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
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：