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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Dr. Yongkang Le
March 5th, 2010
All the rest is stamp collecting.
By Ernest Rutherford
knowledge at our disposal. The rest is poetry, imagination.
By Max Plank
c = (299792.50±0.10) km/s
Difference between measured value
and true value
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
from BIPM and ISO etc., issued in 1993
Important：too large--waste；too small--wrong。
Type A--- Evaluated with statistical methods
Type B---Evaluated with other methods
After n time same measurement of unknown x:
uAdecreases with increasing n
uB2=a/3 : Average distribution,
uB2=a/3 : normal distribution, large n
a: maximum uncertainty of the device, usually
given with the deviceUncertainty type B
d: smallest deviation
For length measurements, since x=x2-x1, we have:
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)
5 - rounding for even endSignificant 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
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
* , / : minimum significant figures
If the results is calculated:
+ , - :
* , / :
Measured quantities are independ from each other
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.
Average value of the diameter：