Chapter 1

Doing Physics

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 C 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

Chapter 1Problem 24

Highways in Canada have speed limits of 100 km/h. How does this compare with the 65 mi/h speed limit common in the United States?

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

Chapter 1Problem 39

The average American uses electrical energy at the rate of about 1.5 kilowatts (kW). Solar energy reaches Earth’s surface at an average rate of about 300 watts on every square meter. What fraction of the United States’ land area would have to be covered with 20% efficient solar cells to provide all of our electrical energy?

Questions?

Answers to the even-numbered problems

Chapter 1

Problem 18:

(a) 15.6 m/s(b) 51.3 ft/s

Answers to the even-numbered problems

Chapter 1

Problem 52:

42 km