EN3: Introduction to Engineering and Statics
Division of Engineering
Brown University
2.2 Measurement – the SI system of units
There are no absolutes in measurement. When we measure something, we really compare it
to something else. For example, if I tell you my weight is 72.7kg, I am telling you that I
weigh 72.7 times more than a certain block of platinum-iridium stored someplace in France.
This is not, in itself, particularly useful information. But fortunately the rest of the
world (except for the USA which stubbornly refuses to abandon inches and lbs) have agreed
to compare all mass to the same metal block. So this allows you to determine whether I
should be signing up for weight watchers.
To set up a common system of measurement, then, we have to agree on a common set of
standards of measurement. This sounds like a daunting task – after all, we measure a
vast number of different things – energies, forces, times, lengths, magnetic
fields… the list goes on and on. Rather surprisingly, however, it turns out that we
only have to set standards for six quantities: length, mass, time, electric current,
temperature and luminous intensity. After that, standard units can be calculated for
everything else – speed, force, electric charge, magnetic field, etc from the
fundamental physical laws defining these quantities (speed=distance/time, F=ma, etc).
BASIC UNITS
The SI system of units defines six basic units:
Length:
The metre. Defined to be 1650763.73 wavelengths of a certain radiation of the
krypton-86 atom
Mass:
The kilogram. Defined to be the mass of a certain platinum-iridium cylinder stored
someplace in France… NIST has an accurate copy if you need it.
Time:
The second. Defined to be the duration of 9192631770 periods of the radiation of a certain
state of the cesium 133 atom.
Electric
current: The ampere.
Temperature:
the degree Kelvin
Luminous
Intensity: The Candela.
These are called basic units because we have to choose them arbitrarily –
we can’t define them through any fundamental physical laws.
DERIVED UNITS
Other quantities (force, acceleration, energy, work, power, magnetic field, electric
potential, etc) are measured using derived units, which can be defined
through physical laws. For example,
There are many other derived units (for speed we could use km/hr, acceleration we could
use gs – you can even define your own, if you want). But you must be able to
express all derived units in terms of two or more of the six basic units. For example
Philosophically speaking, it is remarkable that we have been able to quantify the
universe with only 6 basic units of measurement. But perhaps this is more a reflection of
our ignorance – we just haven’t learned how to measure very much of the universe
yet. For the more practical-minded, the requirement that all measurable quantities must be
expressible in terms of the six basic units has an important consequence, in that it leads
to the consequence of dimensional analysis, to be discussed in a subsequent
section.
Here are tables of the basic dimensions and
derived dimensions (PDF)
PREFIXES
We define the following prefixes to indicate decimal fractions or multiples of a
unit
| tera |
T |
 |
| giga |
G |
 |
| mega |
M |
 |
| kilo |
k |
 |
| deci |
d |
 |
| centi |
c |
 |
| milli |
m |
 |
| micro |
 |
 |
| nano |
n |
 |
| pico |
p |
 |
| femto |
f |
 |
| atto |
a |
 |
SOME TYPICAL MAGNITUDES
Here is a small list of typical values for a few basic and derived units, to get you
started in your personal database of useful information. Some data are from `The
Sizesaurus’ by Stephen Strauss (Avon Science, 1997); some are from memory (so
don’t trust them!)
Lengths
| 10 fm |
Diameter of atomic nucleus |
| 0.1-0.3 nm |
Approx atomic radius in most crystalline solids |
| 17nm |
Smallest virus |
0.1  |
Width of a wire in a typical integrated circuit
(as of August 2000) |
| 50 |
Typical tolerance (precision) of a machined part |
| 50 |
Width of a human hair |
| 0.1mm |
Length of small dust particle |
| 1mm |
Thickness of a nickel |
| 5mm |
Length of a house-fly |
| 1.9 cm |
Diameter of a penny |
| 1m |
Approx. length of a meter ruler |
| 2.74m |
Length of a table-tennis table |
| 10m |
Longest frog jump |
| 18.44m |
Distance between mound & home plate on a
baseball field |
| 50m |
A stone’s throw |
| 293.5m |
Length of QE2 ocean liner |
| 300.5m |
Height of Eiffel tower |
| 381m |
Height of Empire State building |
| 417m |
Height of World Trade Ctr (N tower) |
| 5486m |
Altitude of class A airspace (lowest jet route)
above earths surface |
| 8848m |
Height of Mt. Everest |
| 4000m |
Average depth of Earth’s oceans |
| 11km |
Height of troposphere above earth’s surface
– most weather (clouds, etc) is confined within this layer |
 km |
Approx radius of the earth |
 km |
Altitude of telecommunications satellite |
 km |
Distance from Earth to moon |
 km |
Distance from Earth to Sun |
 km |
Distance to nearest star (Proxima Centauri) |
Mass
Time
 s |
Nuclear events |
 s |
Chemical events |
 s |
Time for light to travel from front to back of
B&H 166 |
 s |
Chains of biochemical reactions |
| 0.01s |
Time a baseball is over the plate |
| 0.001-2s |
Duration of a lightning flash |
| 0.33s |
Blink of an eye |
| 1s |
Human heartbeat |
| 58s |
Average time a person spends in bathroom |
| 500s |
Fastest cell division |
| 4800s |
Actual Length of an EN3 lecture |
 s |
Human life |
| s |
Apparent length of an EN3 lecture |
 s |
Age of the Pyramids |
 s |
Age of mammals |
 s |
Age of life |
 s |
Age of the universe |
Exercise: Construct your own tables of representative values for a few sets of
derived units – for example, velocity, acceleration, force and kinetic energy.
Go To 2.3: Dimensional
Analysis
as the force
required to accelerate 1 kg by 1 
as the work done by a 1 N force in
moving a distance of 1m. 
kg
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