Chapter 1
Measurement and Types of Quantities
Exercises
1-1 Answers will vary.
(a) Food can be sweet, salty, bitter, sour, or umami (savory).
(b) An odour can be musty, smoky, fruity, etc.
1-2 Answers will vary. Examples of qualitative descriptions are friendly, fun-loving, honest;
examples of quantitative descriptions can be height, mass, shoe size.
1-3 (a) quantitative (b) qualitative (c) qualitative (d) quantitative (e) quantitative (f)
quantitative
1-4 Answers will vary.
time: time to recharge a battery; time available between classes
length: height adjustment of a bicycle seat; distance from home to work or school
mass: mass of frozen food defrosting in a microwave oven; mass of a parcel sent
by courier
volume: volume of books that a knapsack can hold; volume of water needed to
keep hydrated during a long-distance run
1-5 Answers will vary. Electrical voltage: 6.0 V; temperature: 100℃; power: 60 W
1-1
,Physics: An Algebra-Based Approach
1-6 Some of the disadvantages are
• Most celestial bodies that are visible at night are not visible during the daytime, and
vice versa.
• Cloudy conditions interfere with observation of any celestial body.
• Accuracy is difficult to achieve.
• Convenience is minimal.
1-7 Theoretical aspects of physics involve posing questions, creating ideas to research
answers to those questions, experimenting, measuring, analyzing, and collaborating,
which leads to theories and more questions. The theoretical research and discovery leads
to applications that, in most cases, help to improve our lives. One example is the
discovery of current electricity, which has led to countless, very useful, electrical devices.
1-8 The original metre was defined in terms of the distance from the equator to the North
Pole, a distance that could only be assumed because it was impossible to measure. The
original second was defined in terms of a mean solar day, a quantity that is not constant
because Earth’s rotation is very gradually slowing down.
Length 2 10 26 m
1-9 (a) 15
2 10 41
length 1 10 m
Time 5 1017 s
(b) 25
1.7 1042
time 3 10 s
Mass 1 1053 kg
(c) 1 1083
mass 9 10 31 kg
Mass has by far the greatest range of values.
1-2
, Chapter 1—Measurement and Types of Quantities
1-10 In seconds, $1 10 9 1 s 1 10 9 s.
$
In years, $1 109 1 s 1 year7 31 years.
$ 3.2 10 s
8 10 41 kg
1-11 # stars = 4 1011 stars
kg
2 1030
star
2 1030 kg
1-12 # atoms = 1 1057 atoms
27 kg
1.7 10
atom
1-13 (a) 8.4 × 1015 (b) 8 × 1036 (c) 8.0 × 108 (d) 1.94 × 105 m/s
1-14 A base unit is a standard unit of measurement from which other units may be derived. In
the SI, examples are the metre (m), kilogram (kg), and second (s). A derived unit is a
measurement unit stated in terms of one or more base units. Examples are a unit for speed
(m/s), a unit for surface area (m²), and a unit for solid volume (m³).
1-15 Four examples are watt (W = kg∙m2∙s–3), pascal (Pa = kg∙s–2), volt (V = kg∙m2∙s–3∙A–1), and
becquerel (Bq = s–1).
1-16 Some of the patterns are the prefixes from 103 to 10–3 change by a factor 101; the
remaining prefixes change by a factor of 103; the symbols for the large numbers (from
mega upward) are capital letters, and all the other symbols are lower case; the origins of
the prefixes are all non-English words; some original meanings relate to the power of 10
1-3
, Physics: An Algebra-Based Approach
(e.g., Greek femten, or 15, is used for 10–15), while some others relate to a power of 103
(e.g., Italian setta or 7 is (103)7 or 1021).
m
1-17 (a) 1.3 10 1 dam 101 1.3 m
dam
1m
(b) 30 nm 3 10 8 m
10 9 nm
1000 m
(c) 1.23 10 4 km 1.23 10 7 m
km
31012 m
(d) 1.486 10 Tm 1.486 109 m
Tm
1s
1-18 (a) 20 ms 2 10 2 s
10 3 ms
1 m 106 μm
(b) 8.6 cm 2
8.6 104 μm
10 cm m
1 Mg
(c) 3.28 g 6
3.28 106 Mg
10 g
103 kHz
(d) 105 MHz 1.05 105 kHz
1 MHz
2.4 103 MW 103 mW 106 W 2.4 106 mW
(e)
m2 W MW m2
9.8 m 1 s 1s 9.8 1012 m
(f)
s2 106 μs 106 μs μs2
4.7 g 1 kg 106 cm3 4.7 103 kg
(g)
cm3 103 g m3 m3
53 people 1 km2 104 m2 0.53 people
(h) 6 2
km2 10 m ha ha
1-4
Measurement and Types of Quantities
Exercises
1-1 Answers will vary.
(a) Food can be sweet, salty, bitter, sour, or umami (savory).
(b) An odour can be musty, smoky, fruity, etc.
1-2 Answers will vary. Examples of qualitative descriptions are friendly, fun-loving, honest;
examples of quantitative descriptions can be height, mass, shoe size.
1-3 (a) quantitative (b) qualitative (c) qualitative (d) quantitative (e) quantitative (f)
quantitative
1-4 Answers will vary.
time: time to recharge a battery; time available between classes
length: height adjustment of a bicycle seat; distance from home to work or school
mass: mass of frozen food defrosting in a microwave oven; mass of a parcel sent
by courier
volume: volume of books that a knapsack can hold; volume of water needed to
keep hydrated during a long-distance run
1-5 Answers will vary. Electrical voltage: 6.0 V; temperature: 100℃; power: 60 W
1-1
,Physics: An Algebra-Based Approach
1-6 Some of the disadvantages are
• Most celestial bodies that are visible at night are not visible during the daytime, and
vice versa.
• Cloudy conditions interfere with observation of any celestial body.
• Accuracy is difficult to achieve.
• Convenience is minimal.
1-7 Theoretical aspects of physics involve posing questions, creating ideas to research
answers to those questions, experimenting, measuring, analyzing, and collaborating,
which leads to theories and more questions. The theoretical research and discovery leads
to applications that, in most cases, help to improve our lives. One example is the
discovery of current electricity, which has led to countless, very useful, electrical devices.
1-8 The original metre was defined in terms of the distance from the equator to the North
Pole, a distance that could only be assumed because it was impossible to measure. The
original second was defined in terms of a mean solar day, a quantity that is not constant
because Earth’s rotation is very gradually slowing down.
Length 2 10 26 m
1-9 (a) 15
2 10 41
length 1 10 m
Time 5 1017 s
(b) 25
1.7 1042
time 3 10 s
Mass 1 1053 kg
(c) 1 1083
mass 9 10 31 kg
Mass has by far the greatest range of values.
1-2
, Chapter 1—Measurement and Types of Quantities
1-10 In seconds, $1 10 9 1 s 1 10 9 s.
$
In years, $1 109 1 s 1 year7 31 years.
$ 3.2 10 s
8 10 41 kg
1-11 # stars = 4 1011 stars
kg
2 1030
star
2 1030 kg
1-12 # atoms = 1 1057 atoms
27 kg
1.7 10
atom
1-13 (a) 8.4 × 1015 (b) 8 × 1036 (c) 8.0 × 108 (d) 1.94 × 105 m/s
1-14 A base unit is a standard unit of measurement from which other units may be derived. In
the SI, examples are the metre (m), kilogram (kg), and second (s). A derived unit is a
measurement unit stated in terms of one or more base units. Examples are a unit for speed
(m/s), a unit for surface area (m²), and a unit for solid volume (m³).
1-15 Four examples are watt (W = kg∙m2∙s–3), pascal (Pa = kg∙s–2), volt (V = kg∙m2∙s–3∙A–1), and
becquerel (Bq = s–1).
1-16 Some of the patterns are the prefixes from 103 to 10–3 change by a factor 101; the
remaining prefixes change by a factor of 103; the symbols for the large numbers (from
mega upward) are capital letters, and all the other symbols are lower case; the origins of
the prefixes are all non-English words; some original meanings relate to the power of 10
1-3
, Physics: An Algebra-Based Approach
(e.g., Greek femten, or 15, is used for 10–15), while some others relate to a power of 103
(e.g., Italian setta or 7 is (103)7 or 1021).
m
1-17 (a) 1.3 10 1 dam 101 1.3 m
dam
1m
(b) 30 nm 3 10 8 m
10 9 nm
1000 m
(c) 1.23 10 4 km 1.23 10 7 m
km
31012 m
(d) 1.486 10 Tm 1.486 109 m
Tm
1s
1-18 (a) 20 ms 2 10 2 s
10 3 ms
1 m 106 μm
(b) 8.6 cm 2
8.6 104 μm
10 cm m
1 Mg
(c) 3.28 g 6
3.28 106 Mg
10 g
103 kHz
(d) 105 MHz 1.05 105 kHz
1 MHz
2.4 103 MW 103 mW 106 W 2.4 106 mW
(e)
m2 W MW m2
9.8 m 1 s 1s 9.8 1012 m
(f)
s2 106 μs 106 μs μs2
4.7 g 1 kg 106 cm3 4.7 103 kg
(g)
cm3 103 g m3 m3
53 people 1 km2 104 m2 0.53 people
(h) 6 2
km2 10 m ha ha
1-4
