Chapter 1 MeasurementChapter 1 Measurement

Despite the mathematical beauty of some

of its most complex and abstract theories,

physics is above all an experimental science.

1-1 Physical quantities, standards and 1-1 Physical quantities, standards and unitsunits

• What will be measured?What will be measured?

Physical quantities: mass, length, time, force…Physical quantities: mass, length, time, force…

• What’s the standard for a measurement?What’s the standard for a measurement?

Maintaining and developing standards is an Maintaining and developing standards is an activeactive

branch of science. branch of science.

• UnitsUnits

There are seven kinds of bThere are seven kinds of base unitsase units in SI system. in SI system.

1-2 The international system of 1-2 The international system of unitsunits

CGPM(CGPM( 国际度量衡大会国际度量衡大会 ) selected as ) selected as base unitsbase units t t

he seven quantities displayed in Table 1-1. This ihe seven quantities displayed in Table 1-1. This i

s the basis of the International System of Units,s the basis of the International System of Units,

abbreviated SI .abbreviated SI .

Table 1-1 SI Base unitsTable 1-1 SI Base units

QuantityQuantity NameName SymbolSymbol

TimeTime SecondSecond ss

LengthLength MeterMeter mm

MassMass KilogramKilogram KgKg

Amount of Amount of substancesubstance

MoleMole MolMol

TemperatureTemperature KelvinKelvin KK

Electric currentElectric current AmpereAmpere AA

Luminous intensityLuminous intensity CandelaCandela cdcd

The use of non-SI units is particularly popular with astronomers, many of whom are in love with the angstrom .

Am I a nine giga-angstrom (109 ) waist or a ten?

A

1-3 The standard of time1-3 The standard of time

• We can use any phenomenon that repeats itself

as a measure of time.

• In 1967, the 13th CGPM adopted a new definition:

• One second was defined to be 1/86400 of one day.

The second is the duration of 9,192,631,770 vibrations of a (specified) radiation emitted by a (specified) isotope of the cesium atom.

1-4 The standard of length1-4 The standard of length

• The first international standard of length was The first international standard of length was a bar of a bar of

a platinum-iridium alloya platinum-iridium alloy called the standard meter. called the standard meter.

• In 1983, the 17th CGPM redefined the meter as the In 1983, the 17th CGPM redefined the meter as the

length of length of the path traveled by lightthe path traveled by light in vacuum during a in vacuum during a

time interval 1/299,792,458 of a second.time interval 1/299,792,458 of a second.

• In 1960, the 11th CGPM defined the meter as the In 1960, the 11th CGPM defined the meter as the

length of 1,650,763.73 wave length of a special length of 1,650,763.73 wave length of a special

radiation of Krradiation of Kr8686..

1-5 The standard of mass1-5 The standard of mass

• The SI standard of mass is a The SI standard of mass is a platinum-iridium

cylinder and assigned as a mass of 1 kilogram and assigned as a mass of 1 kilogram

(prototype). (prototype).

• Secondary standards are sent to standardizing are sent to standardizing

laboratories in other countries.laboratories in other countries.

• Atomic mass unitAtomic mass unit

1-6 Precision and 1-6 Precision and significant figuressignificant figures ((有效数字有效数字 ))

• The number of significant figures tells us the The number of significant figures tells us the

precision of the measuring result.precision of the measuring result.

• There are a few simple rules to follow in deciThere are a few simple rules to follow in deci

ding how many significant figures to keep:ding how many significant figures to keep:

Rule 1Rule 1. x=3.0m and x=0.0030km imply that . x=3.0m and x=0.0030km imply that

we know the value of x to be two significant figuwe know the value of x to be two significant figu

res.res.

Be careful about ambiguous notations: x=300m

Rule 2Rule 2. When multiplying or dividing, the nu. When multiplying or dividing, the nu

mber of significant figures in the product or qumber of significant figures in the product or qu

otient should be no greater than the number of otient should be no greater than the number of

significant figures in the least precise of the facsignificant figures in the least precise of the fac

tors. Thustors. Thus

2.714159.33.2

Be careful of this:

1.1003.18.9

Rule 3. In adding or subtracting, Rule 3. In adding or subtracting, the least signifithe least signifi

cant digitcant digit ( (最小的有效数字最小的有效数字 )of the sum or differenc)of the sum or differenc

e occupies the same relative position as e occupies the same relative position as the least the least

significant digitsignificant digit of the quantities being added or su of the quantities being added or su

btracted. btracted. In this case the number of significant figuIn this case the number of significant figu

res is not important; it is the position that matters.res is not important; it is the position that matters.

Example: Example:

103.9kg+2.10kg+0.319kg=106.319kg=106.3kg103.9kg+2.10kg+0.319kg=106.319kg=106.3kg

Example:

1.A student is calculating the surface area of a single sheet of paper. He measures the length to beL= 27.9cm; He measures the width to be W=21.6 cm. The student should record the area of the paper as (in cm2):

A) 602.64 B) 602.6 C)602 D)603

Correct answer is D).

602.64)27.9(21.6

2. A student is calculating the thickness of a single sheet of paper. She measures the thickness of astack of 80 sheets with vernier calipers, and finds thethickness to be L= 1.27 cm. Which of the following answers has the correct number of significant digits? (in mm):

A) 0.15875 B) 0.159 C) 0.16 D) 0.2

Correct answer is B).

015875)0(1.27/80 .