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

Solution Manual for Physics An Algebra Based Approach 1st Edition by McFarlan Full file at https://TestbankDirect.eu/ Chapter 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 © Copyright 2016 by Nelson Education Ltd Full file at https://TestbankDirect.eu/ Solution Manual for Physics An Algebra Based Approach 1st Edition by McFarlan Full file Physics: at https://TestbankDirect.eu/ 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 1-7 • Cloudy conditions interfere with observation of any celestial body • Accuracy is difficult to achieve • Convenience is minimal 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) Length × 1026 m = = × 1041 −15 length × 10 m (b) Time × 1017 s = = 1.7 × 1042 time × 10−25 s (c) Mass × 1053 kg = = × 1083 −31 mass × 10 kg Mass has by far the greatest range of values © Copyright 2016 by Nelson Education Ltd Full file at https://TestbankDirect.eu/ Solution Manual for Physics An Algebra Based Approach 1st Edition by McFarlan Full file at https://TestbankDirect.eu/ 1-10 In seconds, $1×109 × In years, $1×109 × Chapter 1—Measurement and Types of Quantities 1s = 1×109 s $ 1s year × = 31 years $ 3.2 ×107 s ×1041 kg = ×1011 stars kg × 1030 star 1-11 # stars = 1-12 # atoms = 1-13 (a) 8.4 × 10−15 (b) × 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 × 1030 kg = 1×1057 atoms kg 1.7 ×10−27 atom 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 © Copyright 2016 by Nelson Education Ltd Full file at https://TestbankDirect.eu/ Solution Manual for Physics An Algebra Based Approach 1st Edition by McFarlan Full file Physics: at https://TestbankDirect.eu/ 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 is (103)7 or 1021) 1-17 1-18 m = 1.3 m dam (a) 1.3 × 10−1 dam × 101 (b) 30 nm × (c) 1.23 × 104 km × (d) 1.486 ×10−3 Tm × (a) 20 ms × (b) 8.6 cm × (c) 3.28 g × (d) 103 kHz 105 MHz × = 1.05 ×105 kHz MHz (e) 2.4 × 10−3 MW 103 mW 106 W 2.4 × 106 mW × × = m2 W MW m2 (f) 9.8 m s 1s 9.8 ×10−12 m × × = s2 106 μs 106 μs μs (g) 4.7 g kg 106 cm3 4.7 ×103 kg × × = cm3 103 g m3 m3 (h) 53 people km 104 m 0.53 people × 2× = km 10 m ha 1m = ×10−8 m 109 nm 1000 m = 1.23 × 107 m km 1012 m = 1.486 ×109 m Tm 1s = ×10−2 s 10 ms 1m 106 μm × = 8.6 ×104 μm 102 cm m Mg = 3.28 × 10−6 Mg 10 g © Copyright 2016 by Nelson Education Ltd Full file at https://TestbankDirect.eu/ Solution Manual for Physics An Algebra Based Approach 1st Edition by McFarlan Full file at https://TestbankDirect.eu/ 1-19 Chapter 1—Measurement and Types of Quantities (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 in ft mi 62.1 mi × × × × × = h km m 2.54 cm 12 in 5280 ft h 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 Thus, the dimensions are T equal d , which has dimensions of L ⋅ T −3 or L/T t3 1-25 From d = kt , k = 1-26 From d = vo t + 12 at the left side of the equation has dimension L, and the right side has L L × T + × T2 = L dimension T , so the equation is dimensionally correct T © Copyright 2016 by Nelson Education Ltd Full file at https://TestbankDirect.eu/ Solution Manual for Physics An Algebra Based Approach 1st Edition by McFarlan Full file Physics: at https://TestbankDirect.eu/ An Algebra-Based Approach 1-27 To compare the uncertainties, begin by expressing them in the same unit Thus, ±100 g × kg = ±0.1 kg The most expensive scale is likely the first one, 1000 g 42.40 kg ± 0.005 kg, which provides the greatest number of significant digits and the smallest uncertainty The least expensive scale is likely the last one, which has the largest uncertainty, ±0.1 kg 1-28 (a) (b) (c) (d) 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 × 10−2 μg 1-30 percent error = = measured value − accepted value accepted value 1.08 × 103 kg/m3 − 1.00 × 103 kg/m3 1.00 × 103 kg/m3 = 0.08 × 100% or 8% 1-31 Perimeter: × 100% × 100% p = 2l + 2w = 2(1.18 m)+2(0.378 m) =3.116 m or 3.12 m Thus, the perimeter is 3.12 m, rounded off to one estimated digit Area: A = lw = 1.18 m × 0.378 m = 0.446 m Thus, the area is 0.446 m² (rounded off to three significant digits) © Copyright 2016 by Nelson Education Ltd Full file at https://TestbankDirect.eu/ Solution Manual for Physics An Algebra Based Approach 1st Edition by McFarlan Full file at https://TestbankDirect.eu/ 1-32 (a) Chapter 1—Measurement and Types of Quantities mn − mp = 1.674 927 ×10−27 kg − 1.672 621×10 −27 kg =2.306 × 10−30 kg (b) mp − me = 1.672 621×10−27 kg − 9.109 382 ×10−31kg =1.672 621×10−27 kg − 0.000 910 938 ×10−27 kg =1.671 710 ×10−27 kg Greatest distance = 1.495 988 × 1011 m + 3.844 ×108 m = 1.495 988 × 1011 m + 0.003 844 ×1011 m = 1.499 832 ×1011 m Least distance = 1.495 988 × 1011 m − 3.844 ×108 m = 1.495 988 × 1011 m − 0.003 844 ×1011 m = 1.492 144 ×1011 m 1-33 1-34 d d 1.495 988 ×1011 m From v = , t = = = 499 s 3.00 ×108 m/s t v Thus, the time to three significant digits is 499 s 1-35 In all cases, the actual numerical values will vary (a) # cells = = mass mass/cell 60 kg 1×10−12 kg/cell = about 1×1014 cells Thus, the number would be about 1014 cells (b) First, we must make some assumptions, all of which are approximations © Copyright 2016 by Nelson Education Ltd Full file at https://TestbankDirect.eu/ Solution Manual for Physics An Algebra Based Approach 1st Edition by McFarlan Full file Physics: at https://TestbankDirect.eu/ An Algebra-Based Approach 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 estimated mass = = mass patties × × # of people patty person 0.2 kg 30 patties × × ×108 people patty person = ×109 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 =π d , is about 100 m Assume that the straight line distance from Calgary to Winnipeg is about 1000 km # of rotations = distance distance/rotation = 1×103 km 1×103 m/rotation = 1×103 km 1×10−1 km/rotation = 1×104 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 m, so the total “population arm span” is about × 107 m or × 104 km coastline length 2×105 km # of populations = = = populations length/population 4ì104 km/population â Copyright 2016 by Nelson Education Ltd Full file at https://TestbankDirect.eu/ Solution Manual for Physics An Algebra Based Approach 1st Edition by McFarlan Full file at https://TestbankDirect.eu/ 1-36 Chapter 1—Measurement and Types of Quantities 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 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) © Copyright 2016 by Nelson Education Ltd Full file at https://TestbankDirect.eu/ Solution Manual for Physics An Algebra Based Approach 1st Edition by McFarlan Full file Physics: at https://TestbankDirect.eu/ An Algebra-Based Approach 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 m high Then the height of the building is: height =30 storeys × 3m storey = 90 m = 90 m × dam 10 m = dam Thus, the height is about 90 m, or dam 1-48 10 (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 ì 1021 s, 6.9 ì 103 Es â Copyright 2016 by Nelson Education Ltd Full file at https://TestbankDirect.eu/ Solution Manual for Physics An Algebra Based Approach 1st Edition by McFarlan Full file at https://TestbankDirect.eu/ 1-49 1-50 Chapter 1—Measurement and Types of Quantities Answers depend on each student’s mass Using a mass of 60 kg, the ratios would be (a) 16 Mg 103 kg × 102 × = 60 kg Mg (b) 0.26 kg × 10−3 = 60 kg (c) 5.2 × 102 kg = 60 kg (d) 6.7 ×106 dg kg 1g 1×101 × × = 60 kg 10 g 10 dg (e) 28 g kg × 10−4 × = 60 kg 103 g mass = 3.0 kg × 8.6 × 104 = 2.6 × 105 kg = 2.6 × 102 Mg 1-51 1-52 (a) 2.00 × 102 km − 3.00 × 103 m = 2.00 × 10 km − 3.0 km = 1.97 × 102 km (b) 4.4 ×103 m m = 2.2 ×10−2 2.0 ×10 s s (c) 4.4 ×103 m 4.4 ×103 m m = = 1.1×10−7 10 (2.0 ×10 s) 4.0 ×10 s s (a) r is the radius; b is the base; h is the height (b) The dimension of πr ² is L2, and the dimension of bh/2 is L2 So we conclude that area has the dimension L2 © Copyright 2016 by Nelson Education Ltd Full file at https://TestbankDirect.eu/ 11 Solution Manual for Physics An Algebra Based Approach 1st Edition by McFarlan Full file Physics: at https://TestbankDirect.eu/ An Algebra-Based Approach 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 1-54 (c) [P] = M·L2/T3, [p] = M/LT2 (d) [E] = M·[v]2 (e) [P] = M·[v]·[a] 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 percent error = = = measured value − accepted value accepted value 1.82 × 108 m/s − 1.86 ×108 m/s 1.86 × 108 m/s × 100% × 100% 0.04 m/s × 100% 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 12 © Copyright 2016 by Nelson Education Ltd Full file at https://TestbankDirect.eu/ Solution Manual for Physics An Algebra Based Approach 1st Edition by McFarlan Full file at https://TestbankDirect.eu/ 1-58 Chapter 1—Measurement and Types of Quantities Let M represent the men’s discus, W represent the women’s discus, l represent length or distance, and d represent diameter lM − l W = l lM × 25.0 rev − W × 25.0 rev rev rev = π (d M ) = π (0.221 m) rev × 25.0 rev − rev π (d W ) rev × 25.0 rev − × 25.0 rev π (0.182 m) rev × 25.0 rev = 3.06 m 1-59 A = lw = 7.32 m × 2.44 m =17.9 m 1-60 V = πr h = π ( 4.2 cm ) ( 22.8 cm ) = 1.3 ×103 cm3 1-61 Answers will depend on the assumptions made (a) Assume a normal pace is 0.6 m or × 10−4 km # paces = = distance distance/pace 1.6 km ×10−4 km/pace = 2.7 ×103 paces Thus, the number of paces is likely between × 103 and × 103 © Copyright 2016 by Nelson Education Ltd Full file at https://TestbankDirect.eu/ 13 Solution Manual for Physics An Algebra Based Approach 1st Edition by McFarlan Full file Physics: at https://TestbankDirect.eu/ An Algebra-Based Approach (b) Assume that the size of a kernel of corn is about mm by mm by mm The kernel's volume is V = lwh = (0.3 cm)(0.2 cm)(0.2 cm) = 0.012 cm3 # kernels = = volume volume/kernel (10 cm)3 0.012 cm / kernel = 8.3 ×10 kernels Thus, the estimated number is between 1× 10 and 1× 105 kernels (c) Above-ground pools are often circular Assume the diameter of the pool is m or 40 dm and the height is 0.6 m or dm V = area × height =π r × h = π (20 dm) × dm = ×103 dm3 or ×103 L Thus, the volume would be about 1× 104 L (d) Assume a heartbeat of 72 beats per minute, or 1.2 beats/s For this example, assume an age of 19 years # beats = heart rate × age (in seconds) = 1.2 beats days h s × 19 years × 365 × 24 × 3600 s year day h = 7.2 × 108 beats Thus, the number of beats would be about 1ì 109 14 â Copyright 2016 by Nelson Education Ltd Full file at https://TestbankDirect.eu/ Solution Manual for Physics An Algebra Based Approach 1st Edition by McFarlan Full file at https://TestbankDirect.eu/ (e) Chapter 1—Measurement and Types of Quantities Let’s assume that the average person sleeps about h each day Let’s also make the very simplistic assumption that the human population of about billion is distributed approximately equally around Earth’s time zones # people = fraction sleeping × total population = × × 109 people = 2.3 ×109 people or about × 109 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 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 1-64 Assume the finger is a cylinder of diameter cm and length cm # cells = Vfinger Vcell πrfinger hfinger = πrcell3 = (0.5 cm)2 (5 cm) (5 × 10−4 cm)3 / cell = 7.5 ×109 cells Thus, there are about 109 to 1010 cells © Copyright 2016 by Nelson Education Ltd Full file at https://TestbankDirect.eu/ 15 Solution Manual for Physics An Algebra Based Approach 1st Edition by McFarlan Full file Physics: at https://TestbankDirect.eu/ An Algebra-Based Approach 1-65 If the life expectancy is about 80 yr, the time interval is about 60 yr Vblood = = Vblood × total time 5L 365 d 24 h 60 × 60 yr × × × yr 1d 1h = 1.6 × 108 L or about ×108 L 1-66 Assume that the fingernail takes about a week to grow mm Since there are 106 nm in mm, the time to grow 106 nm would be: week 7d 24 h 3600 s = × × 10 nm 10 nm d 1h = 0.6 s/nm Thus, it takes about s for the fingernail to grow nm 1-67 A lecture usually lasts about 50 minutes μcentury =(10−6 )(100 yr) × 365 d 24 h 60 × × yr 1d 1h = 52.6 Thus, the estimate of one microcentury is very close to the average 50 lecture 1-68 V 1/3, V 2/3 1-69 (a) (b) 16 100 km 1000 m 1h × × = 27.8 m/s 1h km 3600 s 97 m km 3600 s × × = 3.5 × 102 km/h s 1× 10 m 1h © Copyright 2016 by Nelson Education Ltd Full file at https://TestbankDirect.eu/ Solution Manual for Physics An Algebra Based Approach 1st Edition by McFarlan Full file at https://TestbankDirect.eu/ (c) Chapter 1—Measurement and Types of Quantities 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 1-71 increase = (a) ms × 3000 yr = 30 ms 100 yr (b) time 100 yr 103 ms 60 s × × = ×106 yr = ms 1s (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 h 1-72 The field dimensions are 100 m by 60 m and the bill dimensions are about cm by 15 cm When 10 bills are stacked tightly, the approximate thickness is mm # bills = area field area bill = 100 m × 60 m (0.07 m × 0.15 m)/bill = 6×105 bills thickness = 6×105 bills × (1×10 −4 m/bill) = 6ì101 m or about 60 m â Copyright 2016 by Nelson Education Ltd Full file at https://TestbankDirect.eu/ 17 .. .Solution Manual for Physics An Algebra Based Approach 1st Edition by McFarlan Full file Physics: at https://TestbankDirect.eu/ An Algebra- Based Approach 1-6 Some of the disadvantages... Manual for Physics An Algebra Based Approach 1st Edition by McFarlan Full file Physics: at https://TestbankDirect.eu/ An Algebra- Based Approach 1-27 To compare the uncertainties, begin by expressing... Copyright 2016 by Nelson Education Ltd Full file at https://TestbankDirect.eu/ Solution Manual for Physics An Algebra Based Approach 1st Edition by McFarlan Full file Physics: at https://TestbankDirect.eu/