Chapter 1
Measurement
Measurement
• We measure things (such as weight, time, length, speed, etc.)
• We use tools (rulers, clocks, speedometers, etc.) to measure things
• Measurement tools are calibrated
• Calibration is in units (inches, seconds, pounds, mph’s, etc.)
• Units require standards (conventional, habitual, customary)
Modern standards
• Not all quantities in nature are independent (e.g., speed is distance per time)
• Standards are created for independent (base) quantities: length, time, mass, + some other
• Modern day standards should be as invariable as possible
• Should be uniformly defined
• Should be accessible
SI (Systéme Internacional) – most accepted international system of units
• Adopted in 1971
• Is commonly known as metric system
• Standard units are (there are more): 1 m (meter) for length1 s (second) for time1 kg (kilogram) for mass
• All other SI units are defined as derivatives of the base units (e.g., energy: 1 J (Joule) = 1 kg x 1 m2 / s2)
Length
• SI unit – m (meter)
• Initially adopted as one ten-millionth of a distance between the North pole and the equator (standard – platinum-iridium bar)
• Currently - a modern standard:
1 m = the length of the path traveled by light in vacuum during a time interval of 1/299 792 458 of a
second
Time
• SI unit – s (second)
• Historically
1 s = 1 / 8640 day
• Currently - a modern standard:
1 s = 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 Cs133
atom
Time
• SI unit – s (second)
• Historically
1 s = 1 / 8640 day
• Currently - a modern standard:
1 s = 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 Cs133
atom
Mass
• SI unit – kg (kilogram)
• Historically 1 kg – mass of 1 liter of water
• Initially adopted in prototype of the kilogram was made of platinum-iridium and declared: “This prototype shall henceforth be considered to be the unit of mass”
• Currently - an alternative modern standard:
1 kg = mass of C12 atom * 1026 / 1.99264824(Don’t confuse mass and weight: 1 kg is the same on the Earth
and on the Moon)
Scientific notation
237 000 000 s = = 2.37 x 108 s =
= 2.37 E8 s
0.0000664 m = = 6.64 x 10-5 m =
= 6.64 E-5 m
SI system prefixes
Factor Name Symbol
1024 yotta Y
1021 zetta Z
1018 exa E
1015 peta P
1012 tera T
109 giga G
106 mega M
103 kilo k
102 hecto h
101 deka da
Factor Name Symbol
10-1 deci d
10-2 centi c
10-3 milli m
10-6 micro µ
10-9 nano n
10-12 pico p
10-15 femto f
10-18 atto a
10-21 zepto z
10-24 yocto y
Examples: 1.25E4 J = 12.5 kJ2.34 x 10-10 s = 0.234 ns
Good SI web resource:
National Institute of Standards and Technology (NIST)
http://physics.nist.gov/cuu/Units/
Conversion of units
• Need to know a conversion factor
• Use chain-link conversion
(Check Appendix D for SI conversion factors)
1 1
1000
km
m
37 km
km
mkm
1
1000 ) 37(
)1( ) 37( km
m 000,37
Conversion of units
Conversion of units
Order of magnitude
• Order of magnitude is the power of 10 that applies
• Divide the number by the power of 10
• Compare the remaining value to 3.162 ( )
• If the remainder is less than 3.162, the order of magnitude is the power of 10 in the scientific notation
• If the remainder is greater than 3.162, the order of magnitude is one more than the power of 10 in the scientific notation
10
Answers to the even-numbered problems
Chapter 1
Problem 2:
2.15 × 104 kg/m3
Answers to the even-numbered problems
Chapter 1
Problem 10:
9.19 nm/s
Answers to the even-numbered problems
Chapter 1
Problem 22:
(a) 13.4(b) 49.1
Answers to the even-numbered problems
Chapter 1
Problem 60:
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