Exam (elaborations) INSTRUCTOR’S SOLUTIONS MANUAL FOR_SERWAY AND VUILLE’S_COLLEGE PHYSICS NINTH EDITION, VOLUME 1 College Physics, ISBN: 9780840062062

Exam (elaborations) INSTRUCTOR’S SOLUTIONS MANUAL FOR_SERWAY AND VUILLE’S_COLLEGE PHYSICS NINTH EDITION, VOLUME 1 College Physics, ISBN: 2062 INSTRUCTOR’S SOLUTIONS MANUAL FOR SERWAY AND VUILLE’S COLLEGE PHYSICS NINTH EDITION, VOLUME 1 Charles Teague Emeritus, Eastern Kentucky University Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States © 2011 Brooks/Cole, Cengage Learning ALL RIGHTS RESERVED. No part of this work covered by the copyright herein may be reproduced, transmitted, stored, or used in any form or by any means graphic, electronic, or mechanical, including but not limited to photocopying, recording, scanning, digitizing, taping, Web distribution, information networks, or information storage and retrieval systems, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without the prior written permission of the publisher. 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TABLE OF CONTENTS Acknowledgements v Preface vii Part 1 – Mechanics Chapter 1 – Introduction 1 Chapter 2 – Motion in One Dimension 17 Chapter 3 – Vectors and Two-Dimensional Motion 49 Chapter 4 – The Laws of Motion 89 Chapter 5 – Energy 129 Chapter 6 – Momentum and Collisions 169 Chapter 7 – Rotational Motion and the Law of Gravity 209 Chapter 8 – Rotational Equilibrium and Rotational Dynamics 243 Chapter 9 – Solids and Fluids 288 Part 2 – Thermodynamics Chapter 10 – Thermal Physics 322 Chapter 11 – Energy in Thermal Processes 344 Chapter 12 – The Laws of Thermodynamics 371 Part 3 – Vibrations and Waves Chapter 13 – Vibrations and Waves 400 Chapter 14 – Sound 426 iii v ACKNOWLEDGEMENTS The author would like to thank everyone who has contributed to this work. In particular, thanks go to the support staff at Cengage Learning for their excellent guidance and support in all phases of this project. Special mention goes to Physics Acquisitions Editor, Charles Hartford; Development Editor, Ed Dodd; Associate Content Project Manager, Holly Schaff ; Associate Development Editor, Brandi Kirksey; and Editorial Assistant, Brendan Killion. Susan English of Durham Technical Community College served as accuracy reviewer for this manual. Her contributions are deeply appreciated. Any remaining errors in this work are the responsibility of the author alone. I would like to acknowledge the staff of MPS Limited, a Macmillan Company for their excellent work in assembling and typing this manual and preparing diagrams and page layouts. Finally, the author would like to thank his wife, Carol, for her patience, understanding, and great support during this eff ort. PREFACE This manual is written to accompany College Physics, Ninth Edition, by Raymond A. Serway and Chris Vuille. For each chapter in that text, the manual includes solutions to all end-of- chapter problems, more detailed answers to Quick Quizzes and Multiple Choice Questions than available in the main text, and answers to the even-numbered Conceptual Questions. Considerable eff ort has been made to insure that the solutions and answers given in this manual comply with the rules on signifi cant fi gures and rounding given in the Chapter 1 of the textbook. This means that intermediate answers are rounded to the proper number of signifi cant fi gures when written, and that rounded value is used in all subsequent calculations. Users should not be concerned if their answers diff er slightly in the last digit from the answers given here. Most often, this will be caused by choosing to round intermediate answers at diff erent stages of the solution. You are encouraged to keep this manual out of the hands of students as instructors in many colleges throughout the country use this textbook, and many of them use graded problem assignments as part of the fi nal course grade. Additionally, even when the problems are not used in such a direct fashion, it is advantageous for students to struggle with some problems in order to improve their problem-solving skills. Feel free to post answers and solutions to selected questions and problems, but please preserve the manual as a whole. You may also encourage students to purchase a copy of the Student Solutions Manual with Study Guide, which provides chapter summaries as well as detailed solutions to selected problems in the main text. Attempting to keep the manual of manageable size, and recognizing that the primary users will be instructors well versed in the fi eld, answers and solutions are kept fairly brief. Answers to conceptual questions have been shortened by not off ering detailed arguments that lead to the answer. Problem solutions often omit commentary, intermediate steps, as well as initial steps that could be necessary for clear understanding by students. On occasions where selected problem solutions are to be shared with students, you may wish to supply intermediate steps and additional comments as needed. An electronic version of this manual can be obtained by requesting the Instructor’s Power Lecture CD from your local Cengage Learning Sales Representative. Contact information for your sales representative is available under the “Find Your Rep” tab found at the bottom of the page at www. . We welcome your comments on the accuracy of the solutions as presented here, as well as suggestions for alternative approaches. Charles Teague vii 1 Introduction ANSWERS TO MULTIPLE CHOICE QUESTIONS 1. Using a calculator to multiply the length by the width gives a raw answer of 6783 m2, but this answer must be rounded to contain the same number of signifi cant fi gures as the least accurate factor in the product. The least accurate factor is the length, which contains either 2 or 3 signifi cant fi gures, depending on whether the trailing zero is signifi cant or is being used only to locate the decimal point. Assuming the length contains 3 signifi cant fi gures, answer (c) correctly expresses the area as 6.78 ×103 m2 . However, if the length contains only 2 signifi cant fi gures, answer (d) gives the correct result as 6.8 ×103 m2 . 2. Both answers (d) and (e) could be physically meaningful. Answers (a), (b), and (c) must be meaningless since quantities can be added or subtracted only if they have the same dimensions. 3. According to Newton’s second law, Force = mass×acceleration. Thus, the units of Force must be the product of the units of mass (kg) and the units of acceleration (m s2 ). This yields kg⋅m s2, which is answer (a). 4. The calculator gives an answer of 57.573 for the sum of the 4 given numbers. However, this sum must be rounded to 58 as given in answer (d) so the number of decimal places in the result is the same (zero) as the number of decimal places in the integer 15 (the term in the sum containing the smallest number of decimal places). 5. The required conversion is given by: h =( )⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 2 00 1 000 1 00 . . m mm 1.00 m cubitus 445 mm ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ = 4.49 cubiti This result corresponds to answer (c). 6. The given area (1 420 ft2 ) contains 3 signifi cant fi gures, assuming that the trailing zero is used only to locate the decimal point. The conversion of this value to square meters is given by: A = ( × )⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 1 42 103 = 1 32 ×10 2 . ft . 2 1.00 m 3.281 ft 2 m2 = 132 m2 Note that the result contains 3 signifi cant fi gures, the same as the number of signifi cant fi gures in the least accurate factor used in the calculation. This result matches answer (b). 7. You cannot add, subtract, or equate a number apples and a number of days. Thus, the answer is yes for (a), (c), and (e). However, you can multiply or divide a number of apples and a number of days. For example, you might divide the number of apples by a number of days to fi nd the number of apples you could eat per day. In summary, the answers are (a) yes, (b) no, (c) yes, (d) no, and (e) yes. 1 2 Chapter 1 8. The given Cartesian coordinates are x = −5.00, and y = 12.00, with the least accurate containing 3 signifi cant fi gures. Note that the specifi ed point (with x < 0 and y > 0) is in the second quadrant. The conversion to polar coordinates is then given by: r = x2 + y2 = (− )2 + ( )2 = 5.00 12.00 13.0 tan . . θ = = . θ . − y = − = − (− x 12 00 5 00 2 40 and tan 1 2 40) = −67.3°+180° = 113° Note that 180° was added in the last step to yield a second quadrant angle. The correct answer is therefore (b) (13.0, 113°). 9. Doing dimensional analysis on the fi rst 4 given choices yields: (a) [v] ⎡⎣ ⎤⎦ = = t 2 2 3 L T T L T (b) [v] ⎡⎣ ⎤⎦ = = − − x2 2 L T 1 1 L L T (c) v2 2 2 2 3 L T T L T T L T ⎡⎣ ⎤⎦ [ ] =( )= = t 2 (d) v2 2 2 2 L T L L T L L T ⎡⎣ ⎤⎦ [ ] =( )= = x 2 Since acceleration has units of length divided by time squared, it is seen that the relation given in answer (d) is consistent with an expression yielding a value for acceleration. 10. The number of gallons of gasoline she can purchase is # gallons total expenditure cost per gallon E = ≈ 33 uros Euros L L quart quarts 1 5 1 1 4 . ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ⎛ ⎝ ⎜⎜ ⎞ ⎠ ⎟⎟ 1 5 gal gal ⎛ ⎝ ⎜⎜ ⎞ ⎠ ⎟⎟ ≈ so the correct answer is (b). 11. The situation described is shown in the drawing at the right. From this, observe that tan 26 45 ° = h m , or h = (45 m) tan 26° = 22 m Thus, the correct answer is (a). 12. Note that we may write 1.365 248 0 ×107 as 136.524 80 ×105. Thus, the raw answer, including the uncertainty, is x = (136.524 80 ± 2) ×105. Since the fi nal answer should contain all the digits we are sure of and one estimated digit, this result should be rounded and displayed as 137 ×105 = 1.37 ×107 (we are sure of the 1 and the 3, but have uncertainty about the 7). We see that this answer has three signifi cant fi gures and choice (d) is correct. ANSWERS TO EVEN NUMBERED CONCEPTUAL QUESTIONS 2. Atomic clocks are based on the electromagnetic waves that atoms emit. Also, pulsars are highly regular astronomical clocks. 45 m h 26 Introduction 3 4. (a) ~0.5 lb ≈ 0.25 kg or ~10 −1 kg (b) ~4 lb ≈ 2 kg or ~100 kg (c) ~4000 lb ≈ 2000 kg or ~10 3 kg 6. Let us assume the atoms are solid spheres of diameter 10−10 m. Then, the volume of each atom is of the order of 10−30 m3. (More precisely, volume = 4πr3 3 = πd3 6.) Therefore, since 1 cm3 = 10−6 m3, the number of atoms in the 1 cm3 solid is on the order of 10−6 10−30 = 1024 atoms. A more precise calculation would require knowledge of the density of the solid and the mass of each atom. However, our estimate agrees with the more precise calculation to within a factor of 10. 8. Realistically, the only lengths you might be able to verify are the length of a football fi eld and the length of a housefl y. The only time intervals subject to verifi cation would be the length of a day and the time between normal heartbeats. 10. In the metric system, units differ by powers of ten, so it’s very easy and accurate to convert from one unit to another. ANSWERS TO EVEN NUMBERED PROBLEMS 2. (a) L T2 (b) L 4. All three equations are dimensionally incorrect. 6. (a) kg⋅m s (b) Ft = p 8. (a) 22.6 (b) 22.7 (c) 22.6 is more reliable 10. (a) 3.00 ×108 m s (b) 2.997 9 ×108 m s (c) 2.997 925×108 m s 12. (a) 346 m2 ±13 m2 (b) 66.0 m ±1.3 m 14. (a) 797 (b) 1.1 (c) 17.66 16. 3.09 cm s 18. (a) 5.60 ×102 km = 5.60 ×105 m = 5.60 ×107 cm (b) 0.491 2 km = 491.2m = 4.912 ×104 cm (c) 6.192 km = 6.192 ×103 m = 6.192 ×105 cm (d) 2.499 km = 2.499 ×103 m = 2.499 ×105 cm 20. 10 6. kmL 22. 9 2. nms 24. 2.9×102 m3 = 2.9×108 cm3 26. 2.57×106 m3 4 Chapter 1 28. ∼ 108 steps 30. ~108 people with colds on any given day 32. (a) 4.2 ×10−18 m3 (b) ~10−1 m3 (c) ~1016 cells 34. (a) ∼ 1029 prokaryotes (b) ~1014 kg (c) The very large mass of prokaryotes implies they are important to the biosphere. They are responsible for fi xing carbon, producing oxygen, and breaking up pollutants, among many other biological roles. Humans depend on them! 36. 2.2 m 38. 8.1 cm 40. Δs = r + r − r r ( − ) 1 2 2 2 1 2 1 2 2 cosθ θ 42. 2.33 m 44. (a) 1.50 m (b) 2.60 m 46. 8.60 m 48. (a) and (b) (c) y x = tan12.0°, y (x −1.00 km) = tan14.0° (d) 1.44×103 m 50. y d = ⋅ ⋅ − tan tan tan tan θ φ φ θ 52. (a) 1.609 km h (b) 88 km h (c) 16 km h 54. Assumes population of 300 million, average of 1 can week per person, and 0.5 oz per can. (a) ∼ 1010 cans yr (b) ∼ 105 tons yr 56. (a) 7.14×10−2 gal s (b) 2.70×10−4 m3 s (c) 1.03 h 58. (a) A A 2 1 = 4 (b) V V 2 1 = 8 60. (a) ∼ 102 yr (b) ∼ 104 times 62. ∼ 104 balls yr. Assumes 1 lost ball per hitter, 10 hitters per inning, 9 innings per game, and 81 games per year. Introduction 5 PROBLEM SOLUTIONS 1.1 Substituting dimensions into the given equation T = 2π