Transcript
Wilson, College Physics, 6th Edition
Chapter 1
Exercises*
MC = Multiple Choice Question, CQ = Conceptual Question, and IE = Integrated Exercise. Throughout the text, many exercise sections will include “paired” exercises. These exercise pairs, identified with red numbers, are intended to assist you in problem solving and learning. In a pair, the first exercise (even numbered) is worked out in the Study Guide so that you can consult it should you need assistance in solving it. The second exercise (odd numbered) is similar in nature, and its answer is given at the back of the book.
1.2 SI Units of Length, Mass, and Time
1. MC How many base units are there in the SI: (a) 3, (b) 5, (c) 7, or (d) 9? (c)
2. MC The only SI standard represented by material standard is the (a) meter, (b) kilogram, (c) second, (d) electric charge. (b)
3. MC Which of the following is not an SI base quantity: (a) mass; (b) weight; (c) length; or (d) time? (b)
4. MC Which of the following is the SI base unit for mass: (a) pound; (b) gram; (c) kilogram; (d) ton? (c)
5. CQ Why are there not more SI base units? no more fundamental quantities
6. CQ Why is weight not a base quantity? weight changes depending on gravity of locations
7. CQ What replaced the original definition of the second and why? Is the replacement still used? mean solar day, no, atomic clocks now used
8. CQ Give a couple of major differences between the SI and the British system. decimal vs. duodecimal bases
1.3 More about the Metric System
9. MC The prefix giga- means (a) (b) (c) (d) (b)
10. MC The prefix micro- means (a) (b) (c) (d) (b)
11. MC A new technology is concerned with objects the size of what metric prefix? (a) nano- (b) micro- (c) mega- (d) giga- (a)
12. MC One liter of water has a volume of (a) (b) 1 qt, (c) (d) (c)
13. CQ If a fellow student tells you he saw a 3-cm-long ladybug, would you believe him? How about another student saying she caught a 10-kg salmon? no, yes
14. CQ Explain why 1 mL is equivalent to and
15. CQ Explain why a metric ton is equivalent to 1000 kg. see ISM
16. The metric system is a decimal (base-10) system, and the British system is, in part, a duodecimal (base-12) system. Discuss the ramifications if our monetary system had a duodecimal base. What would be the possible values of our coins if this were the case? see ISM
17. (a) In the British system, and Is something wrong here? Explain. (b) Here’s an old one: A pound of feathers weighs more than a pound of gold. How can that be? [Hint: Look up ounce in the dictionary.] see ISM
18. A sailor tells you that if his ship is traveling at 25 knots (nautical miles per hour), it is moving faster than the your car travels. How can that be?
1.4 Unit Analysis*
19. MC Both sides of an equation are equal in (a) numerical value, (b) units, (c) dimensions, (d) all of the preceding. (d)
20. MC Unit analysis of an equation cannot tell you if (a) the equation is dimensionally correct, (b) the equation is physically correct, (c) the numerical value is correct, (d) both b and c. (d)
21. MC Which of the following is true for the quantity (a) It may have the same dimensions but different units; (b) it may have the same units but different dimensions; or (c) both a and b are true. (a)
22. CQ Can unit analysis tell you whether you have used the correct equation in solving a problem? Explain. no
23. CQ The equation for the area of a circle from two sources is given as and Can unit analysis tell you which is correct? Explain. no
24. CQ How might unit analysis help determine the units of a quantity? by putting in units and solving for those of unknown quantity
25. Show that the equation is dimensionally correct, where is velocity and x and are lengths, and t is time.
26. If x refers to distance, and to speeds, a to acceleration, and t to time, which of the following equations is dimensionally correct: (a) (b) (c) or (d) (d)
27. Use SI unit analysis to show that the equation where A is the area and r is the radius of a sphere, is dimensionally correct.
28. You are told that the volume of a sphere is given by where V is the volume and d is the diameter of the sphere. Is this equation dimensionally correct? (Use SI unit analysis to find out.) yes;
29. The correct equation for the volume of a sphere is where r is the radius of the sphere. Is the equation in Exercise 28 correct? If not, what should it be when expressed in terms of d? no;
30. The kinetic energy (K) of an object of mass m moving with speed is given by The name for the unit of kinetic energy in the SI system is the joule (J). What are the units of the joule in terms of SI base units?
31. The general equation for a parabola is where a, b, and c are constants. What are the units of each constant if y and x are in meters? a, b, dimensionless; c, m
32. The units for pressure (p) in terms of SI base units are known to be For a physics class assignment, a student derives an expression for the pressure exerted by the wind on a wall in terms of the air density and wind speed and her result is Use SI unit analysis to show that her result is dimensionally consistent. Does this prove that this relationship is physically correct? no
33. Density is defined as the mass of an object divided by the volume of the object. Using SI unit analysis, determine the SI unit for density. (See Section 1.4 for units of mass and volume.)
34. Is the equation for the area of a trapezoid, where a is the height and and are the bases, dimensionally correct? (Fig. 1.14.) yes
35. One student, using unit analysis, says that the equation is dimensionally correct. Another says it isn’t. With whom do you agree, and why? the first student; see ISM
36. Newton’s second law of motion (Chapter 4) is expressed by the equation where F represents force, m is mass, and a is acceleration. (a) The SI unit of force is, appropriately, called the newton (N). What are the units of the newton in terms of base quantities? (b) An equation for force associated with uniform circular motion (Chapter 7) is where is speed and r is the radius of the circular path. Does this equation give the same units for the newton? (a) (b) yes
37. The angular momentum (L) of a particle of mass m moving at a constant speed in a circle of radius r is given by (a) What are the units of angular momentum in terms of SI base units? (b) The units of kinetic energy in terms of SI base units are Using SI unit analysis, show that the expression for the kinetic energy of this particle in terms of its angular momentum, is dimensionally correct. (c) In the previous equation, the term is called the moment of inertia of the particle in the circle. What are the units of moment of inertia in terms of SI base units? (a) (b) see ISM (c)
38. Einstein’s famous mass–energy equivalence is expressed by the equation where E is energy, m is mass, and c is the speed of light. (a) What are the SI base units of energy? (b) Another equation for energy is where m is mass, g is the acceleration due to gravity, and h is height. Does this equation give the same units as in part (a)? (a) (b) yes
1.5 Unit Conversions*
39. MC A good way to ensure proper unit conversion is to (a) use another measurement instrument, (b) always work in the same system of units, (c) use unit analysis, (d) have someone check your math. (c)
40. MC You often see This expression means that (a) 1 kg is equivalent to 2.2 lb, (b) this is a true equation, (c) (d) none of the preceding. (a)
41. MC You have a quantity of water and wish to express this in volume units that give the largest number. Should you use (a) (b) mL; (c) or (d) (c)
42. CQ Are an equation and an equivalence statement the same? Explain. no
43. CQ Does it make any difference whether you multiply or divide by a conversion factor? Explain. yes
44. CQ Does unit analysis apply to unit conversions? Explain. yes
45. Figure 1.8 (top) shows the elevation of a location in both feet and meters. If a town is 130 ft above sea level, what is the elevation in meters? 39.6 m
46. IE (a) If you wanted to express your height with the largest number, you would use (1) meters, (2) feet, (3) inches, (4) centimeters. Why? (b) If you are 6.00 ft tall, what is your height in centimeters? (a) (4) cm (b) 183 cm
47. If the capillaries of an average adult were unwound and spread out end to end, they would extend to a length over (Fig. 1.9). If you are 1.75 m tall, how many times your height would the capillary length equal? times
48. IE (a) Compared with a 2-L soda bottle, a half-gallon soda bottle holds (1) more, (2) the same amount of, (3) less soda. (b) Verify your answer for part (a). (a) (3) less soda (b) 2 L by 0.11 L more
49. (a) A football field is 300 ft long and 160 ft wide. What are the field’s dimensions in meters? (b) A football is 11.0 to long. What is its length in centimeters? (a) 91.5 m by 48.8 m (b) 27.9 cm to 28.6 cm
50. Suppose that when the United States goes completely metric, the dimensions of a football field are established as 100 m by 54 m. Which would be larger, the metric football field or a current football field (see Exercise 49a), and what would be the difference between the areas? metric;
51. If blood flows with an average speed of in the human circulatory system, how many miles does a blood cell travel in 1.0 h? 0.78 mi
52. Driving a jet-powered car, Royal Air Force pilot Andy Green broke the sound barrier on land for the first time and achieved a record land speed of more than in Black Rock Desert, Nevada, on October 15, 1997 (Fig. 1.15). (a) What is this speed expressed in (b) How long would it take the jet-powered car to travel the length of a 300-ft football field at this speed? (a) (b) 0.268 s
53. IE (a) Which of the following represents the greatest speed: (1) (2) (3) or (4) (b) Express the speed in (a) (1) (b)
54. An automobile speedometer is shown in Fig. 1.16. (a) What would be the equivalent scale readings (for each empty box) in kilometers per hour? (b) What would be the speed limit in kilometers per hour? (a) for each (b)
55. A person weighs 170 lb. (a) What is her mass in kilograms? (b) Assuming the density of the average human body is about that of water (which is true), estimate her body’s volume in both cubic meters and liters. Explain why the smaller unit of the liter is more appropriate (convenient) for describing this size volume. (a) 77.3 kg (b) or about 77.3 L
56. If the components of the human circulatory system (arteries, veins, and capillaries) were completely extended and placed end to end, the length would be on the order of Would the length of the circulatory system reach around the circumference of the Moon? If so, how many times? yes, 9.1 times
57. The human heartbeat, as determined by the pulse rate, is normally about If the heart pumps 75 mL of blood per beat, what volume of blood is pumped in one day in liters?
58. A typical wide receiver in American football can run the 40-yd dash in about 4.5 s starting from rest. (a) What is his average speed in (b) What is his average speed in (a) (b)
59. Some common product labels are shown in Fig. 1.17. From the units on the labels, find (a) the number of milliliters in 2 fl. oz and (b) the number of ounces in 100 g. (a) 59.1 mL (b) 3.53 oz
60. Fig. 1.18 is a picture of red blood cells seen under a scanning electron microscope. Normally, women possess about 4.5 million of these cells in each cubic millimeter of blood. If the blood flow to the heart organ is how many red blood cells does a woman’s heart receive each second?
61. A student was 18 in. long when she was born. She is now 5 ft 6 in. tall and 20 years old. How many centimeters a year did she grow on average? 6.1 cm
62. The density of metal mercury is (a) What is this density as expressed in kilograms per cubic meter? (b) How many kilograms of mercury would be required to fill a 0.250-L container? (a) (b) 3.40 kg
63. The Roman Coliseum used to be flooded with water to recreate ancient naval battles. Assuming the floor of the Coliseum to be 250 m in diameter and the water to have a depth of 10 ft, (a) how many cubic meters of water are required? (b) How much mass would this water have in kilograms? (c) How much would the water weigh in pounds? (a) (b) (c)
64. In the Bible, Noah is instructed to build an ark 300 cubits long, 50.0 cubits wide, and 30.0 cubits high (Fig. 1.19). Historical records indicate a cubit is equal to half a yard. (a) What would the dimensions of the ark be in meters? (b) What would the ark’s volume be in cubic meters? To approximate, assume that the ark is to be rectangular. (a) (b)
1.6 Significant Figures
65. MC Which of the following has the greatest number of significant figures: (a) 103.07; (b) 124.5; (c) 0.09916; or (d) (a)
66. MC Which of the following numbers has four significant figures: (a) 140.05; (b) 276.02; (c) or (d) (c)
67. MC In a multiplication and/or division operation involving the numbers 201.08, and the result should have how many significant figures? (a) 3 (b) 4 (c) 5 (d) any number (b)
68. CQ What is the purpose of significant figures? to provide an estimation of accuracy
69. CQ Are all the significant figures reported for a measured value accurately known? Explain. no
70. CQ How are the number of significant figures determined for the results of calculations involving (a) multiplication, (b) division, (c) addition, and (d) subtraction? see ISM
71. Express the length (micrometers) in centimeters, decimeters, and meters, to three significant figures. 5.05 cm;
72. Using a meterstick, a student measures a length and reports it to be 0.8755 m. What is the smallest division on the meterstick scale? 0.001 m, or 1 mm
73. Determine the number of significant figures in the following measured numbers: (a) 1.007 m; (b) 8.03 cm; (c) 16.272 kg; (d) (microseconds). (a) 4 (b) 3 (c) 5 (d) 2
74. Express each of the numbers in Exercise 73 with two significant figures (a) 1.0 m (b) 8.0 cm (c) 16 kg (d)
75. Which of the following quantities has three significant figures: (a) 305.0 cm; (b) 0.0500 mm; (c) 1.000 81 kg; or (d) (b) and (d); (a) has four and (c) has six
76. The cover of your physics book measures 0.274 m long and 0.222 m wide. What is its area in square meters?
77. The interior storage compartment of a restaurant refrigerator measures 1.3 m high, 1.05 m wide, and 67 cm deep. Determine its volume in cubic feet.
78. IE The top of a rectangular table measures 1.245 m by 0.760 m. (a) The smallest division on the scale of the measurement instrument is (1) m, (2) cm, (3) mm. Why? (b) What is the area of the tabletop? (a) (2) cm (b)
79. IE The outside dimensions of a cylindrical soda can are reported as 12.559 cm for the diameter and 5.62 cm for the height. (a) How many significant figures will the total outside area have: (1) two; (2) three; (3) four; or (4) five? Why? (b) What is the total outside surface area of the can in cubic centimeters? (a) (2) three (b)
80. Express the following calculations to the proper number of significant figures: (a) (b) (c) (d) (a) 14.7 (b) 11.4 (c) (d) 0.82
81. IE In doing a problem, a student adds 46.9 m and 5.72 m and then subtracts 38 m from the result. (a) How many decimal places will the final answer have: (1) zero; (2) one; or (3) two? Why? (b) What is the final answer? (a) (1) zero (b) 15 m
82. Work this exercise by the two given procedures as directed, commenting on and explaining any difference in the answers. Use your calculator for the calculations. Compute where given and (a) First compute and then p. (b) Compute without an intermediate step. (c) Are the results the same? If not, why? (a) (b) (c) no, rounding difference
1.7 Problem Solving
83. MC An important step in problem solving before mathematically solving an equation is (a) checking units, (b) checking significant figures, (c) checking with a friend, (d) checking to see if the result will be reasonable. (a)
84. MC An important final step in problem solving before reporting an answer is (a) saving your calculations, (b) reading the problem again, (c) seeing if the answer is reasonable, (d) checking your results with another student. (c)
85. MC In order-of-magnitude calculations, you should (a) pay close attention to significant figures, (b) work primarily in the British system, (c) get results within a factor of 100, (d) express a quantity to the power of 10 closest to the actual value. (d)
86. CQ How many steps are in a good problem-solving procedure as suggested in this chapter? six
87. CQ What are the main steps in a problem-solving procedure? all six steps as listed in the chapter
88. CQ When you do order-of-magnitude calculations, should you be concerned about significant figures? Explain. no
89. CQ When doing an order-of-magnitude calculation, how accurate can you expect the answer to be? Explain. within an order of 10
90. A corner construction lot has the shape of a right triangle. If the two sides perpendicular to each other are 37 m long and 42.3 m long, respectively, what is the length of the hypotenuse? 56 m
91. The lightest solid material is silica aerogel, which has a typical density of only about The molecular structure of silica aerogel is typically 95% empty space. What is the mass of of silica aerogel? 100 kg
92. Nutrition Facts labels now appear on most foods. An abbreviated label concerned with fat is shown in Fig. 1.20. When burned in the body, each gram of fat supplies 9 Calories. (A food Calorie is really a kilocalorie, as we shall see in Chapter 11.) (a) What percentage of the Calories in one serving is supplied by fat? (b) You may notice that our answer doesn’t agree with the listed Total Fat percentage in Fig. 1.20. This is because the given Percent Daily Values are the percentages of the maximum recommended amounts of nutrients (in grams) contained in a 2000-Calorie diet. What are the maximum recommended amounts of total fat and saturated fat for a 2000-Calorie diet? (a) 52% (b) 64 g, 20 g
93. The thickness of the total of numbered pages of a textbook is measured to be 3.75 cm. (a) If the last page of the book is numbered 860, what is the average thickness of a page? (b) Repeat the calculation by using order-of-magnitude calculations. (a) (b) about
94. IE To go to a football stadium from your house, you first drive 1000 m north, then 500 m west, and finally 1500 m south. (a) Relative to your home, the football stadium is (1) north of west, (2) south of east, (3) north of east, (4) south of west. (b) What is the straight-line distance from your house to the stadium? (a) (4) south of west (b) 707 m
95. Two chains of length 1.0 m are used to support a lamp, as shown in Fig. 1.21. The distance between the two chains is 1.0 m along the ceiling. What is the vertical distance from the lamp to the ceiling? 0.87 m
96. Tony’s Pizza Palace sells a medium 9.0-in. (diameter) pizza for $7.95, and a large 12-in. pizza for $13.50. Which pizza is the better buy? 12-in. better buy; 9.0-in.: 12-in.:
97. In Fig. 1.22, which black region has the greater area, the center circle or the outer ring? same area for both,
98. The Channel Tunnel, or “Chunnel,” which runs under the English Channel between Great Britain and France, is 31 mi long. (There are actually three separate tunnels.) A shuttle train that carries passengers through the tunnel travels with an average speed of On average, how long, in minutes, does the shuttle take to make a one-way trip through the Chunnel? 25 min
99. Human adult blood contains on the average white blood cells (leukocytes) and platelets (thrombocytes). If a person has a blood volume of 5.0 L, estimate the total number of white cells and platelets in the blood.
100. A 10-ft by 20-ft lawn area is to be made into an outdoor patio by placing 2.0-ft-diameter circular concrete “pads” in an array so they touch each other. The existing grass will fill the spaces. (a) How many of these pads are required to do the job? (b) When the project is completed, what percentage of the original grass will still remain? (a) 50 (b) 21.5%
101. Experimentally, the force felt on an auto due to its movement through the (still) air varies approximately as the square of the car’s speed. (This force is sometimes called “air resistance.”) Assume this force varies exactly as the square of the speed. Around town at measurements indicate that a certain car experiences an air resistance force of 100 lb. What size force would you expect to the car to experience traveling on highway at
102. The average number of hairs on the normal human scalp is 125 000. A healthy person loses about 65 hairs per day. (New hair from the hair follicle pushes the old hair out.) (a) How many hairs are lost in one month? (b) Pattern baldness (top-of-the-head hair loss) affects about 35 million men in the United States. With an average of 15% of the scalp bald, how many hairs are lost per year by one of these “bald is beautiful” people? (a) 1950 hairs (b)
103. Approximately 118 mi wide and 307 mi long and averaging 279 ft in depth, Lake Michigan is the second-largest Great Lake by volume. Estimate its volume of water in cubic meters. about
104. IE In the Tour de France, a rider races up two successive (straight) hills of different slope and length. The first is 2.00 km long at an angle of 5° above the horizontal. This is immediately followed by one 3.00 km long at 7°. (a) What will be the overall (net) angle from start to finish: (1) smaller than 5°; (2) between 5° and 7°; or (3) greater than 7°? (b) Calculate the actual overall (net) angle of rise experienced by this racer from start to finish, to corroborate your reasoning in part (a). (a) (2) between 5? and 7? (b) 6.2?
105. A student wants to determine the distance of a small island from the lakeshore (Fig. 1.23). He first draws a 50-m line parallel to the shore. Then, he goes to the ends of the line and measures the angles of the lines of sight from the island relative to the line he has drawn. The angles are 30° and 40°. How far is the island from the shore? 17 m
Comprehensive Exercises
106. IE A car is driven 13 mi east and then a certain distance due north and ends up at a position 25° north of east of its initial position. (a) The distance traveled by the car due north is (1) less than, (2) equal to, (3) greater than 13 mi. Why? (b) What distance does the car go due north? (a) (1) less than (b) 6.1 mi
107. An airplane flies 100 mi south from city A to city B, 200 mi east from city B to city C, and then 300 mi north from city C to city D. (a) What is the straight-line distance from city A to city D? (b) What is the direction of city D relative to city A? (a) 283 mi (b) 45° north of east
108. In a radioactivity experiment, a solid lead brick (same measurements as a patio brick, except with a density that is 11.4 times that of water) is to be modified to hold a solid cylindrical piece of plastic. To accomplish this, the machinists are told to drill a cylindrical hole 2.0 cm in diameter through the center of the brick parallel to the longest side of the brick. (a) What is the mass of lead (in kilograms) removed from the brick? (b) What percentage of the original lead remains in the brick? (c) Assuming the cylindrical hole is completely filled with plastic (with a density twice that of water), determine the overall (average) density of the brick/plastic combination after fabrication is complete. (a) 0.727 kg (b) 93.9% (c)
109. On a certain night, an observer on the Earth determines that the angle between the direction to Mars and the direction to the Sun is 50°. On that night, assuming circular orbits, determine the distance to Mars from the Earth using the known radii of the orbits of both planets.
110. Estimate the number of water molecules in a cup (8 oz. exactly) of water [Hint: You may find it helpful to recall that the mass of a hydrogen atom is about and that an oxygen atom’s mass is about sixteen times that value.] on the order of mole cules
111. IE At the Indianapolis 500 time trials, each car gets a chance to make four consecutive laps, with its overall or average speed determining that car’s place on race day. Each lap covers 2.5 mi (exact). During a practice run, cautiously and gradually taking his car faster and faster, a driver records the following average speed for each successive lap: and (a) Will his average speed be (1) exactly the average of these speeds (2) greater than or (3) less than Explain. (b) To corroborate your conceptual reasoning, calculate the car’s average speed. (a) (3) less than (b) 187
112. A student doing a lab experiment drops a small solid cube into a cylindrical gas of water. The inner diameter of the glass is 6.00 cm. The cube sinks to the bottom, and the water level in the glass rises 1.00 cm. If the mass of the cube is 73.6 g, (a) determine the length of one side of the cube, and (b) calculate the cube’s density. (Work the exercise in cgs units for convenience). (a) 3.05 cm (b)
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