We begin our discussion of systems of units with the International System (SI) of units, because SI is the most common system of units used in the world. The origin of the present day Inter- national System of units can be traced back to 1799 with meter and kilogram as the first two base units. By promoting the use of the second as a base unit of time in 1832, Carl Friedrich Gauss (1777–1855), an important figure in mathematics and physics, including magnetism and astronomy, had a great impact in many areas of science and engineering. It was not until 1946 that the proposal for the ampere as a base unit for electric current was approved by the General Conference on Weights and Measures (CGPM). In 1954, CGPM included ampere, kelvin, and candela as base units. The mole was added as a base unit by the 14th CGPM in 1971. A list of SI base (fundamental) units is given in Table 6.1.
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TABLE 6.1 A List of SI Base (Fundamental) Units
Physical Quantity Name of SI Base Unit SI Symbol
Length Meter m
Mass Kilogram kg
Time Second s
Thermodynamic temperature Kelvin K
Electric current Ampere A
Amount of substance Uranium 238 ←One of the Mole mol
Gold 197 heaviest Silver 108 atoms known
Copper 64
Calcium 40
Aluminum 27
Carbon 12 ← Common Carbon is Helium 4 used as a standard Hydrogen 1 ← Lightest atom
Luminous intensity Candela cd
50 kg–120 kg
Range of mass for most adults Fastest person can run 100 meters in approximately 10 seconds
120 volts
1.25 amps 150 watts Comfortable room temperature: 295 kelvin
Ice water:
273 kelvin
A candle has luminous intensity of approximately 1 candela
1.6 m–2.0 m Range of height for most adults
Listed below are formal definitions of base units as provided by the Bureau International des Poids et Mesures.
Themeteris the length of the path traveled by light in a vacuum during a time interval of 1/299,792,458 of a second.
Thekilogramis the unit of mass; it is equal to the mass of the international prototype of the kilogram.
Thesecond is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.
Theampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross section, and placed 1 meter apart in a vacuum, would produce between these conductors a force equal to 2107 newton per meter of length.
Thekelvin, a unit of thermodynamic temperature, is the fraction 1/273.16 of the thermody- namic temperature of the triple point of water (a point at which ice, liquid water, and water vapor coexist). The unit of Kelvin is related to the degree celsius, according to
K C273.16.
Themoleis the amount of substance of a system that contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles.
Thecandelais the luminous intensity, in a given direction, of a source that emits monochro- matic radiation of frequency 5401012hertz and that has a radiant intensity in that direc- tion of 1/683 watt per steradian.
You need not memorize the formal definitions of these units. From your everyday life expe- riences you have a pretty good idea about some of them. For example, you know how short a time period a second is, or how long a period a year is. However, you may need to develop a
“feel” for some of the other base units. For example, How long is a meter? How tall are you?
Under 2 meters or perhaps above 5 meters? Most adult people’s height is approximately between 1.6 meters and 2 meters. There are exceptions of course. What is your mass in kilograms? Devel- oping a “feel” for units will make you a better engineer. For example, assume you are design- ing and sizing a new type of hand-held tool, and based on your stress calculation, you arrive at an average thickness of 1 meter. Having a “feel” for these units, you will be alarmed by the value of the thickness and realize that somewhere in your calculations you must have made a mistake. We will discuss in detail the role of the base dimensions and other derived units in the upcoming chapters in this book.
The CGPM in 1960 adapted the first series of prefixes and symbols of decimal multiples of SI units. Over the years, the list has been extended to include those listed in Table 6.2. SI is the most common system of units used in the world.
The units for other physical quantities used in engineering can be derived from the base units. For example, the unit for force is the newton. It is derived from Newton’s second law of motion. One newton is defined as a magnitude of a force that when applied to 1 kilogram of mass, will accelerate the mass at a rate of 1 meter per second squared (m/s2). That is:
1 N(1 kg)(1 m/s2).
Examples of commonly derived SI units used by engineers are shown in Table 6.3. The physical quantities shown in Table 6.3. will be discussed in detail in the following chapters of
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6.2 Systems of Units
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TABLE 6.2 The List of Decimal Multiples and Prefixes Used with SI Base Units
Multiplication Factors Prefix SI Symbol
1,000,000,000,000,000,000,000,0001024 yotta Y 1,000,000,000,000,000,000,0001021 zetta Z
1,000,000,000,000,000,0001018 exa E
1,000,000,000,000,0001015 peta P
1,000,000,000,0001012 tera T
1,000,000,000109 giga G
1,000,000106 mega M
1000103 kilo k
100102 hecto h
10101 deka da
0.1101 deci d
0.01102 centi c
0.001103 milli m
0.000,001106 micro m
0.000,000,001109 nano n
0.000,000,000,0011012 pico p
0.000,000,000,000,0011015 femto f
0.000,000,000,000,000,0011018 atto a 0.000,000,000,000,000,000,0011021 zepto z 0.000,000,000,000,000,000,000,0011024 yocto y
this book. Starting in Chapter 7, we will discuss their physical meaning, their significance and relevance in engineering, and their use in engineering analysis.