86713406 physics-solutions-manual

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86713406 physics-solutions-manual

  1. 1. GLENCOEPHYSICSPrinciples and Problems Problems andSolutions Manual
  2. 2. GLENCOEPHYSICSPrinciples and ProblemsStudent Edition TechnologyTeacher Wraparound Edition TestCheck Software (Win/Mac) MindJogger VideoquizzesTeacher Classroom Resources Interactive Lesson Planner Transparency Package with Transparency Interactive Teacher Edition Masters Website at science.glencoe.com Laboratory Manual SE and TE Physics for the Computer Age CD-ROM Physics Lab and Pocket Lab Worksheets (Win/Mac) Study Guide SE and TE Chapter Assessment The Glencoe Science Professional Tech Prep Applications Development Series Critical Thinking Graphing Calculators in the Science Classroom Reteaching Cooperative Learning in the Science Classroom Enrichment Alternate Assessment in the Science Classroom Physics Skills Performance Assessment in the Science Supplemental Problems Classroom Problems and Solutions Manual Lab and Safety Skills in the Science Classroom Spanish Resources Lesson Plans with block schedulingGlencoe/McGraw-HillCopyright © by the McGraw-Hill Companies, Inc. All rights reserved. Permission isgranted to reproduce the material contained herein on the condition that suchmaterial be reproduced only for classroom use; be provided to students, teachers,and families without charge; and be used solely in conjunction with the Physics:Principles and Problems program. Any other reproduction, for use or sale, isprohibited without prior written permission of the publisher.Send all inquiries to:Glencoe/McGraw-Hill8787 Orion PlaceColumbus, Ohio 43240ISBN 0-07-825936-3Printed in the United States of America.1 2 3 4 5 6 7 8 9 024 07 06 05 04 03 02 01
  3. 3. Contents To the Teacher . . . . . . . . . . . . . . . . . . . . . . . . iv Title Page 1 What is physics? . . . . . . . . . . . . . . . . . . . .1 12 Thermal Energy . . . . . . . . . . . . . . . . . . .121 Chapter Review Problems . . . . . . . . . . . . .1 Practice Problems . . . . . . . . . . . . . . . . .121 Chapter Review Problems . . . . . . . . . . .124 2 A Mathematical Toolkit . . . . . . . . . . . . . . .2 13 States of Matter . . . . . . . . . . . . . . . . . . .128 Practice Problems . . . . . . . . . . . . . . . . . . .2 Practice Problems . . . . . . . . . . . . . . . . .128 Chapter Review Problems . . . . . . . . . . . . .6 Chapter Review Problems . . . . . . . . . . .130 3 Describing Motion . . . . . . . . . . . . . . . . .12 14 Waves and Energy Transfer . . . . . . . . . .134 Practice Problems . . . . . . . . . . . . . . . . . .12 Practice Problems . . . . . . . . . . . . . . . . .134 Chapter Review Problems . . . . . . . . . . . .12 Chapter Review Problems . . . . . . . . . . .135 4 Vector Addition . . . . . . . . . . . . . . . . . . . .15 15 Sound . . . . . . . . . . . . . . . . . . . . . . . . . .139 Practice Problems . . . . . . . . . . . . . . . . . .15 Practice Problems . . . . . . . . . . . . . . . . .139 Chapter Review Problems . . . . . . . . . . . .18 Chapter Review Problems . . . . . . . . . . .140 5 A Mathematical Model of Motion . . . . .23 16 Light . . . . . . . . . . . . . . . . . . . . . . . . . . .146 Practice Problems . . . . . . . . . . . . . . . . . .23 Practice Problems . . . . . . . . . . . . . . . . .146 Chapter Review Problems . . . . . . . . . . . .30 Chapter Review Problems . . . . . . . . . . .147 6 Forces . . . . . . . . . . . . . . . . . . . . . . . . . . .46 17 Reflection and Refraction . . . . . . . . . . .150 Practice Problems . . . . . . . . . . . . . . . . . .46 Practice Problems . . . . . . . . . . . . . . . . .150 Chapter Review Problems . . . . . . . . . . . .49 Chapter Review Problems . . . . . . . . . . .151 7 Forces and Motion in Two Dimensions . .55 18 Mirrors and Lenses . . . . . . . . . . . . . . . .158 Practice Problems . . . . . . . . . . . . . . . . . .55 Practice Problems . . . . . . . . . . . . . . . . .158 Chapter Review Problems . . . . . . . . . . . .60 Chapter Review Problems . . . . . . . . . . .161 8 Universal Gravitation . . . . . . . . . . . . . . .68 19 Diffraction and Interference of Light . .165 Practice Problems . . . . . . . . . . . . . . . . . .68 Practice Problems . . . . . . . . . . . . . . . . .165 Chapter Review Problems . . . . . . . . . . . .71 Chapter Review Problems . . . . . . . . . . .166 9 Momentum and Its Conservation . . . . . .78 20 Static Electricity . . . . . . . . . . . . . . . . . . .170 Practice Problems . . . . . . . . . . . . . . . . . .78 Practice Problems . . . . . . . . . . . . . . . . .170 Chapter Review Problems . . . . . . . . . . . .84 Chapter Review Problems . . . . . . . . . . .171 10 Energy, Work, and Simple Machines . . . .94 21 Electric Fields . . . . . . . . . . . . . . . . . . . .177 Practice Problems . . . . . . . . . . . . . . . . . .94 Practice Problems . . . . . . . . . . . . . . . . .177 Chapter Review Problems . . . . . . . . . . . .96 Chapter Review Problems . . . . . . . . . . .179 11 Energy . . . . . . . . . . . . . . . . . . . . . . . . . .106 22 Current Electricity . . . . . . . . . . . . . . . . .185 Practice Problems . . . . . . . . . . . . . . . . .106 Practice Problems . . . . . . . . . . . . . . . . .185 Chapter Review Problems . . . . . . . . . . .111 Chapter Review Problems . . . . . . . . . . .188Physics: Principles and Problems iii
  4. 4. 23 Series and Parallel Circuits . . . . . . . . . .194 28 The Atom . . . . . . . . . . . . . . . . . . . . . . .228 Practice Problems . . . . . . . . . . . . . . . . .194 Practice Problems . . . . . . . . . . . . . . . . .228 Chapter Review Problems . . . . . . . . . . .196 Chapter Review Problems . . . . . . . . . . .229 24 Magnetic Fields . . . . . . . . . . . . . . . . . . .202 29 Solid State Electronics . . . . . . . . . . . . . .234 Practice Problems . . . . . . . . . . . . . . . . .202 Practice Problems . . . . . . . . . . . . . . . . .234 Chapter Review Problems . . . . . . . . . . .203 Chapter Review Problems . . . . . . . . . . .235 25 Electromagnetic Induction . . . . . . . . . . .210 30 The Nucleus . . . . . . . . . . . . . . . . . . . . .238 Practice Problems . . . . . . . . . . . . . . . . .210 Practice Problems . . . . . . . . . . . . . . . . .238 Chapter Review Problems . . . . . . . . . . .212 Chapter Review Problems . . . . . . . . . . .240 26 Electromagnetism . . . . . . . . . . . . . . . . .216 31 Nuclear Applications . . . . . . . . . . . . . . .243 Practice Problems . . . . . . . . . . . . . . . . .216 Practice Problems . . . . . . . . . . . . . . . . .243 Chapter Review Problems . . . . . . . . . . .217 Chapter Review Problems . . . . . . . . . . .245 27 Quantum Theory . . . . . . . . . . . . . . . . .222 Appendix B Extra Practice Problems . . . . . .249 Practice Problems . . . . . . . . . . . . . . . . .222 Chapter Review Problems . . . . . . . . . . .223 Appendix D Additional Topics in Physics . .331 To the The Problems and Solutions Manual is a supplement of Glencoe’s Physics: Principles and Problems. The manual is a comprehensive resource of Teacher all student text problems and solutions. Practice Problems follow most Example Problems. Answers to these problems are found in the margin of the Teacher Wraparound Edition. Complete solutions to these problems are available to the student in Appendix C of the student text. Chapter Review Problem and Critical Thinking Problem answers are found in the margins of the Teacher Wraparound Edition. Each Practice Problem, Chapter Review Problem, and Critical Thinking Problem with the solution is restated in this manual. Complete solutions for the Extra Practice Problems in Appendix B, as well as solutions for the Additional Topics in Physics in Appendix D, can be found at the end of this manual.iv Physics: Principles and Problems
  5. 5. 1 What is physics? No Practice Problems. Critical Thinking Problems page 13 11. It has been said that a fool can ask more questions than a wise man can answer. In science, it is frequently the case that a wise man is needed to ask the right ques- tion rather than to answer it. Explain. Both asking a question and answer- ing a question are important. Often, however, the training, experience, and imagination necessary to know just what question to ask have pro- vided the insight necessary to find the answer.Copyright © by Glencoe/McGraw-Hill Physics: Principles and Problems Problems and Solutions Manual 1
  6. 6. 2 A Mathematical Toolkit Practice Problems page 21 4. Convert each of the following length 2.1 The Measures of Science measurements as directed. pages 16–23 a. 1.1 cm to meters page 20 1 ؋ 10–2 m 1. Express the following quantities in ΂ (1.1 cm) ᎏᎏ ϭ 1.1 ؋ 10–2 m 1 cm ΃ scientific notation. b. 76.2 pm to millimeters a. 5800 m 1 ؋ 10؊12 m 5.8 ؋ 103 m (76.2 pm) ᎏᎏ ΂ 1 pm ΃ 1 ؋ 103 mm b. 450 000 m ؋ ᎏᎏ 1m΂ ΃ 4.5 ؋ 105 m ϭ 76.2 ؋ 10–9 mm c. 302 000 000 m ϭ 7.62 ؋ 10–8 mm 3.02 ؋ 108 m c. 2.1 km to meters d. 86 000 000 000 m 1 ؋ 103 m 8.6 ؋ 1010 m ΂ (2.1 km) ᎏᎏ ‫ 301 ؋ 1.2 ؍‬m 1 km ΃ 2. Express the following quantities in d. 2.278 ϫ 1011 m to kilometers scientific notation. ΂ ΃ 1 km a. 0.000 508 kg (2.278 ؋ 1011 m) ᎏᎏ 1 ؋ 103 m 5.08 ؋ 10–4 kg ‫ 801 ؋ 872.2 ؍‬km b. 0.000 000 45 kg 5. Convert each of the following mass 4.5 ؋ 10–7 kg measurements to its equivalent c. 0.000 360 0 kg in kilograms. Copyright © by Glencoe/McGraw-Hill 3.600 ؋ 10–4 kg a. 147 g d. 0.004 kg 1 kg ϭ 1 ؋ 103 g 4 ؋ 10–3 kg 1 kg 3. Express the following quantities in ΂ so 147 g ᎏ 3ᎏ 1 ؋ 10 g ΃ scientific notation. ϭ 147 ؋ 10–3 kg a. 300 000 s ϭ 1.47 ؋ 10–1 kg 3 ؋ 105 s b. 11 Mg b. 186 000 s 1 Mg ‫ 601 ؋ 1 ؍‬g and 1 kg ‫ 301 ؋ 1 ؍‬g 1.86 ؋ 105 s 1 ؋ 106 g ΂ ΃ ΂ᎏ1ᎏ΃ 1 kg so 11 Mg ᎏᎏ c. 93 000 000 s 1 Mg 1؋ 0 g 3 9.3 ؋ 107 s ϭ 11 ؋ 106 ؋ 10–3 kg ϭ 1.1 ؋ 104 kg2 Problems and Solutions Manual Physics: Principles and Problems
  7. 7. 5. (continued) 8. a. 5.0 ϫ 10–7 mg ϩ 4 ϫ 10–8 mg c. 7.23 µg ϭ 5.0 ؋ 10–7 mg ϩ 0.4 ؋ 10–7 mg ϭ 5.4 ؋ 10–7 mg ΂ ΃ 1g 7.23 µg ᎏᎏ 1 ؋ 106 µg b. 6.0 ϫ 10–3 mg ϩ 2 ϫ 10–4 mg 1 kg ΂ ؋ ᎏᎏ 1 ؋ 103 g ΃ ϭ 6.0 ؋ 10–3 mg ϩ 0.2 ؋ 10–3 mg ϭ 7.23 ؋ 10–6 ؋ 10–3 kg ϭ 6.2 ؋ 10–3 mg ‫ 9–01 ؋ 32.7 ؍‬kg c. 3.0 ϫ 10–2 pg Ϫ 2 ϫ 10–6 ng d. 478 mg ϭ 3.0 ؋ 10–2 ؋ 10–12 g Ϫ 2 ؋ 10–6 ؋ 10–9 g 1 ؋ 10–3 g 478 mg ᎏᎏ ΂ 1 mg ΃ ϭ 3.0 ؋ 10–14 g Ϫ 0.2 ؋ 10–14 g ΂ ΃ 1 kg ϭ 2.8 ؋ 10–14 g ؋ ᎏᎏ 1 ؋ 103 g d. 8.2 km Ϫ 3 ϫ 102 m ϭ 4.78 ؋ 10–4 kg ϭ 8.2 ؋ 103 m Ϫ 0.3 ؋ 103 m page 22 ϭ 7.9 ؋ 103 m Solve the following problems. Write your answers page 23 in scientific notation. Find the value of each of the following quantities. 6. a. 5 ϫ 10–7 kg ϩ 3 ϫ 10–7 kg 9. a. (2 ϫ 104 m)(4 ϫ 108 m) ‫ 7–01 ؋ )3 ؉ 5( ؍‬kg ϭ (2 ؋ 4) ؋ 104+8 m2 ϭ 8 ؋ 10–7 kg ϭ 8 ؋ 1012 m2 b. 4 ϫ 10–3 kg ϩ 3 ϫ 10–3 kg b. (3 ϫ 104 m)(2 ϫ 106 m) ϭ 7 ؋ 10–3 kg ‫ 6+401 ؋ )2 ؋ 3( ؍‬m2 c. 1.66 ϫ 10–19 kg ϩ 2.30 ϫ 10–19 kg ϭ 6 ؋ 1010 m2 ϭ 3.96 ؋ 10–19 kg c. (6 ϫ 10–4 m)(5 ϫ 10–8 m) d. 7.2 ϫ 10–12 kg Ϫ 2.6 ϫ 10–12 kg ϭ 30 ؋ 10–4–8 m2 ‫ 21–01 ؋ )6.2 ؊ 2.7( ؍‬kg ϭ 3 ؋ 10–11 m2 ϭ 4.6 ؋ 10–12 kg d. (2.5 ϫ 10–7 m)(2.5 ϫ 1016 m) 7. a. 6 ϫ 10–8 m2 Ϫ 4 ϫ 10–8 m2 ϭ 6.25 ؋ 10–7+16 m2Copyright © by Glencoe/McGraw-Hill ϭ 2 ؋ 10–8 m2 ϭ 6.25 ؋ 109 m2 b. 3.8 ϫ 10–12 m2 Ϫ 1.90 ϫ 10–11 m2 6 ϫ 10 8 kg ‫ 21–01 ؋ 8.3 ؍‬m2 ؊ 19.0 ؋ 10–12 m2 10. a. ᎏᎏ 2 ϫ 104 m3 ‫ 21–01 ؋ )0.91 ؊ 8.3( ؍‬m2 ‫ 4–801 ؋ 3 ؍‬kg/m3 ‫ 21–01 ؋ 2.51– ؍‬m2 ϭ 3 ؋ 104 kg/m3 ϭ –1.52 ؋ 10–11 m2 6 ϫ 108 kg c. 5.8 ϫ 10–9 m2 Ϫ 2.8 ϫ 10–9 m2 b. ᎏᎏ 2 ϫ 10–4 m3 ϭ 3.0 ؋ 10–9 m2 ϭ 3 ؋ 108–(–4) kg/m3 d. 2.26 ϫ 10–18 m2 Ϫ 1.8 ϫ 10–18 m2 ϭ 3 ؋ 1012 kg/m3 ϭ 0.46 ؋ 10–18 m2 ϭ 4.6 ؋ 10–19 m2 Physics: Principles and Problems Problems and Solutions Manual 3
  8. 8. 2.8 ϫ 10– 2 mg 10. (continued) 13. a. ᎏᎏ 2.0 ϫ 104 g 6 ϫ 10–8 m c. ᎏᎏ 2.8 ϫ 10–2 ϫ 10–3 g 2 ϫ 104 s ϭ ᎏᎏᎏ ϭ 1.4 ؋ 10–9 2.0 ϫ 104 g ϭ 3 ؋ 10–8–4 m/s (6 ϫ 102 kg)(9 ϫ 103 m) ϭ 3 ؋ 10–12 m/s b. ᎏᎏᎏ (2 ϫ 104 s)(3 ϫ 106 ms) 6 ϫ 10–8 m d. ᎏᎏ (6 ϫ 102 kg)(9 ϫ 103 m) 2 ϫ 10–4 s ϭ ᎏᎏᎏᎏ (2 ϫ 104 s)(3 ϫ 106 ϫ 10–3 s) ϭ 3 ؋ 10–8–(–4) m/s ϭ 3 ؋ 10–4 m/s 54 ؋ 105 kg и m ϭ ᎏᎏ 6 ؋ 107 s2 (3 ϫ 104 kg)(4 ϫ 104 m) 11. a. ᎏᎏᎏ 6 ϫ 104 s ϭ 9 ؋ 10–2 kg и m/s2 12 ϫ 104+4 kg и m (7 ϫ 10–3 m) ϩ (5 ϫ 10–3 m) ϭ ᎏᎏᎏ 14. ᎏᎏᎏᎏ 6 ϫ 104 s (9 ϫ 107 km) ϩ (3 ϫ 107 km) ϭ 2 ؋ 108–4 kg и m/s 12 ؋ 10–3 m ϭ ᎏᎏ ϭ 2 ؋ 104 kg и m/s 12 ؋ 107 km The evaluation may be done in several 12 ؋ 10–3 m 12 ؋ 10؊3 m ϭ ᎏᎏᎏ ϭ ᎏᎏ other ways. For example 12 ϫ 107 ؋ 103 m 12 ؋ 1010 m (3 ϫ 104 kg)(4 ϫ 104 m) ϭ 1 ؋ 10–13 ᎏᎏᎏ 6 ϫ 104 s ϭ (0.5 ؋ 104–4 kg/s)(4 ؋ 104 m) 2.2 Measurement Uncertainties pages 24–29 ϭ (0.5 kg/s)(4 ؋ 104 m) page 27 ϭ 2 ؋ 104 kg и m/s (2.5 ϫ 106 kg)(6 ϫ 104 m) State the number of significant digits in each b. ᎏᎏᎏ measurement. 5 ϫ 10–2 s2 15 ϫ 106+4 kg и m 15. a. 2804 m ϭ ᎏᎏᎏ 5 ϫ 10–2 s2 4 ϭ 3 ؋ 1010–(–2) kg и m/s2 b. 2.84 km ϭ 3 ؋ 1012 kg и m/s2 3 Copyright © by Glencoe/McGraw-Hill 12. a. (4 ϫ 103 mg)(5 ϫ 104 kg) c. 0.0029 m ϭ (4 ؋ 103 ؋ 10–3 g)(5 ؋ 104 ؋ 103 g) 2 ϭ 20 ؋ 107 g2 d. 0.003 068 m ϭ 2 ؋ 108 g2 4 b. (6.5 ϫ 10–2 m)(4.0 ϫ 103 km) e. 4.6 ϫ 105 m ϭ (6.5 ؋ 10–2 m)(4.0 ؋ 103 ؋ 103 m) 2 ϭ 26 ؋ 104 m2 f. 4.06 ϫ 10–5 m ϭ 2.6 ؋ 105 m2 3 c. (2 ϫ 103 ms)(5 ϫ 10–2 ns) 16. a. 75 m ϭ (2 ؋ 103 ؋ 10–3 s)(5 ؋ 10–2 ؋ 10–9 s) 2 ϭ 10 ؋ 10–11 s2 b. 75.00 m ϭ 1 ؋ 10–10 s2 4 16. (continued)4 Problems and Solutions Manual Physics: Principles and Problems
  9. 9. c. 0.007 060 kg 19. a. 131 cm ϫ 2.3 cm 4 3.0 ؋ 102 cm2 (the result 301.3 cm2 d. 1.87 ϫ 106 mL expressed to two significant digits. Note that the expression in the form 3 300 cm2 would not indicate how many of the digits are significant.) e. 1.008 ϫ 108 m 4 b. 3.2145 km ϫ 4.23 km 13.6 km2 (the result 13.597335 km2 f. 1.20 ϫ 10–4 m expressed to three significant digits) 3 c. 5.761 N ϫ 6.20 m page 28 35.7 N и m (the result 35.7182 N ؒ m Solve the following addition problems. expressed to three significant digits) 17. a. 6.201 cm, 7.4 cm, 0.68 cm, and Solve the following division problems. 12.0 cm 20. a. 20.2 cm Ϭ 7.41 s 6.201 cm 2.73 cm/s (the result 2.726045 . . . 7.4 cm cm/s expressed to three significant 0.68 cm digits) 12.0 cm 26.281 cm b. 3.1416 cm Ϭ 12.4 s ‫ 3.62 ؍‬cm 0.253 cm/s (the result 0.253354 . . . cm/s expressed to three significant b. 1.6 km, 1.62 m, and 1200 cm digits) 1.6 km ‫0061 ؍‬ m c. 13.78 g Ϭ 11.3 mg 1.62 m ‫؍‬ 1.62 m 1200 cm ‫؍‬ 12 m 13.78 g Ϭ 11.3 ؋ 10–3 g 1613.62 m 1.22 ؋ 103 g (the result 1.219469 . . . ‫ 0061 ؍‬m or 1.6 km ؋ 103 g expressed to three significant digits) Solve the following subtraction problems. d. 18.21 g Ϭ 4.4 cm3 18. a. 8.264 g from 10.8 g 4.1 g/cm3 (the result 4.138636 . . . 10.8 g g/cm3 expressed to two significant –8.264 g digits)Copyright © by Glencoe/McGraw-Hill 2.536 g 2.5 g (rounded from 2.536 g) 2.3 Visualizing Data b. 0.4168 m from 475 m pages 30–36 475 m page 36 – 0.4168 m 21. The total distance a lab cart travels during 474.5832 m specified lengths of time is given in the 475 m (rounded from 474.5832 m) following data table. Solve the following multiplication problems. 21. (continued) Physics: Principles and Problems Problems and Solutions Manual 5
  10. 10. 5 ؋ 1012 m TABLE 2-4 b. 0.000 000 000 166 m Time (s) Distance (m) 1.66 ؋ 10–10 m 0.0 0.00 c. 2 003 000 000 m 1.0 0.32 2.003 ؋ 109 m 2.0 0.60 d. 0.000 000 103 0 m 3.0 0.95 4.0 1.18 1.030 ؋ 10–7 m 5.0 1.45 31. Convert each of the following a. Plot distance versus time from the measurements to meters. values given in the table and draw the a. 42.3 cm curve that best fits all points. 42.3 cm 1 ؋ 10–2 m b. Describe the resulting curve. 1 ΂ ᎏᎏ ᎏᎏ ϭ 0.423 m 1 cm ΃ 1.50 b. 6.2 pm Distance (m) 1.25 6.2 pm 1 ؋ 10–12 m 1.00 .75 ᎏᎏ ᎏᎏ 1 ΂ 1 pm ΃ .50 ϭ 6.2 ؋ 10–12 m .25 0 c. 21 km 0.0 1.0 2.0 3.0 4.0 5.0 21 km 1 ؋ 103 m Time (s) 1 ΂ ᎏᎏ ᎏᎏ ϭ 2.1 ؋ 104 m 1 km ΃ straight line d. 0.023 mm c. According to the graph, what type of 0.023 mm 1 ؋ 10–3 m relationship exists between the total distance traveled by the lab cart and ᎏ ᎏ ᎏᎏ 1 1 mm ΂ ΃ the time? ϭ 2.3 ؋ 10–5 m linear relationship e. 214 µm d. What is the slope of this graph? 214 µm 1 ؋ 10؊6 m ∆y 1.5 – 0.60 M ‫ ؍‬ᎏᎏ ‫ ؍‬ᎏᎏ ‫ ؍‬ᎏᎏ ∆x 5.0 – 2.0 0.90 3.0 ᎏ ᎏᎏ 1 1 µm΂ ΃ ‫ 4؊01 ؋ 41.2 ؍‬m ‫ 03.0 ؍‬m/s Copyright © by Glencoe/McGraw-Hill e. Write an equation relating distance and f. 570 nm time for this data. 1 ؋ 10–9 m d ‫(03.0 ؍‬t ) 570 nm ᎏᎏ ΂ 1 nm ΃ ϭ 5.70 ؋ 10–7 mChapter Review Problems 32. Add or subtract as indicated.pages 39–41 a. 5.80 ϫ 109 s ϩ 3.20 ϫ 108 spage 39 5.80 ؋ 109 s ϩ 0.320 ؋ 109 s ϭ 6.12 ؋ 109 sSection 2.1 32. (continued)Level 1 b. 4.87 ϫ 10–6 m Ϫ 1.93 ϫ 10–6 m30. Express the following numbers in scientific notation: ϭ 2.94 ؋ 10–6 m a. 5 000 000 000 000 m c. 3.14 ϫ 10–5 kg ϩ 9.36 ϫ 10–5 kg6 Problems and Solutions Manual Physics: Principles and Problems
  11. 11. ϭ 12.50 ؋ 10–5 kg ϭ 1.25 ؋ 10–4 kg 3 d. 8.12 ϫ 107 g Ϫ 6.20 ϫ 106 g b. 6 ϫ 108 kg 8.12 ؋ 107 g Ϫ 0.620 ؋ 107 g 1 ϭ 7.50 ؋ 107 g c. 4.07 ϫ 1016 m Level 2 3 33. Rank the following mass measurements 36. Add or subtract as indicated. from smallest to largest: 11.6 mg, a. 16.2 m ϩ 5.008 m ϩ 13.48 m 1021 µg, 0.000 006 kg, 0.31 mg. 16.2 m 11.6 mg 1 ؋ 10–3 5.008 m ΂ ΃ g ᎏᎏ ᎏᎏ ϭ 1.16 ؋ 10–2 g 1 1 mg 13.48 m 34.688 m ‫ 7.43 ؍‬m or 11.6 ؋ 10–3 g b. 5.006 m ϩ 12.0077 m ϩ 8.0084 m 1021 µg 1 ؋ 10–6 ΂ ΃ g 5.006 m ᎏᎏ ᎏ ᎏ 1 1 µg 12.0077 m ϭ 1.021 ؋ 10–3 g 8.0084 m 25.0221 m ‫ 220.52 ؍‬m 0.000 006 kg 103 g ΂ ᎏᎏ ᎏᎏ ‫ 3–01 ؋ 6 ؍‬g 1 1 kg ΃ c. 78.05 cm2 Ϫ 32.046 cm2 78.05 cm2 0.31 mg 1 ؋ 10–3 g ΂ ᎏᎏ ᎏᎏ ‫ 4–01 ؋ 1.3 ؍‬g 1 1 mg ΃ –32.046 cm2 46.004 cm2 ‫ 00.64 ؍‬cm2 or 0.31 ؋ 10–3 g d. 15.07 kg Ϫ 12.0 kg 0.31 mg, 1021 µg, 0.000 006 kg, 15.07 kg 11.6 mg –12.0 kg 3.07 kg ‫ 1.3 ؍‬kg Section 2.2 37. Multiply or divide as indicated. Level 1 a. (6.2 ϫ 1018 m)(4.7 ϫ 10–10 m) 34. State the number of significant digits in ‫ 801 ؋ 41.92 ؍‬m2 each of the following measurements. ‫ 901 ؋ 9.2 ؍‬m2 a. 0.000 03 m 5.6 ϫ 10–7 m b. ᎏ –12 ᎏCopyright © by Glencoe/McGraw-Hill 1 2.8 ϫ 10 s b. 64.01 fm ‫ 501 ؋ 0.2 ؍‬m/s 4 c. (8.1 ϫ 10–4 km)(1.6 ϫ 10–3 km) c. 80.001 m ‫ 7–01 ؋ 69.21 ؍‬km2 5 ‫ 6–01 ؋ 3.1 ؍‬km2 d. 0.720 µg 3 35. State the number of significant digits in each of the following measurements. 37. (continued) a. 2.40 ϫ 106 kg Physics: Principles and Problems Problems and Solutions Manual 7
  12. 12. 6.5 ϫ 105 kg is to be fertilized? d. ᎏᎏ 3.4 ϫ 103 m3 Area ϭ lw ‫؋ . . . 67119.1 ؍‬ 102 kg/m3 ϭ (33.21 m)(17.6 m) ‫ 201 ؋ 9.1 ؍‬kg/m3 ‫ 694.485 ؍‬m2 ϭ 584 m238. Using a calculator, Chris obtained the 42. The length of a room is 16.40 m, its following results. Give the answer to each width is 4.5 m, and its height is 3.26 m. operation using the correct number of What volume does the room enclose? significant digits. V ϭ lwh a. 5.32 mm ϩ 2.1 mm ϭ 7.4200000 mm ϭ (16.40 m)(4.5 m)(3.26 m) 7.4 mm ‫ 885.042 ؍‬m3 ϭ 2.4 ؋ 102 m3 b. 13.597 m ϫ 3.65 m ϭ 49.62905 m2 43. The sides of a quadrangular plot of land 49.6 m2 are 132.68 m, 48.3 m, 132.736 m, and c. 83.2 kg Ϫ 12.804 kg ϭ 70.3960000 kg 48.37 m. What is the perimeter of the plot? 70.4 kg Perimeterpage 40 ϭ 132.68 m ϩ 48.3 m ϩ 132.736 m39. A rectangular floor has a length of ϩ 48.37 m 15.72 m and a width of 4.40 m. Calculate the area of the floor. ‫ 680.263 ؍‬m Area ‫ ؍‬lw ‫ 27.51( ؍‬m)(4.40 m) ϭ 362.1 m ‫ 861.96 ؍‬m2 ‫ 2.96 ؍‬m2 Section 2.340. A water tank has a mass of 3.64 kg when Level 1 it is empty and a mass of 51.8 kg when it 44. Figure 2–14 shows the mass of the three is filled to a certain level. What is the substances for volumes between 0 and mass of the water in the tank? 60 cm3. 51.8 kg –3.64 kg Mass Versus Volume 600 48.16 kg ϭ 48.2 kgLevel 2 500 Copyright © by Glencoe/McGraw-Hill41. A lawn is 33.21 m long and 17.6 m wide. 400 Mass (g) a. What length of fence must be 300 purchased to enclose the entire lawn? Perimeter ϭ 2l ϩ 2w 200 ‫ 12.33(2 ؍‬m) ϩ 2(17.6 m) 100 ‫ 24.66 ؍‬m ϩ 35.2 m 0 0 10 20 30 40 50 60 ‫ 26.101 ؍‬m Volume (cm3) ‫ 6.101 ؍‬m 44. (continued) b. What area must be covered if the lawn8 Problems and Solutions Manual Physics: Principles and Problems
  13. 13. a. What is the mass of 30 cm3 of each relating the volume to the mass of substance? alcohol. d (a) 80 g, (b) 260 g, (c) 400 g. m ϭ ᎏᎏ, where m is the slope V b. If you had 100 g of each substance, d. Find the units of the slope of the what would their volumes be? graph. What is the name given to this quantity? (a) 34 cm3, (b) 11 cm3, (c) 7 cm3. m d ‫ ؍‬ᎏᎏ c. In one or two sentences, describe the V g meaning of the steepness of the lines so the units of m are ᎏᎏ cm3 in this graph. g/cm3; density The steepness represents the increased mass of each additional 46. During a class demonstration, a physics cubic centimeter of the substance. instructor placed a 1.0-kg mass on a horizontal table that was nearly Level 2 frictionless. The instructor then applied 45. During an experiment, a student various horizontal forces to the mass and measured the mass of 10.0 cm3 of measured the rate at which it gained alcohol. The student then measured the speed (was accelerated) for each force mass of 20.0 cm3 of alcohol. In this way, applied. The results of the experiment are the data in Table 2–5 were collected. shown in Table 2–6. TABLE 2-5 TABLE 2-6 Volume (cm3) Mass (g) Force (N) Acceleration (m/s2) 10.0 7.9 5.0 4.9 20.0 15.8 10.0 9.8 30.0 23.7 15.0 15.2 40.0 31.6 20.0 20.1 50.0 39.6 25.0 25.0 a. Plot the values given in the table and 30.0 29.9 draw the curve that best fits all points. page 41 b. Describe the resulting curve. a. Plot the values given in the table and M draw the curve that best fits the results.Copyright © by Glencoe/McGraw-Hill 40 a 30 30 Acceleration (m/s 2 ) Mass (g) 25 20 20 a ϭF 15 10 10 5 0 V 0 F 0 10 20 30 40 50 0 5 10 15 20 25 30 Volume (cm3 ) Volume (cm3 ) a straight line c. Use the graph to write an equation Physics: Principles and Problems Problems and Solutions Manual 9
  14. 14. 46. (continued) b. Describe the resulting curve. b. Describe, in words, the relationship hyperbola between force and acceleration c. According to the graph, what is the according to the graph. relationship between mass and the The acceleration varies directly with acceleration produced by a constant the force. force? c. Write the equation relating the force Acceleration varies inversely with and the acceleration that results from the mass. the graph. d. Write the equation relating acceleration F ϭ ma, where m is the slope to mass given by the data in the graph. d. Find the units of the slope of the c a ϭ ᎏᎏ graph. m a (m/s2) c ϭ constant ϭ 12 m ϭ ᎏᎏ so the units of m are ᎏᎏ F N m ‫ ؍‬mass m ϭ ᎏᎏ e. Find the units of the constant in the (s2 и N) equation.47. The physics instructor who performed the experiment in problem 46 changed the c ϭ ma procedure. The mass was varied while the so the units of c are (kg)(m/s2) force was kept constant. The acceleration ϭ kg и m/s2 of each mass was recorded. The results of the experiment are shown in Table 2–7. Critical Thinking Problems TABLE 2-7 48. Find the approximate time needed for a Mass (kg) Acceleration (m/s2) pitched baseball to reach home plate. 1.0 12.0 Report your result to one significant digit. 2.0 5.9 (Use a reference source to find the distance thrown and the speed of 3.0 4.1 a fastball.) 4.0 3.0 5.0 2.5 Answers will vary with the data available. Answer should be 6.0 2.0 calculated from the equation: Copyright © by Glencoe/McGraw-Hill a. Plot the values given in the table and time ‫ ؍‬distance ، speed. draw the curve that best fits all points. 49. Have a student walk across the front of a the classroom. Estimate his or her 12 walking speed. Acceleration (m/s2) 10 Estimates will vary. Answers 8 should be calculated from 12 6 aϭ aϭ m speed ‫ ؍‬distance ، time 4 50. How high can you throw a ball? Find a 2 tall building whose height you can 0 m estimate and compare the height of your 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 throw to that of the building. Estimates will vary.10 Problems and Solutions Manual Physics: Principles and Problems
  15. 15. 51. Use a graphing calculator or computer 52. If the sun suddenly ceased to shine, how graphing program to graph reaction and long would it take Earth to become dark? braking distances versus original speed. You will have to look up the speed of Use the calculator or computer to find light in a vacuum and the distance from the slope of the reaction distance and the the sun to Earth. How long would it take best quadratic fit to the braking distance. to become dark on the surface of Jupiter? Speed of light ϭ 3.00 ؋ 108 m/s Reaction Distance (m) 25 20 Mean distance from the sun to 15 Earth ϭ 1.50 ؋ 1011 m 10 Mean distance from the sun to 5 Jupiter ϭ 7.78 ؋ 1011 m 0 distance 0 5 10 15 20 25 30 time ‫ ؍‬ᎏᎏ speed Original Speed (m/s) time for Earth to become dark: 70 1.50 ؋ 1011 m ᎏᎏ ‫ 201 ؋ 00.5 ؍‬s Braking Distance (m) 60 3.00 ؋ 108 m/s 50 40 time for the surface of Jupiter to 30 become dark: 20 7.78 ؋ 1011 m ᎏᎏ ‫ 301 ؋ 95.2 ؍‬s 10 3.00 ؋ 108 m/s 0 0 5 10 15 20 25 30 Original Speed (m/s)Copyright © by Glencoe/McGraw-Hill Physics: Principles and Problems Problems and Solutions Manual 11
  16. 16. 3 Describing Motion Practice Problems v0 ‫ 0 ؍‬m/s v1 ‫ 0.4 ؍‬m/s d0 ‫ 0 ؍‬m d1 ‫? ؍‬ 3.1 Picturing Motion pages 44–46 t0 ‫ 0 ؍‬s t1 ‫ 4 ؍‬s No practice problems. Begin End ϩ 3.2 Where and When? v v v v pages 47–51 a No practice problems. 19. A student drops a ball from a window 3.3 Velocity and Acceleration 3.5 m above the sidewalk. The ball pages 53–59 accelerates at 9.80 m/s2. How fast is it moving when it hits the sidewalk? No practice problems. d0 ϭ 3.5 m d1 ϭ 0 v0 ϭ 0 v1 ‫? ؍‬ Chapter Review Problems a ϭ –9.80 m/s2 page 61 ϩ Begin Create pictorial and physical models for the d0 following problems. v Section 3.3 v Level 1 17. A bike travels at a constant speed of a v 4.0 m/s for 5 s. How far does it go? v0 ϭ 4.0 m/s v1 ‫ 0.4 ؍‬m/s Copyright © by Glencoe/McGraw-Hill v d0 ϭ 0 m d1 ‫? ؍‬ End t0 ϭ 0 s t1 ‫ 5 ؍‬s 0 d1 Level 2 Begin End 20. A bike first accelerates from 0.0 m/s to ϩ 5.0 m/s in 4.5 s, then continues at this d0 d1 v v v v v constant speed for another 4.5 s. What is the total distance traveled by the bike? a ϭ0 t0 ϭ 0 t1 ϭ 4.5 s t2 ϭ 4.5 s ϩ 4.5 s 18. A bike accelerates from 0.0 m/s to ϭ 9.0 s 4.0 m/s in 4 s. What distance does v0 ϭ 0.0 v1 ϭ 5.0 m/s v2 ϭ 5.0 m/s it travel? d0 ϭ 0 d2 ‫? ؍‬12 Problems and Solutions Manual Physics: Principles and Problems
  17. 17. Begin Middle End 23. If you throw the ball in problem 22 up instead of down, how fast is it moving ϩ when it hits the sidewalk? Hint: Its 0 d0 d1 d2 acceleration is the same whether it is moving up or down. v v v v d0 ‫ 5.2 ؍‬m d1 ‫ 0 ؍‬m a01 a12ϭ0 v0 ‫ 0.2 ؍‬m/s v1 ‫? ؍‬ 21. A car is traveling 20 m/s when the driver a ‫ 08.9– ؍‬m/s2 sees a child standing in the road. He takes 0.8 s to react, then steps on the v v brakes and slows at 7.0 m/s2. How far ϩ Begin v does the car go before it stops? v d0 a01 ϭ 0 a12 ϭ –7.0 m/s2 v0 ϭ 20 m/s v1 ϭ 20 m/s v2 ϭ 0 v t0 ϭ 0 t1 ϭ 0.8 s t2 ‫? ؍‬ a d2 ‫? ؍‬ v Begin Middle End ϩ v d0 d1 d2 End v v v v v 0 d1 a 01ϭ0 a 12ϭϪ7.0 m/s2 Critical Thinking Problems 22. You throw a ball downward from a Each of the following problems involves two objects. window at a speed of 2.0 m/s. The ball Draw the pictorial and physical models for each. accelerates at 9.80 m/s2. How fast is it Use different symbols to represent the position, moving when it hits the sidewalk velocity, and acceleration of each object. Do not 2.5 m below? solve the problem. d0 ‫ 5.2 ؍‬m d1 ‫ 0 ؍‬m 24. A truck is stopped at a stoplight. When v0 ‫ 0.2– ؍‬m/s v1 ‫? ؍‬ the light turns green, it accelerates at a ‫ 08.9– ؍‬m/s2 2.5 m/s2. At the same instant, a car passes ϩ the truck going 15 m/s. Where and whenCopyright © by Glencoe/McGraw-Hill Begin d0 does the truck catch up with the car? v Begin End v ϩ d 0ϭ0 v 0ϭ15 m/s a ϭ0 d 1ϭ? a v D 0ϭ0 V0ϭ0 Aϭ2.5 m/s2 d 1ϭD1ϭ? v v v v v car v End V V V V V truck 0 d1 A The lowercase symbols represent the car’s position, velocity, and accleration. The uppercase symbols represent the truck’s position, velocity, and acceleration. Physics: Principles and Problems Problems and Solutions Manual 13
  18. 18. 25. A truck is traveling at 18 m/s to the north. The driver of a car, 500 m to the north and traveling south at 24 m/s, puts on the brakes and slows at 3.5 m/s2. Where do they meet? Begin End Begin ϩ D 0ϭ0 D1ϭd 1ϭ? d 0ϭ500 m V0ϭ18 m/s a ϭϩ3.5 m/s2 v 0ϭϪ24 m/s V V V truck v v v car a The lowercase symbols represent the car’s position, velocity, and accleration. The uppercase symbols represent the truck’s position, velocity, and acceleration. Copyright © by Glencoe/McGraw-Hill14 Problems and Solutions Manual Physics: Principles and Problems
  19. 19. 4 Vector Addition Practice Problems 4.5 km 45˚ 45 4.1 Properties of Vectors 135˚ 135 pages 64–71 6.4 km page 67 Resultantϭ1.0 ϫ101 km 1. A car is driven 125 km due west, then 65 km due south. What is the magnitude of its displacement? R ϭ [(4.5 km)2 ϩ (6.4 km)2 125 km west Ϫ (2)(4.5 km)(6.4 km)(cos 135°)]1/2 R ϭ 1.0 ϫ 101 km 65 km 4. What is the magnitude of your south displacement when you follow directions Resultantϭ140 km that tell you to walk 225 m in one direction, make a 90° turn to the left and R2 ‫ ؍‬A2 + B2 walk 350 m, then make a 30° turn to the R2 ‫ 56( ؍‬km)2 + (125 km)2 right and walk 125 m? R2 ‫ 058 91 ؍‬km2 t ␪1 R ‫ 041 ؍‬km R2 225 m R1 2. A shopper walks from the door of the t2 mall to her car 250 m down a lane of cars, then turns 90° to the right and walks 350 m 30˚ 125 m an additional 60 m. What is the magnitude of the displacement of her car R1 ϭ [(225 m)2 ϩ (350 m)2]1/2 ϭ 416 m from the mall door? 350 mCopyright © by Glencoe/McGraw-Hill ␪1 ϭ tan–1 ᎏᎏ ϭ 57.3° 250 m 225 m ␪2 ϭ 180 Ϫ (60 Ϫ 57.3) ϭ 177.3° 60 m R2 ϭ [(416 m)2 ϩ (125 m)2 Resultantϭ300 m Ϫ 2(416 m)(125 m) R2 ϭ (250 m)2 + (60 m)2 (cos 177.3°)]1/2 R2 ϭ 66 100 m2 R2 ϭ 540 m R ϭ 260 m, or 300 m to one significant digit page 71 3. A hiker walks 4.5 km in one direction, 5. A car moving east at 45 km/h turns and then makes a 45° turn to the right and travels west at 30 km/h. What are the walks another 6.4 km. What is the magnitude and direction of the change magnitude of her displacement? in velocity? R2 ϭ A2 ϩ B2 Ϫ 2AB cos ␪ Physics: Principles and Problems Vector Addition 15
  20. 20. 5. (continued) 9. An airplane flies due north at 150 km/h Magnitude of change in velocity with respect to the air. There is a wind blowing at 75 km/h to the east relative ‫ 57 ؍ )03–( ؊ 54 ؍‬km/h to the ground. What is the plane’s speed direction of change is from east to with respect to the ground? west vwϭ75 km/h 6. You are riding in a bus moving slowly through heavy traffic at 2.0 m/s. You hurry to the front of the bus at 4.0 m/s vpϭ150 km/h v relative to the bus. What is your speed relative to the street? ؉2.0 m/s ؉ 4.0 m/s v ϭ [vp + vw ]1/2 2 2 ‫ 0.6 ؍‬m/s relative to street ϭ [(150 km/h)2 ϩ (75 km/h)2]1/2 7. A motorboat heads due east at 11 m/s relative to the water across a river that ϭ 170 km/h flows due north at 5.0 m/s. What is the 10. An airplane flies due west at 185 km/h velocity of the motorboat with respect to with respect to the air. There is a wind the shore? blowing at 85 km/h to the northeast vresult relative to the ground. What is the plane’s vrϭ5.0 m/s speed with respect to the ground? v bϭ11 m/s vwϭ85 km/h v 2 2 vresult ‫؍‬[vb ؉ v r ]1/2 45˚ 45 ‫ 11([ ؍‬m/s)2 ؉ (5.0 m/s)2]1/2 vpϭ185 km/h ‫ 21 ؍‬m/s vϭ ϩ vw Ϫ 2vpvw cos ␪]1/2 2 [vp 2 5.0 m/s ␪ ‫ ؍‬tan–1 ᎏᎏ ‫°42 ؍‬ ϭ [(185 km/h)2 ϩ (85 km/h)2 11 m/s Ϫ (2)(185 km/h)(85 km/h)(cos 45°)]1/2 vresult ‫ 21 ؍‬m/s, 66° east of north ϭ 140 km/h 8. A boat is rowed directly upriver at a speed of 2.5 m/s relative to the water. Viewers on the shore find that it is moving at only 4.2 Components of Vectors 0.5 m/s relative to the shore. What is the pages 72–76 Copyright © by Glencoe/McGraw-Hill speed of the river? Is it moving with or page 74 against the boat? 11. What are the components of a vector of 2.5 m/s magnitude 1.5 m at an angle of 35° from → boat the positive x-axis? 2.0 m/s river ϩy ← → dϭ1.5 m 0.5 m/s Resultant dy 2.5 m/s Ϫ 0.5 m/s 35˚ ϭ 2.0 m/s against the boat ϩx dx16 Problems and Solutions Manual Physics: Principles and Problems
  21. 21. 11. (continued) page 76 dx ϭ 1.5 m cos 35° ϭ 1.2 m 15. A powerboat heads due northwest at dy ϭ 1.5 m sin 35° ϭ 0.86 m 13 m/s with respect to the water across a river that flows due north at 5.0 m/s. 12. A hiker walks 14.7 km at an angle 35° What is the velocity (both magnitude and south of east. Find the east and north direction) of the motorboat with respect components of this walk. to the shore? N dE N E 35˚ dN vrϭ5.0 m/s 14.7 km vR dE ϭ 14.7 km cos 35° ϭ 12.0 km vbbϭ13 m/s v ␪ t dN ϭ –14.7 km sin 35° ϭ –8.43 km 45˚ 45 E 13. An airplane flies at 65 m/s in the direction 149° counterclockwise from east. What are the east and north vbW ϭ (13 m/s) cos 45° ϭ 9.2 m/s components of the plane’s velocity? vbN ϭ (13 m/s) sin 45° ϭ 9.2 m/s N vRN ϭ 5.0 m/s, vrW ‫0.0 ؍‬ vRW ϭ 9.2 m/s ؉ 0.0 ‫ 2.9 ؍‬m/s 65 m/s vN vRN ϭ 9.2 m/s ϩ 5.0 m/s ϭ 14.2 m/s vR ϭ [(9.2 m/s)2 ϩ (14.2 m/s)2]1/2 31˚ E ؊v E ϭ 17 m/s vE ϭ –65 m/s cos 31° ‫ 17.55– ؍‬m/s 9.2 m/s ␪ ϭ tan–1 ᎏᎏ ϭ tan–1 0.648 14.2 m/s ϭ –56 m/s ϭ 33° vN ϭ 65 m/s sin 31° ‫ 74.33 ؍‬m/s vR ϭ 17 m/s, 33° west of north ϭ 33 m/s 16. An airplane flies due south at 175 km/h 14. A golf ball, hit from the tee, travels 325 m with respect to the air. There is a windCopyright © by Glencoe/McGraw-Hill in a direction 25° south of the east axis. blowing at 85 km/h to the east relative to What are the east and north components the ground. What are the plane’s speed of its displacement? and direction with respect to the ground? N N E 85 km/h 25˚ E ␪ t 325 m vR 175 km/h dE ϭ 325 m cos 25° ϭ 295 m dN ϭ –325 m sin 25° ϭ –137 m Physics: Principles and Problems Problems and Solutions Manual 17

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