Transcript chapter 1_2x

Chapter 1
1.2 Units of Length, Mass, and Time
1.2 Units of Length, Mass, and Time
• Length, Mass, and Time are the fundamental
quantities used to describe the Physical
World.
• All other quantities such as Force, Energy,
Power, and, velocity are derived from these 3
base units.
1.2 Units of Length
• Early units of distance were often associated with
the human body.
– An Egyptian cubit was the distance from the elbow to
the tip of the middle finger.
– The foot was defined as the length of the royal foot of
King Louis XIV of France.
– The precise origin of the Yard is not definitely known.
Some claim that the measure was invented by Henry I
of England as being the distance between the tip of
his nose and the end of his thumb.
1.2 Units of Length
• The question of measurement reform was placed
in the hands of the Academy of Sciences who
appointed a commission chaired by Jean-Charles
de Borda.
• This commission decided that the new measure
should be equal to one ten-millionth of the
distance from the North Pole to the Equator (the
quadrant of the Earth's circumference), measured
along the meridian passing through Paris.
1.2 Units of Length
• The S.I. unit of length is the Meter.
• 1⁄10,000,000 part of the quarter of a meridian,
measurement (North Pole to Equator) (1793)
• Platinum-iridium bar at melting point of ice,
atmospheric pressure, supported by two rollers
(1927)
• 1,650,763.73 wavelengths of light from a
specified transition in krypton-86 (1960)
• Length of the path travelled by light in a vacuum
in 1⁄299,792,458 of a second (1983)
[1]
Table 1-1
Typical Distances
Distance from the Earth to the nearest large galaxy (the
Andromeda Galaxy, M31)
2 x 1022 m
Diameter of our galaxy (the Milky Way)
8 x 1020 m
Distance from the Earth to the nearest star (other than
the Sun)
4 x 1016 m
One light year
9.46 x 1015 m
Average radius of Pluto’s orbit
6 x 1012 m
Distance from Earth to the Sun
1.5 x 1011 m
Radius of Earth
6.37 x 106 m
Length of football field
102 m
Height of a person
2m
Diameter of a CD
0.12 m
Diameter of the aorta
0.018 m
Diameter of the period in a sentence
5 x 10–4 m
Diameter of a red blood cell
8 x 10–6 m
Diameter of the hydrogen atom
10–10 m
Diameter of a proton
2 x 10–15 m
1.2 Units of Mass
• The S.I. unit of Mass is a kilogram.
• The gram was originally defined in 1795 as the
mass of one cubic centimeter of water at 4 °C,
making the kilogram equal to the mass of one
liter of water.
• The kilogram is currently defined as the mass
of a particular platinum-iridium alloy cylinder
at eh International Bureau of Weights and
Standards in Sevres, France.
1.2 Units of Mass
• The kilogram is the only SI base unit with an SI
prefix ("kilo", symbol "k") as part of its name.
• It is also the only SI unit that is still directly
defined by an artifact rather than a
fundamental physical property that can be
reproduced in different laboratories.
Table 1-2
Typical Masses
Galaxy (Milky Way)
4 x 1041 kg
Sun
2 x 1030 kg
Earth
5.97 x 1024 kg
Space Shuttle
2 x 106 kg
Elephant
5400 kg
Automobile
1200 kg
Human
70 kg
Baseball
0.15 kg
Honeybee
1.5 x 10–4 kg
Red blood cell
10–13 kg
Bacterium
10–15 kg
Hydrogen atom
1.67 x 10–27 kg
Electron
9.11 x 10–31 kg
1.2 Units of Time
• The S.I. unit of time is the Second.
• The Egyptians subdivided daytime and nighttime
into twelve hours each since at least 2000 BC,
hence the seasonal variation of their hours.
• The Hellenistic astronomers Hipparchus (c. 150
BC) and Ptolemy (c. AD 150) subdivided the day
sexadesimally and also used a mean hour (1⁄24
day), simple fractions of an hour (1⁄4, 2⁄3, etc.) and
time-degrees (1⁄360 day or four modern minutes),
but not modern minutes or seconds.
1.2 Time
• The earliest clocks to display seconds
appeared during the last half of the 16th
century.
• In 1581, Tycho Brahe redesigned clocks that
displayed minutes at his observatory so they
also displayed seconds. However, they were
not yet accurate enough for seconds. In 1587,
Tycho complained that his four clocks
disagreed by plus or minus four seconds.
1.2 Time
• The second first became accurately
measurable with the development of
pendulum clocks keeping mean time (as
opposed to the apparent time displayed by
sundials).
• In 1956, the second was redefined in terms of
a year: the fraction 1/31,556,925.9747 of the
tropical year for 1900 January 0 at 12 hours
ephemeris time.
1.2 Time
• In 1960 the second was defined as 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 caesium-133 atom.
• This is the modern definition and the basis for
atomic clocks.
Table 1-3
Typical Times
Age of the universe
5 x 1017 s
Age of the Earth
1.3 x 1017 s
Existence of human species
6 x 1013 s
Human lifetime
2 x 109 s
One year
3 x 107 s
One day
8.6 x 104 s
Time between heartbeats
0.8 s
Human reaction time
0.1 s
One cycle of a high-pitched sound wave
5 x 10–5 s
One cycle of an AM radio wave
10–6 s
One cycle of a visible light wave
2 x 10–15 s
Power
Table 1-4
Common Prefixes
Prefix
Abbreviation
1015
peta
P
1012
tera
T
109
giga
G
106
mega
M
103
kilo
k
102
hecto
h
101
deka
da
10–1
deci
d
10–2
centi
c
10–3
milli
m
10–6
micro
m
10–9
nano
n
10–12
pico
p
10–15
femto
f