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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