationEric A. Cornell Wolfgang Ketterle Carl E. Wieman,7,Purposes of the Class of Physical Experiment,Learning of Experimental K
5、nowledge Training of Experimental Ability Enhancing of Experimental Accomplishment,8,Learning 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 f
6、rame of physics.,9,Training of Experimental 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 re
7、ports； Proper design of experiments in accord with experimental purposes and instruments in hand.,10,Enhancing of Experimental Accomplishment,(scientific) Style； (serious and earnest) Attitude ( of work)； (exploring) Spirit ( of research and innovation； Virtues ( of abiding by discipline, cooperatin
8、g, and taking good care of facilities ).,11,Hopefully, all of you pay attention to the course, and really get what you want!,12,2. Measurement, Error and Uncertainty,2.1 Measurement and Significant Figures 2.2 Error and Basic Knowledge of the Estimate of Uncertainty,13,Measurement and Significant Fi
9、gures,Measurement Readings of Significant Figures Operation of Significant Figures Rules of Rounding off Significant Figures,14,Measurement,Measurement: with the aid of scientific methods, by using proper tools or instruments, a characterizing physical quantity( measured quantities ) is compared wit
10、h the selected unit of the same kind of the physical quantity, and the ratio is the value of the measured quantity.,15,Direct measurement：to directly compare, such as length； Indirect measurement：to calculate the value of the measured quantity, with the help of the known function between the measure
11、d quantity and the direct measured ones. Value = reading numbers( significant figures )+unit Significant figurescredible digitsdoubtable digits,16,Reading of significant figures,15.2mm15.0mm,17,Operation of significant figures,Addition, subtraction：when numbers are added or subtracted，the last signi
12、ficant figure occurs in the first column (counting from right) containing a number that results from a sum of digits that are all significant.4.1786.30+ 21.3 31.778 = 31.8,18,Multiplication, division：when numbers are multiplied or divided, the final answer has a number of significant figures that eq
13、uals the smallest number of significant figures in any of the original factors.4.178 10.14178 417842.1978=42.2,19,Power, extraction: a number of significant figures in the answer are the same as a number of the base 。3.253 = 34.3 logarithm: the number of digits of the mantissa has the same number of
14、 . lg1.938 = 0.2973lg1938 = 3 + lg1.938 = 3.2973 Exponent: 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 = 1.008,20,Trigonometric function: the digits vary with the sig
15、nificant figures of the angle.Sin3000= 0.5000Cos2016= 0.9381 An 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.,21,rules of rounding off significant figures,If the value of the
16、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 the value of the eliminated part equals a half unit o
17、f 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 4.327614.3284.327504.328 4.328504.328 Generally speaking：four off six up，five even.,22,Error and Basic Knowledge of the Estimate of Uncertainty,Error Disposal of random erro
18、r Expression of uncertainty of a measured result Composition of uncertainty of indirect measurement,23,As to a physical quantity x being measured Error dx measurement value x true value ,True value：the actual value of a physical quantity under a certain experiment,Error,24,There exist errors in all
19、measurements. An error can be made smaller and smaller, but never zero. Therefore, a measurement without an error is meaningless.,Error,25,Systematic error,Definition：In the course of measuring a quantity many times，the absolute values and the signs of errors remain unchanged or vary in a fixed way
20、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 multimeter,and errors due to ignoring of inner resistors. quantified systematic er
21、ror： estimate of the range of an error.such as thread interval tolerance.,26,Random error,Definition：In the course of measuring a quantity many times，the absolute values and the signs of errors vary in an unpredictable manner.Reason ：Fluctuations of experimental conditions and environmental factors.
22、,27,(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 arithmetic average of measurement values can eliminate or cancel the ran
23、dom error.,Characteristic of random error,28,Degree of dispersion of measured values,l,29,This probability is called fiducial probability, and the corresponding range is called fiducial range.,30,If the fiducial range is enlarged, the fiducial probability can increase.,31,Mean value Suppose that a p
24、hysical 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.,32,When n is finite, the arithmetical average is not equal to the true value, an
25、d his deviation is as follows：The meaning of ： the probability of the quantity to be measured in the range is 0.683.,33,In physical experiments，the fiducial probability is taken as 0.95,and then the fiducial range of T-type distribution can be written as following:In general，the measurement time n i
26、s taken as six.,34,Expression 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!,35,Type A : the component which can be estimated by using statistics,The type of uncer
27、tainty,36,Type B : the component which cannot be estimated by using statistics, for example, systematic error. c is fiducial factor. When the fiducial probability is 0.95, c = 1.05,37,Uncertainty:Relative uncertainty:Result:,38,Attentions：,1. Number of significant figures of the arithmetical average
28、 doesnt exceed that of the measured value; 2. Uncertainty and relative uncertainty have one or two digits of significant figures； 3. The last digit of uncertainty is even with that of the average.,39,Example one：measurement of diameter of a wire by using a screw micrometer.,Datum table,40,Solution f
29、or example one：,None of abnormal data,41,42,Result:,43,Calculation of uncertainty of indirect measurement,The measured quantity x as a function of directly measured quantities xi：（1） for addition or subtraction. （2） for multiplication, division, power, or exponent.,44,Often used formulas,45,Example,
30、All the sizes of a ring are measured as follows. Please, give the final result of its volume.,Resolution：,2. Resulting uncertainty,1.,46,3. Relative uncertainty,4. Final result,47,3.Graph and Method of Least Squares,3.1 Disposal of data by graphic method 3.2 Linear Fitting by method of minimum squar
31、es,48,2.Choose proper scales for axes to determine the size of coordinate paper.,Data table of voltmeter-ammeter method for resistance,Procedure of disposal of data by the graphic method,1. Make a table of data.,49,3.Mark the axes：broadened line，arrow，sign, name, and unit.,5.Connect the data points
32、smoothly with a line or curve.,4.Symbolize data points.,50,6.Give a legend of the graph.,7.Give a name of graph,51,: Improper figures,52,Corrected：,53,Volt-ampere characteristics,54,Corrected：,55,56,Suppose the quantities x, y abide by the linear relation y = a + b x.xi，yi i = 1,n 当When a sum of squ
33、are differences between the measured yi and amount of a +b xi is minimum, that is, a and b are fitting parameters.,Linear Fitting by method of minimum squares,57,58,59,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 li
34、nearity between x and y, and the linear fitting is meaningless.In physical experiments, |r| is greater than 0.999.,where,60,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 a
35、re removed from data!,61,4. How do your best during the class?,Preparation Operation Report,62,Preparation,Objective，Principle，Precaution。,63,Name, objective； Sketch（electric or optical）， Formula； Data table（known, given, directly-measured, indirectly-measured quantity, and unit）。Do not copy princip
36、les！,Content of preparation report：,64,Operation,Abide by rules； Understand usage of instruments； Do some tentative operations before formal measurements； Look around and anatomize experimental phenomena； Faithfully record data and phenomena;Record data in pen or ball pen. No change in original data
37、! 7. Tidy instruments，and clean up labs.,65,Contents of a report,Name； Objective； Principle（sketch, formula）； Instruments； Data, calculation, figure, and result； Analysis, error evaluation, brief summary, and discussion.,66,Cautions,Be in time; It is absenteeism to be late more than ten minutes. Bef
38、ore you leave lab, the data must be checked and sealed by teacher. 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.,67,Rules of credit,Two credits for th
39、e class with eight experiments One credit for the first four experiments; another one for the other four experiments. Five grades: A, B, C, D, F; Above D, one credit. A:=90,B:89-80;C:79-70;D:69-60;F=59. Final score is an average on the four scores.,68,One hundred points. Preparation: 10; Operation: 40; Integrity of a report: 40; New ideas( innovation ): 10.,Criterion of score,69,Friday: form week 2 to week 14, except week 5 first period： 8:00-10:40 second period: 12:00-14:40third period: 15:20-18:00,Class hour,70,No Pain, No Gain！,
