Solution manual for physics an algebra based approach 1st edition by mcfarland

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

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

1-6 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

1-9 (a)

26

41 15

Length 2 10 m

2 10 length 1 10 m−

×

×

(b)

17

42 25

Time 5 10 s

1.7 10 time 3 10 s−

×

×

31

Mass 1 10 kg

1 10 mass 9 10 kg−

×

× Mass has by far the greatest range of values

1-10 In seconds, 9 1 s 9

$

In years, 9

7

1 s 1 year

$ 3.2 10 s

×

30

8 10 kg

kg

2 10

star

×

1-12

30

57 27

2 10 kg

kg 1.7 10

atom

−

×

1-13 (a) 8.4 × 10−15 (b) 8 × 10−36 (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);

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

(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)

dam

−

9

1 m

10 nm

−

km

(d)

12

Tm

−

3

1 s

10 ms

−

(b)

6

4 2

1 m 10 μm

6

1 Mg

10 g

−

(d)

3

5

10 kHz

1 MHz

(e) 2.4 10 MW 10 mW 10 W23 3 6 2.4 10 mW26

−

(f)

12

9.8 m 1 s 1 s 9.8 10 m

−

×

(g)

4.7 g 1 kg 10 cm 4.7 10 kg

×

(h)

53 people 1 km 10 m 0.53 people

1-19 (a) 280 mm + 37 cm = 28 cm + 37 cm = 65 cm

(b) 9850 mm – 1.68 m = 9.85 m – 1.68 m = 8.17 m

1-20 100 km 1000 m 100 cm 1 in 1 ft 1 mi 62.1 mi

1-21 (a) L/T (b) L/T (c) L/T2 (d) M/L3

1-22 (a) speed (b) length (c) density (d) acceleration

1-23 (a) M·L/T2 (b) M·L2/T3 (c) T −1

1-24 From d = vt, the left side = L and the right side = L T = L

T× Thus, the dimensions are equal

3

t

= = which has dimensions of L T or L/T ⋅ − 3 3

d =v t+ at the left side of the equation has dimension L, and the right side has

T× +T × = , so the equation is dimensionally correct.

1-27 To compare the uncertainties, begin by expressing them in the same unit Thus,

1 kg

1000 g

± × = ± The most expensive scale is likely the first one,

smallest uncertainty The least expensive scale is likely the last one, which has the largest uncertainty, ±0.1 kg

1-28 (a) 1 (b) 5 (c) 3 (d) 4

1-29 (a) 3.85 × 104 Gm (b) 9.40 × 10−4 MW (c) 5.51 × 101 dam (d) 8.77 × 102 kL (e) 7.66 ×

10−2μg

1-30

measured value accepted value

accepted value 1.08 10 kg/m 1.00 10 kg/m

1.00 10 kg/m 0.08 100% or 8%

−

×

×

2(1.18 m)+2(0.378 m)

=3.116 m or 3.12 m

p= +l w

=

Thus, the perimeter is 3.12 m, rounded off to one estimated digit

Area:

2

1.18 m 0.378 m

= 0.446 m

A lw=

Thus, the area is 0.446 m² (rounded off to three significant digits)

1-32 (a) 27 27

30

1.674 927 10 kg 1.672 621 10 kg

=2.306 10 kg

−

×

27

1.672 621 10 kg 9.109 382 10 kg

=1.672 621 10 kg 0.000 910 938 2 10 kg

=1.671 710 10 kg

−

×

1-33

11

11

Greatest distance = 1.495 988 10 m 3.844 10 m

= 1.495 988 10 m + 0.003 844 10 m

= 1.499 832 10 m Least distance = 1.495 988 10 m 3.844 10 m

= 1.495 988 10 m 0.003 844 10 m

= 1.492144 10 m

×

×

1-34

11 8

1.495 988 10 m

3.00 10 m/s

×

×

Thus, the time to three significant digits is 499 s

1-35 In all cases, the actual numerical values will vary

(a)

12 14

mass

#cells =

mass/cell

60 kg

1 10 kg/cell about 1 10 cells

−

=

×

Thus, the number would be about 10 cells.14

(b) First, we must make some assumptions, all of which are approximations

North American population (including Canada, the USA, and Mexico) is about

500 million; the average number of patties consumed per year per person is about 30; and the average mass of a patty is about 0.2 kg

8

9

mass patties estimated mass # of people

patty person 0.2 kg 30 patties

patty person

= 3 10 kg

× Thus, the total mass is about 109 kg to 1010 kg

(c) Assume that the diameter of the Ferris wheel is about 20 m to 30 m, which means

that the circumference, C=πd, is about 100 m Assume that the straight line distance from Calgary to Winnipeg is about 1000 km

3 3 3 1 4

distance

# of rotations =

distance/rotation

1 10 km

1 10 m/rotation

1 10 km

1 10 km/rotation

1 10 rotations

−

×

=

×

×

=

×

= × Thus, the number of rotations is about 10 000 or 104 rotations

(d) Assume Canada’s population (including children) is about 3.6 × 102 people with

an average arm span slightly more than 1 m, so the total “population arm span” is about 4 × 107 m or 4 × 104 km

5 4

coastline length 2 10 km

length/population 4 10 km/population

×

×

1-36 Answers will vary Some examples of scalar quantities are area, volume, speed, density,

energy, power, and frequency

1-37 Answers will vary Two examples of displacement are a ball tossed 10 m west and a walk

of 100 m south from the bus stop to the residence Two examples of velocity are a motorbike travelling at 50 km/h north and a jogger running along a path at 5 m/s southeast

CHAPTER REVIEW

Multiple-Choice Questions

1-38 (c)

1-39 (e)

1-40 (a)

1-41 (c)

1-42 (c)

1-43 (c)

Review Questions and Problems

1-44 Measurement is important

(a) in society in order to have efficient communication in numerous aspects of our lives,

including manufacturing, building infrastructure, selling, and buying

(b) in physics in order to design and perform experiments and develop theories and

applications resulting from experiments and discoveries

1-45 The base units are the metre (m) for length, the second (s) for time, and the kilogram (kg)

for mass

1-46 It isn’t necessary to have a base unit for area because area can be expressed in terms of

the base unit for length

1-47 Assume each storey is 3 m high Then the height of the building is:

3 m height =30 storeys

storey

90 m

1 dam

= 90 m

10 m

9 dam

×

=

×

= Thus, the height is about 90 m, or 9 dam

1-48 (a) 8.85 × 103 m, 8.85 × 104 dm, 8.85 × 105 cm

(b) 1.90 × 105 kg, 1.90 × 108 g, 1.90 × 1010 cg (c) 6.9 × 1015 s, 6.9 × 1021μs, 6.9 × 10−3 Es

1-49 Answers depend on each student’s mass Using a mass of 60 kg, the ratios would be

(a)

16 Mg 10 kg 3 10

×

(b)

3

0.26 kg 4 10

−

×

=

(c)

2

5.2 10 kg 9

(d)

3

6.7 10 dg 1 kg 1 g 1 10

60 kg 10 g 10 dg 1

(e)

4 3

28 g 1 kg 5 10

60 kg 10 g 1

−

×

5 2

mass = 3.0 kg 8.6 10

2.6 10 kg

= 2.6 10 Mg

×

(b)

3

2

2.2 10

−

×

(c)

7

1.1 10

−

1-52 (a) r is the radius; b is the base; h is the height

(b) The dimension of πr² is L2, and the dimension of bh/2 is L2 So we conclude that

area has the dimension L2

1-53 (a) The symbols are dimensions: M for mass, L for length, and T for time

(b) speed (v): [v] = L/T

acceleration (a): [a] = L/T2

area (A): [A] = L2

(c) [P] = M·L2/T3, [p] = M/LT2

(d) [E] = M·[v]2

(e) [P] = M·[v]·[a]

1-54 It is possible for the measurements to be multiplied (e.g., area × length = volume, or L² ×

L = L³), but it is not possible to add them (e.g., you can’t add area and length)

1-55 Wood contracts as it dries, so it must be fully dried (cured) and totally contracted before

being marked to ensure accurate scale divisions

1-56

8

measured value accepted value

accepted value 1.82 10 m/s 1.86 10 m/s

1.86 10 m/s 0.04 m/s

1.86 m/s 2%

−

×

×

×

=

1-57 length remaining = 500 m 3(120 cm)

= 500 m 3(1.20 m)

= 500 m 3.60 m

= 496 m

−

−

−

1-58 Let M represent the men’s discus, W represent the women’s discus, l represent length or

distance, and d represent diameter

W M

W M

= 3.06 m

l l

d

π

1-59

2

7.32 m 2.44 m

=17.9 m

=

A lw

1-60

2

2

π

1.3 10 cm

=

=

1-61 Answers will depend on the assumptions made

(a) Assume a normal pace is 0.6 m or 4

6 10× − km

4 3

distance

# paces =

distance/pace 1.6 km

6 10 km/pace 2.7 10 paces

−

=

×

Thus, the number of paces is likely between 3 3

(b) Assume that the size of a kernel of corn is about 3 mm by 2 mm by 2 mm

3

The kernel's volume is

(0.3 cm)(0.2 cm)(0.2 cm)

= 0.012 cm

=

=

V lwh

3 3 4

volume

# kernels =

volume/kernel (10 cm) 0.012 cm / kernel 8.3 10 kernels

=

Thus, the estimated number is between 1 10 and 1 10 kernels.× 4 × 5

(c) Above-ground pools are often circular Assume the diameter of the pool is 4 m or

40 dm and the height is 0.6 m or 6 dm

2

2

area height

= (20 dm) 6 dm

= 8 10 dm or 8 10 L

×

V

r h

π π

Thus, the volume would be about 1 10 L.× 4

(d) Assume a heartbeat of 72 beats per minute, or 1.2 beats/s For this example, assume

an age of 19 years

8

# beats = heart rate age (in seconds)

7.2 10 beats

×

Thus, the number of beats would be about 1 10 × 9

(e) Let’s assume that the average person sleeps about 8 h each day Let’s also make

the very simplistic assumption that the human population of about 7 billion is distributed approximately equally around Earth’s time zones

9

# people = fraction sleeping total population

1

3

= 2.3 10 people or about 2 10 people

×

× ×

1-62 (a) vector (b) scalar (c) scalar (d) scalar (e) vector (f) scalar

Applying Your Knowledge

1-63 The meanings are not exactly the same, but they are close The SI is based on multiples

of 10, whereas computers and data storage are based on powers of 2 For example, in the

SI, kilo means 103, or 1000, and mega means 106, but a kilobyte is 210 bytes, or 1024 bytes, and a megabyte is 220 bytes or 1.05 10 bytes.× 6

1-64 Assume the finger is a cylinder of diameter 1 cm and length 5 cm

finger cell 2 finger finger 3 cell 2

9

# cells =

π 4 π 3 (0.5 cm) (5 cm) 4

(5 10 cm) / cell 3

7.5 10 cells

−

=

=

×

V V

r

Thus, there are about 109 to 1010 cells

1-65 If the life expectancy is about 80 yr, the time interval is about 60 yr

blood blood

8 8

1 min

1.6 10 L

or about 1 10 L

×

V V

1-66 Assume that the fingernail takes about a week to grow 1 mm Since there are 106 nm in

1 mm, the time to grow 106 nm would be:

0.6 s/nm

=

Thus, it takes about 1 s for the fingernail to grow 1 nm

1-67 A lecture usually lasts about 50 minutes

6 365 d 24 h 60 min

1 μcentury =(10 )(100 yr)

1 yr 1 d 1 h 52.6 min

= Thus, the estimate of one microcentury is very close to the average 50 min lecture

1-68 V1/3, V2/3

1-69 (a) 100 km 1000 m 1 h 27.8 m/s

3

3.5 10 km/h

×

(c) To change m/s to km/h, multiply by 3.6 (as in (b) above); to change km/h to m/s,

divide by 3.6 (as in (a) above)

1-70 (a) increase = 1 ms 3000 yr = 30 ms

100 yr×

(b)

3

6

time 100 yr 10 ms 60 s

min 1 ms × 1 s ×1 min = ×

1-71 (a) The apparent rate of revolution is 360°/(24 h), or 15°/h

(b) The stars appear to move about 30° around the North Star, so the time-lapse

photograph lasted approximately 2 h

1-72 The field dimensions are 100 m by 60 m and the bill dimensions are about 7 cm by

15 cm When 10 bills are stacked tightly, the approximate thickness is 1 mm

5 field

bill

×

×