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- 1. Solutions Manual
- 2. A Glencoe ProgramStudent EditionTeacher Wraparound EditionTeacher Chapter ResourcesMini Lab WorksheetsPhysics Lab WorksheetsStudy GuideSection QuizzesReinforcementEnrichmentTransparency MastersTransparency WorksheetsChapter AssessmentTeacher Classroom ResourcesTeaching TransparenciesLaboratory Manual, Student EditionLaboratory Manual, Teacher EditionProbeware Laboratory Manual, StudentEditionProbeware Laboratory Manual, TeacherEditionForensics Laboratory Manual, StudentEditionForensics Laboratory Manual, TeacherEditionSupplemental ProblemsAdditional Challenge ProblemsPre-AP/Critical Thinking ProblemsPhysics Test Prep: Studying for theEnd-of-Course Exam, Student EditionPhysics Test Prep: Studying for theEnd-of-Course Exam, Teacher EditionConnecting Math to PhysicsSolutions ManualTechnologyAnswer Key MakerExamView® ProInteractive ChalkboardMcGraw-Hill Learning NetworkStudentWorks™ CD-ROMTeacherWorks™ CD-ROMphysicspp.com Web siteCopyright © by The McGraw-Hill Companies, Inc. All rights reserved. Permission is grantedto reproduce the material contained herein on the condition that such material be repro-duced only for classroom use; be provided to students, teachers, and families withoutcharge; and be used solely in conjunction with the Physics: Principles and Problemsprogram. Any other reproduction, for use or sale, is prohibited without prior written permissionof the publisher.Send all inquiries to:Glencoe/McGraw-Hill8787 Orion PlaceColumbus, Ohio 43240ISBN 0-07-865893-4Printed in the United States of America1 2 3 4 5 6 7 8 9 045 09 08 07 06 05 04
- 3. To the Teacher . . . . . . . . . . . . . . . . . . . . . . ivChapter 1A Physics Toolkit . . . . . . . . . . . . . . . . . . . . 1Chapter 2Representing Motion . . . . . . . . . . . . . . . . 15Chapter 3Accelerated Motion . . . . . . . . . . . . . . . . . 29Chapter 4Forces in One Dimension . . . . . . . . . . . . 61Chapter 5Forces in Two Dimensions . . . . . . . . . . . 87Chapter 6Motion in Two Dimensions . . . . . . . . . 115Chapter 7Gravitation . . . . . . . . . . . . . . . . . . . . . . . 141Chapter 8Rotational Motion . . . . . . . . . . . . . . . . . 169Chapter 9Momentum and Its Conservation . . . . 193Chapter 10Energy, Work, and Simple Machines . . 225Chapter 11Energy and Its Conservation . . . . . . . . . 247Chapter 12Thermal Energy . . . . . . . . . . . . . . . . . . . 271Chapter 13States of Matter . . . . . . . . . . . . . . . . . . . 287Chapter 14Vibrations and Waves . . . . . . . . . . . . . . 311Chapter 15Sound . . . . . . . . . . . . . . . . . . . . . . . . . . . 329Chapter 16Fundamentals of Light . . . . . . . . . . . . . 345Chapter 17Reflection and Mirrors . . . . . . . . . . . . . . 357Chapter 18Refraction and Lenses . . . . . . . . . . . . . . 377Chapter 19Interference and Diffraction . . . . . . . . . 399Chapter 20Static Electricity . . . . . . . . . . . . . . . . . . . 413Chapter 21Electric Fields . . . . . . . . . . . . . . . . . . . . . 427Chapter 22Current Electricity . . . . . . . . . . . . . . . . . 445Chapter 23Series and Parallel Circuits . . . . . . . . . . 463Chapter 24Magnetic Fields . . . . . . . . . . . . . . . . . . . 485Chapter 25Electromagnetic Induction . . . . . . . . . . 501Chapter 26Electromagnetism . . . . . . . . . . . . . . . . . . 517Chapter 27Quantum Theory . . . . . . . . . . . . . . . . . . 531Chapter 28The Atom . . . . . . . . . . . . . . . . . . . . . . . . 545Chapter 29Solid-State Electronics . . . . . . . . . . . . . . 559Chapter 30Nuclear Physics . . . . . . . . . . . . . . . . . . . 573Appendix BAdditional Problems . . . . . . . . . . . . . . . 591ContentsCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Physics: Principles and Problems Contents iii
- 4. iv To the Teacher Physics: Principles and ProblemsTo the TeacherCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.The Solutions Manual is a comprehensive guide to the questions and problems in the Student Edition ofPhysics: Principles and Problems. This includes the Practice Problems, Section Reviews, Chapter Assessments,and Challenge Problems for each chapter, as well as the Additional Problems that appear in Appendix Bof the Student Edition. The Solutions Manual restates every question and problem so that you do not haveto look back at the text when reviewing problems with students.
- 5. Physics: Principles and Problems Solutions Manual 1Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.1 A Physics ToolkitCHAPTERPractice Problems1.1 Mathematics and Physicspages 3–10page 5For each problem, give the rewritten equation youwould use and the answer.1. A lightbulb with a resistance of 50.0 ohmsis used in a circuit with a 9.0-volt battery.What is the current through the bulb?I ϭ ᎏRVᎏ ϭ ᎏ509..00ovhomltsᎏ ϭ 0.18 ampere2. An object with uniform acceleration a,starting from rest, will reach a speed of vin time t according to the formula v ϭ at.What is the acceleration of a bicyclist whoaccelerates from rest to 7 m/s in 4 s?a ϭ ᎏvtᎏ ϭ ᎏ74ms/sᎏ ϭ 1.75 m/s23. How long will it take a scooter acceleratingat 0.400 m/s2 to go from rest to a speed of4.00 m/s?t ϭ ᎏvaᎏ ϭ ᎏ04.4.0000mm//ss2ᎏ ϭ 10.0 s4. The pressure on a surface is equal to theforce divided by the area: P ϭ F/A.A 53-kg woman exerts a force (weight) of520 Newtons. If the pressure exerted onthe floor is 32,500 N/m2, what is the areaof the soles of her shoes?A ϭ ᎏPFᎏ ϭ ᎏ32,550200NN/m2ᎏ ϭ 0.016 m2page 7Use dimensional analysis to check your equationbefore multiplying.5. How many megahertz is 750 kilohertz?750 kHzᎏ1010k0HHzzᎏᎏ1,0010M,0H00zHzᎏ ϭ0.75 MHz6. Convert 5021 centimeters to kilometers.5021 cmᎏ1010mcmᎏᎏ1100k0mmᎏ ϭ5.021ϫ10؊2 km7. How many seconds are in a leap year?366 daysᎏ124dahyᎏᎏ601mhinᎏᎏ16m0 sinᎏ ϭ31,622,400 s8. Convert the speed 5.30 m/s to km/h.ᎏ5.310smᎏᎏ16m0 sinᎏᎏ601mhinᎏᎏ1100k0mmᎏ ϭ19.08 km/hpage 8Solve the following problems.9. a. 6.201 cm ϩ 7.4 cm ϩ 0.68 cm ϩ12.0 cm6.201 cm7.4 cm0.68 cmϩ 12.0 cm26.281 cmϭ 26.3 cm after roundingb. 1.6 km ϩ 1.62 m ϩ 1200 cm1.6 km ϭ 1600 m1.62 m ϭ 1.62 m1200 cm ϭ ϩ 12 m1613.62 mϭ 1600 m or 1.6 km after rounding10. a. 10.8 g Ϫ 8.264 g10.8 gϪ 8.264 g2.536 gϭ 2.5 g after rounding
- 6. b. 4.75 m Ϫ 0.4168 m4.75 mϪ0.4168 m4.3332 mϭ 4.33 m after rounding11. a. 139 cm ϫ 2.3 cm320 cm2 or 3.2ϫ102 cm2b. 3.2145 km ϫ 4.23 km13.6 km212. a. 13.78 g Ϭ 11.3 mL1.22 g/mLb. 18.21 g Ϭ 4.4 cm34.1 g/cm3Section Review1.1 Mathematics and Physicspages 3–10page 1013. Math Why are concepts in physicsdescribed with formulas?The formulas are concise and can beused to predict new data.14. Magnetism The force of a magnetic fieldon a charged, moving particle is given byF ϭ Bqv, where F is the force in kgиm/s2, q isthe charge in Aиs, and v is the speed in m/s.B is the strength of the magnetic field,measured in teslas, T. What is 1 tesladescribed in base units?F ϭ Bqv, so B ϭ ᎏqFvᎏT ϭ ϭ ᎏAkиgs2ᎏ1 T ϭ 1 kg/Aиs215. Magnetism A proton with charge1.60ϫ10Ϫ19 Aиs is moving at 2.4ϫ105 m/sthrough a magnetic field of 4.5 T. You wantto find the force on the proton.a. Substitute the values into the equationyou will use. Are the units correct?F ϭ Bqvϭ (4.5 kg/Aиs2)(1.60ϫ10Ϫ19 Aиs)(2.4ϫ105 m/s)Force will be measured in kgиm/s2,which is correct.b. The values are written in scientificnotation, mϫ10n. Calculate the 10n partof the equation to estimate the size ofthe answer.10Ϫ19ϫ105 ϭ 10Ϫ14; the answer willbe about 20ϫ10Ϫ14, or 2ϫ10Ϫ13.c. Calculate your answer. Check it againstyour estimate from part b.1.7ϫ10Ϫ13 kgиm/s2d. Justify the number of significant digitsin your answer.The least-precise value is 4.5 T, with2 significant digits, so the answer isrounded to 2 significant digits.16. Magnetism Rewrite F ϭ Bqv to find v interms of F, q, and B.v ϭ ᎏBFqᎏ17. Critical Thinking An accepted value forthe acceleration due to gravity is 9.801 m/s2.In an experiment with pendulums, youcalculate that the value is 9.4 m/s2. Shouldthe accepted value be tossed out to accom-modate your new finding? Explain.No. The value 9.801 m/s2 has beenestablished by many other experiments,and to discard the finding you wouldhave to explain why they were wrong.There are probably some factorsaffecting your calculation, such asfriction and how precisely you canmeasure the different variables.kgиm/s2ᎏᎏ(Aиs)(m/s)2 Solutions Manual Physics: Principles and ProblemsCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 1 continued
- 7. Physics: Principles and Problems Solutions Manual 3Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Section Review1.2 Measurementpages 11–14page 1418. Accuracy Some wooden rulers do not startwith 0 at the edge, but have it set in a fewmillimeters. How could this improve theaccuracy of the ruler?As the edge of the ruler gets worn awayover time, the first millimeter or two ofthe scale would also be worn away ifthe scale started at the edge.19. Tools You find a micrometer (a tool usedto measure objects to the nearest 0.01 mm)that has been badly bent. How would itcompare to a new, high-quality meterstickin terms of its precision? Its accuracy?It would be more precise but lessaccurate.20. Parallax Does parallax affect the precisionof a measurement that you make? Explain.No, it doesn’t change the fineness ofthe divisions on its scale.21. Error Your friend tells you that his heightis 182 cm. In your own words, explain therange of heights implied by this statement.His height would be between 181.5 and182.5 cm. Precision of a measurementis one-half the smallest division on theinstrument. The height 182 cm wouldrange Ϯ 0.5 cm.22. Precision A box has a length of 18.1 cm anda width of 19.2 cm, and it is 20.3 cm tall.a. What is its volume?7.05ϫ103 cm3b. How precise is the measure of length?Of volume?nearest tenth of a cm; nearest10 cm3c. How tall is a stack of 12 of these boxes?243.6 cmd. How precise is the measure of theheight of one box? Of 12 boxes?nearest tenth of a cm; nearest tenthof a cm23. Critical Thinking Your friend states in areport that the average time required tocircle a 1.5-mi track was 65.414 s. This wasmeasured by timing 7 laps using a clockwith a precision of 0.1 s. How muchconfidence do you have in the results ofthe report? Explain.A result can never be more precise thanthe least precise measurement. Thecalculated average lap time exceedsthe precision possible with the clock.Practice Problems1.3 Graphing Datapages 15–19page 1824. The mass values of specified volumes ofpure gold nuggets are given in Table 1-4.a. Plot mass versus volume from thevalues given in the table and drawthe curve that best fits all points.1 2 3Volume (cm3)4 50204060Mass(g)80100Table 1-4Mass of Pure Gold NuggetsVolume (cm3) Mass (g)1.0 19.42.0 38.63.0 58.14.0 77.45.0 96.5Chapter 1 continued
- 8. b. Describe the resulting curve.a straight linec. According to the graph, what type ofrelationship exists between the mass ofthe pure gold nuggets and their volume?The relationship is linear.d. What is the value of the slope of thisgraph? Include the proper units.slope ϭ ᎏ⌬⌬yxᎏ ϭϭ 19.3 g/cm3e. Write the equation showing mass as afunction of volume for gold.m ϭ (19.3 g/cm3)Vf. Write a word interpretation for the slopeof the line.The mass for each cubic centimeterof pure gold is 19.3 g.Section Review1.3 Graphing Datapages 15–19page 1925. Make a Graph Graph the following data.Time is the independent variable.26. Interpret a Graph What would be themeaning of a nonzero y-intercept to a graphof total mass versus volume?There is a nonzero total mass when thevolume of the material is zero. Thiscould happen if the mass valueincludes the material’s container.27. Predict Use the relation illustrated inFigure 1-16 to determine the mass requiredto stretch the spring 15 cm.16 g28. Predict Use the relation in Figure 1-18 topredict the current when the resistance is16 ohms.7.5 A29. Critical Thinking In your own words,explain the meaning of a shallower line, ora smaller slope than the one in Figure 1-16,in the graph of stretch versus total mass fora different spring.The spring whose line has a smallerslope is stiffer, and therefore requiresmore mass to stretch it one centimeter.Chapter AssessmentConcept Mappingpage 2430. Complete the following concept map usingthe following terms: hypothesis, graph,mathematical model, dependent variable,measurement.Speed(m/s)1284010 20Time (s)30 40Time (s)Speed (m/s)0 5 10 15 20 25 30 3512 10 8 6 4 2 2 296.5 g Ϫ 19.4 gᎏᎏᎏ5.0 cm3 Ϫ 1.0 cm34 Solutions Manual Physics: Principles and ProblemsCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 1 continuedhypothesisexperimentmeasurementindependentvariabledependentvariablegraphmathematicalmodel
- 9. Physics: Principles and Problems Solutions Manual 5Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Mastering Conceptspage 2431. Describe a scientific method. (1.1)Identify a problem; gather informationabout it by observing and experimenting;analyze the information to arrive at ananswer.32. Why is mathematics important to science?(1.1)Mathematics allows you to be quantita-tive, to say “how fast,” not just “fast.”33. What is the SI system? (1.1)The International System of Units, or SI,is a base 10 system of measurementthat is the standard in science. The baseunits are the meter, kilogram, second,kelvin, mole, ampere, and candela.34. How are base units and derived unitsrelated? (1.1)The derived units are combinations ofthe base units.35. Suppose your lab partner recorded ameasurement as 100 g. (1.1)a. Why is it difficult to tell the number ofsignificant digits in this measurement?Zeros are necessary to indicate themagnitude of the value, but there isno way of knowing whether or not theinstrument used to measure the val-ues actually measured the zeros.Thezeros may serve only to locate the 1.b. How can the number of significantdigits in such a number be made clear?Write the number in scientificnotation, including only thesignificant digits.36. Give the name for each of the followingmultiples of the meter. (1.1)a. mcentimeterb. mmillimeterc. 1000 mkilometer37. To convert 1.8 h to minutes, by whatconversion factor should you multiply? (1.1)ᎏ601mhinᎏ, because the units will cancelcorrectly.38. Solve each problem. Give the correct numberof significant digits in the answers. (1.1)a. 4.667ϫ104 g ϩ 3.02ϫ105 g3.49ϫ105 gb. (1.70ϫ102 J) Ϭ (5.922ϫ10Ϫ4 cm3)2.87ϫ105 J/cm339. What determines the precision of ameasurement? (1.2)the precision of a measuring device,which is limited by the finest divisionon its scale40. How does the last digit differ from theother digits in a measurement? (1.2)The final digit is estimated.41. A car’s odometer measures the distancefrom home to school as 3.9 km. Usingstring on a map, you find the distance to be4.2 km. Which answer do you think is moreaccurate? What does accurate mean? (1.2)The most accurate measure is themeasure closest to the actual distance.The odometer is probably moreaccurate as it actually covered thedistance. The map is a model madefrom measurements, so your measure-ments from the map are more removedfrom the real distance.42. How do you find the slope of a lineargraph? (1.3)The slope of a linear graph is the ratioof the vertical change to the horizontalchange, or rise over run.1ᎏ10001ᎏ100Chapter 1 continued
- 10. 43. For a driver, the time between seeing astoplight and stepping on the brakes iscalled reaction time. The distance traveledduring this time is the reaction distance.Reaction distance for a given driver andvehicle depends linearly on speed. (1.3)a. Would the graph of reaction distanceversus speed have a positive or anegative slope?Positive. As speed increases,reaction distance increases.b. A driver who is distracted has a longerreaction time than a driver who is not.Would the graph of reaction distanceversus speed for a distracted driver havea larger or smaller slope than for anormal driver? Explain.Larger.The driver who was distractedwould have a longer reaction timeand thus a greater reaction distanceat a given speed.44. During a laboratory experiment, thetemperature of the gas in a balloon is variedand the volume of the balloon is measured.Which quantity is the independentvariable? Which quantity is the dependentvariable? (1.3)Temperature is the independent vari-able; volume is the dependent variable.45. What type of relationship is shown inFigure 1-20? Give the general equation forthis type of relation. (1.3)s Figure 1-20quadratic; y ϭ ax2 ϩ bx ϩ c46. Given the equation F ϭ mv2/R, whatrelationship exists between each of thefollowing? (1.3)a. F and Rinverse relationshipb. F and mlinear relationshipc. F and vquadratic relationshipApplying Conceptspages 25–2647. Figure 1-21 gives the height above theground of a ball that is thrown upwardfrom the roof of a building, for the first1.5 s of its trajectory. What is the ball’sheight at t ϭ 0? Predict the ball’s height att ϭ 2 s and at t ϭ 5 s.s Figure 1-21When t ϭ 0 and t ϭ 2, the ball’s heightwill be about 20 m. When t ϭ 5, the ballwill have landed on the ground so theheight will be 0 m.48. Is a scientific method one set of clearlydefined steps? Support your answer.There is no definite order of specificsteps. However, whatever approachis used, it always includes closeobservation, controlled experimentation,summarizing, checking, and rechecking.41 2 30252015105Height(m)Time (s)Height of Ball v. Timexy6 Solutions Manual Physics: Principles and ProblemsCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 1 continued
- 11. Physics: Principles and Problems Solutions Manual 7Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.49. Explain the difference between a scientifictheory and a scientific law.A scientific law is a rule of nature, wherea scientific theory is an explanation ofthe scientific law based on observation.A theory explains why something hap-pens; a law describes what happens.50. Density The density of a substance is itsmass per unit volume.a. Give a possible metric unit for density.possible answers include g/cm3 orkg/m3b. Is the unit for density a base unit or aderived unit?derived unit51. What metric unit would you use to measureeach of the following?a. the width of your handcmb. the thickness of a book covermmc. the height of your classroommd. the distance from your home to yourclassroomkm52. Size Make a chart of sizes of objects.Lengths should range from less than 1 mmto several kilometers. Samples mightinclude the size of a cell, the distance lighttravels in 1 s, and the height of a room.sample answer:radius of the atom, 5ϫ10Ϫ11 m; virus,10Ϫ7 m; thickness of paper, 0.1 mm;width of paperback book, 10.7 cm;height of a door, 1.8 m; width of town,7.8 km; radius of Earth, 6ϫ106 m;distance to the Moon, 4ϫ108 m53. Time Make a chart of time intervals.Sample intervals might include the timebetween heartbeats, the time betweenpresidential elections, the average lifetimeof a human, and the age of the UnitedStates. Find as many very short and verylong examples as you can.sample answer:half-life of polonium-194, 0.7 s;time between heartbeats, 0.8 s; time towalk between physics class and mathclass, 2.4 min; length of school year,180 days; time between elections forthe U.S. House of Representatives,2 years; time between U.S. presidentialelections, 4 years; age of the UnitedStates, (about) 230 years54. Speed of Light Two students measurethe speed of light. One obtains(3.001 Ϯ 0.001)ϫ108 m/s; the other obtains(2.999 Ϯ 0.006)ϫ108 m/s.a. Which is more precise?(3.001 Ϯ 0.001)ϫ108 m/sb. Which is more accurate?(2.999 Ϯ 0.006)ϫ108 m/s55. You measure the dimensions of a desk as132 cm, 83 cm, and 76 cm. The sum ofthese measures is 291 cm, while the productis 8.3ϫ105 cm3. Explain how the significantdigits were determined in each case.In addition and subtraction, you askwhat place the least precise measure isknown to: in this case, to the nearestcm. So the answer is rounded to thenearest cm. In multiplication anddivision, you look at the number ofsignificant digits in the least preciseanswer: in this case, 2. So the answer isrounded to 2 significant digits.56. Money Suppose you receive $5.00 at thebeginning of a week and spend $1.00 eachday for lunch. You prepare a graph of theamount you have left at the end of each dayfor one week. Would the slope of this graphbe positive, zero, or negative? Why?negative, because the change invertical distance is negative for apositive change in horizontal distanceChapter 1 continued
- 12. 57. Data are plotted on a graph, and the valueon the y-axis is the same for each value ofthe independent variable. What is theslope? Why? How does y depend on x?Zero. The change in vertical distance iszero. y does not depend on x.58. Driving The graph of braking distanceversus car speed is part of a parabola. Thus,the equation is written d ϭ av2 ϩ bv ϩ c.The distance, d, has units in meters, andvelocity, v, has units in meters/second.How could you find the units of a, b, and c?What would they be?The units in each term of the equationmust be in meters because distance, d,is measured in meters.av2 ϭ a(m/s)2, so a is in s2/m;bv ϭ b(m/s), so b is in sϪ1.59. How long is the leaf in Figure 1-22?Include the uncertainty in yourmeasurement.s Figure 1-228.3 cm Ϯ 0.05 cm, or 83 mm Ϯ 0.5 mm60. The masses of two metal blocks aremeasured. Block A has a mass of 8.45 gand block B has a mass of 45.87 g.a. How many significant digits areexpressed in these measurements?A: three; B: fourb. What is the total mass of block A plusblock B?54.32 gc. What is the number of significant digitsfor the total mass?fourd. Why is the number of significant digitsdifferent for the total mass and theindividual masses?When adding measurements, theprecision matters: both masses areknown to the nearest hundredth of agram, so the total should be given tothe nearest hundredth of a gram.Significant digits sometimes aregained when adding.61. History Aristotle said that the speed of afalling object varies inversely with the densityof the medium through which it falls.a. According to Aristotle, would a rock fallfaster in water (density 1000 kg/m3), orin air (density 1 kg/m3)?Lower density means faster speed,so the rock falls faster in air.b. How fast would a rock fall in a vacuum?Based on this, why would Aristotle saythat there could be no such thing as avacuum?Because a vacuum would have azero density, the rock should fallinfinitely fast. Nothing can fall thatfast.62. Explain the difference between a hypothesisand a scientific theory.A scientific theory has been testedand supported many times before itbecomes accepted. A hypothesis is anidea about how things might work—ithas much less support.63. Give an example of a scientific law.Newton’s laws of motion, law of conser-vation of energy, law of conservation ofcharge, law of reflection8 Solutions Manual Physics: Principles and ProblemsCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 1 continued
- 13. Physics: Principles and Problems Solutions Manual 9Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.64. What reason might the ancient Greekshave had not to question the hypothesisthat heavier objects fall faster than lighterobjects? Hint: Did you ever question whichfalls faster?Air resistance affects many lightobjects. Without controlled experi-ments, their everyday observations toldthem that heavier objects did fall faster.65. Mars Explain what observations led tochanges in scientists’ ideas about the surfaceof Mars.As telescopes improved and laterprobes were sent into space, scientistsgained more information about thesurface. When the information didnot support old hypotheses, thehypotheses changed.66. A graduated cylinder is marked every mL.How precise a measurement can you makewith this instrument?Ϯ0.5 mLMastering Problemspages 26–281.1 Mathematics and Physics67. Convert each of the followingmeasurements to meters.a. 42.3 cm0.423 mb. 6.2 pm6.2ϫ10Ϫ12 mc. 21 km2.1ϫ104 md. 0.023 mm2.3ϫ10Ϫ5 me. 214 m2.14ϫ10Ϫ4 mf. 57 nm5.7ϫ10Ϫ8 m68. Add or subtract as indicated.a. 5.80ϫ109 s ϩ 3.20ϫ108 s6.12ϫ109 sb. 4.87ϫ10Ϫ6 m Ϫ 1.93ϫ10Ϫ6 m2.94ϫ10Ϫ6 mc. 3.14ϫ10Ϫ5 kg ϩ 9.36ϫ10Ϫ5 kg1.250ϫ10Ϫ4 kgd. 8.12ϫ107 g Ϫ 6.20ϫ106 g7.50ϫ107 g69. Rank the following mass measurementsfrom least to greatest: 11.6 mg, 1021 g,0.000006 kg, 0.31 mg.0.31 mg, 1021 µg, 0.000006 kg, 11.6 mg70. State the number of significant digits ineach of the following measurements.a. 0.00003 m1b. 64.01 fm4c. 80.001 m5d. 0.720 g3e. 2.40ϫ106 kg3f. 6ϫ108 kg1g. 4.07ϫ1016 m371. Add or subtract as indicated.a. 16.2 m ϩ 5.008 m ϩ 13.48 m34.7 mb. 5.006 m ϩ 12.0077 m ϩ 8.0084 m25.022 mc. 78.05 cm2 Ϫ 32.046 cm246.00 cm2d. 15.07 kg Ϫ 12.0 kg3.1 kgChapter 1 continued
- 14. 72. Multiply or divide as indicated.a. (6.2ϫ1018 m)(4.7ϫ10Ϫ10 m)2.9ϫ109 m2b. (5.6ϫ10Ϫ7 m)/(2.8ϫ10Ϫ12 s)2.0ϫ105 m/sc. (8.1ϫ10Ϫ4 km)(1.6ϫ10Ϫ3 km)1.3ϫ10Ϫ6 km2d. (6.5ϫ105 kg)/(3.4ϫ103 m3)1.9ϫ102 kg/m373. Gravity The force due to gravity is F ϭ mgwhere g ϭ 9.80 m/s2.a. Find the force due to gravity on a41.63-kg object.408 kgиm/s2b. The force due to gravity on an object is632 kgиm/s2. What is its mass?64.5 kg74. Dimensional Analysis Pressure is mea-sured in pascals, where 1 Pa ϭ 1 kg/mиs2.Will the following expression give apressure in the correct units?No; it is in kg/s31.2 Measurement75. A water tank has a mass of 3.64 kg when itis empty and a mass of 51.8 kg when it isfilled to a certain level. What is the mass ofthe water in the tank?48.2 kg76. The length of a room is 16.40 m, its widthis 4.5 m, and its height is 3.26 m. Whatvolume does the room enclose?2.4ϫ102 m377. The sides of a quadrangular plot of landare 132.68 m, 48.3 m, 132.736 m, and48.37 m. What is the perimeter of the plot?362.1 m78. How precise a measurement could youmake with the scale shown in Figure 1-23?s Figure 1-23Ϯ0.5 g79. Give the measure shown on the meter inFigure 1-24 as precisely as you can. Includethe uncertainty in your answer.s Figure 1-243.6 Ϯ 0.1 A80. Estimate the height of the nearest doorframe in centimeters. Then measure it.How accurate was your estimate? Howprecise was your estimate? How precisewas your measurement? Why are the twoprecisions different?A standard residential doorframe heightis 80 inches, which is about 200 cm. Theprecision depends on the measurementinstrument used.012 345AACLASS A(0.55 kg)(2.1 m/s)ᎏᎏᎏ9.8 m/s210 Solutions Manual Physics: Principles and ProblemsCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 1 continued
- 15. Physics: Principles and Problems Solutions Manual 11Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.81. Base Units Give six examples of quantitiesyou might measure in a physics lab. Includethe units you would use.Sample: distance, cm; volume, mL;mass, g; current, A; time, s;temperature, °C82. Temperature The temperature drops from24°C to 10°C in 12 hours.a. Find the average temperature change perhour.1.2°C/hb. Predict the temperature in 2 more hoursif the trend continues.8°Cc. Could you accurately predict thetemperature in 24 hours?No. Temperature is unlikely to con-tinue falling sharply and steadilythat long.1.3 Graphing Data83. Figure 1-25 shows the masses of threesubstances for volumes between 0 and60 cm3.a. What is the mass of 30 cm3 of eachsubstance?(a) 80 g, (b) 260 g, (c) 400 gb. If you had 100 g of each substance,what would be their volumes?(a) 36 cm3, (b) 11 cm3, (c) 7 cm3c. In one or two sentences, describe themeaning of the slopes of the lines inthis graph.The slope represents the increasedmass of each additional cubiccentimeter of the substance.d. What is the y-intercept of each line?What does it mean?The y-intercept is (0,0). It means thatwhen V ϭ 0 cm3, there is none of thesubstance present (m ϭ 0 g).s Figure 1-2584. During a class demonstration, a physicsinstructor placed a mass on a horizontaltable that was nearly frictionless. Theinstructor then applied various horizontalforces to the mass and measured thedistance it traveled in 5 seconds for eachforce applied. The results of the experimentare shown in Table 1-5.a. Plot the values given in the table anddraw the curve that best fits all points.0.04080120Distance(cm)160Force (N)10.0 20.0 30.0Table 1-5Distance Traveled withDifferent ForcesForce (N) Distance (cm)5.0 2410.0 4915.0 7520.0 9925.0 12030.0 145ABC5020 4010 300800700600500400300200100Mass(g)Volume (cm3)Mass ofThree SubstancesChapter 1 continued
- 16. b. Describe the resulting curve.a straight linec. Use the graph to write an equationrelating the distance to the force.d ϭ 4.9Fd. What is the constant in the equation?Find its units.The constant is 4.9 and has unitscm/N.e. Predict the distance traveled when a22.0-N force is exerted on the objectfor 5 s.108 cm or 110 cm using 2 significantdigits85. The physics instructor from the previousproblem changed the procedure. The masswas varied while the force was kept con-stant. Time and distance were measured,and the acceleration of each mass was cal-culated. The results of the experiment areshown in Table 1-6.a. Plot the values given in the table anddraw the curve that best fits all points.b. Describe the resulting curve.a hyperbolac. According to the graph, what is therelationship between mass and theacceleration produced by a constantforce?Acceleration varies inversely withmass.d. Write the equation relating accelerationto mass given by the data in the graph.a ϭ ᎏ1m2ᎏe. Find the units of the constant in theequation.kgиm/s2f. Predict the acceleration of an 8.0-kgmass.1.5 m/s286. During an experiment, a student measuredthe mass of 10.0 cm3 of alcohol. The studentthen measured the mass of 20.0 cm3 ofalcohol. In this way, the data in Table 1-7were collected.a. Plot the values given in the table anddraw the curve that best fits all the points.0.010.020.030.0Mass(g)40.0Volume (cm3)10.0 20.0 30.0 40.0 50.0 60.0Table 1-7The Mass Values ofSpecific Volumes of AlcoholVolume (cm3) Mass (g)10.0 7.920.0 15.830.0 23.740.0 31.650.0 39.60.03.06.09.0Acceleration(m/s2)12.0Mass (kg)2.0 4.0 6.0Table 1-6Acceleration of Different MassesMass (kg) Acceleration (m/s2)1.0 12.02.0 5.93.0 4.14.0 3.05.0 2.56.0 2.012 Solutions Manual Physics: Principles and ProblemsCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 1 continued
- 17. Physics: Principles and Problems Solutions Manual 13Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.b. Describe the resulting curve.a straight linec. Use the graph to write an equationrelating the volume to the mass of thealcohol.m ϭ 0.79Vd. Find the units of the slope of the graph.What is the name given to this quantity?g/cm3; densitye. What is the mass of 32.5 cm3 ofalcohol?25.7 gMixed Reviewpage 2887. Arrange the following numbers from mostprecise to least precise0.0034 m 45.6 m 1234 m0.0034 m, 45.6 m, 1234 m88. Figure 1-26 shows the toroidal (doughnut-shaped) interior of the now-dismantledTokamak Fusion Test Reactor. Explain why awidth of 80 m would be an unreasonablevalue for the width of the toroid. Whatwould be a reasonable value?s Figure 1-2680 meters is equivalent to about 260 feet,which would be very large. 10 meterswould be a more reasonable value.89. You are cracking a code and havediscovered the following conversionfactors: 1.23 longs ϭ 23.0 mediums, and74.5 mediums ϭ 645 shorts. How manyshorts are equal to one long?1 longᎏ12.32.30lmonedgᎏᎏ67445.5smhoerdtᎏ ϭ 162 shorts90. You are given the following measurementsof a rectangular bar: length ϭ 2.347 m,thickness ϭ 3.452 cm, height ϭ 2.31 mm,mass ϭ 1659 g. Determine the volume, incubic meters, and density, in g/cm3, of thebeam. Express your results in proper form.volume ϭ 1.87ϫ10Ϫ4 m3, or 187 cm3;density ϭ 8.87 g/cm391. A drop of water contains 1.7ϫ1021 mole-cules. If the water evaporated at the rate ofone million molecules per second, howmany years would it take for the drop tocompletely evaporate?ϭ 1.7ϫ1015 s(1.7ϫ1015 s)ᎏ36100hsᎏᎏ124dahyᎏᎏ3651dyaysᎏ ϭ5.4ϫ107 y92. A 17.6-gram sample of metal is placed in agraduated cylinder containing 10.0 cm3 ofwater. If the water level rises to 12.20 cm3,what is the density of the metal?density ϭ ᎏmVᎏϭϭ 8.00 g/cm3Thinking Criticallypage 2893. Apply Concepts It has been said thatfools can ask more questions than the wisecan answer. In science, it is frequently thecase that one wise person is needed to askthe right question rather than to answer it.Explain.The “right” question is one that pointsto fruitful research and to otherquestions that can be answered.94. Apply Concepts Find the approximate massof water in kilograms needed to fill a con-tainer that is 1.40 m long and 0.600 m wideto a depth of 34.0 cm. Report your result toone significant digit. (Use a reference sourceto find the density of water.)17.6 gᎏᎏᎏ12.20 cm3 Ϫ 10.0 cm3Chapter 1 continued1.7ϫ1021 molecules 1,000,000 moleculesᎏᎏᎏ1 s
- 18. Vw ϭ (140 cm)(60.0 cm)(34.0 cm) ϭ285,600 cm3. Because the density ofwater is 1.00 g/cm3, the mass of waterin kilograms is 286 kg.95. Analyze and Conclude A container of gaswith a pressure of 101 kPa has a volumeof 324 cm3 and a mass of 4.00 g. If thepressure is increased to 404 kPa, what isthe density of the gas? Pressure and volumeare inversely proportional.Pressure and volume are inverselyproportional. Since the pressure is4 times greater, the volume will be ᎏ14ᎏof the original volume.ᎏ3244cm3ᎏ ϭ 81.0 cm3ᎏ814..000cmg3ᎏ ϭ 0.0494 g/cm396. Design an Experiment How high can youthrow a ball? What variables might affectthe answer to this question?mass of ball, footing, practice, andconditioning97. Calculate If the Sun suddenly ceased toshine, how long would it take Earth tobecome dark? (You will have to look up thespeed of light in a vacuum and the distancefrom the Sun to Earth.) How long would ittake the surface of Jupiter to become dark?tE ϭ ᎏdvEᎏ ϭ ᎏ13..40906ϫϫ110081m1/msᎏϭ 499 s ϭ 8.31 mintJ ϭ ᎏdvJᎏ ϭ ᎏ37..0708ϫϫ1100811mm/sᎏϭ 2593 s ϭ 43.2 minWriting in Physicspage 2898. Research and describe a topic in the historyof physics. Explain how ideas about thetopic changed over time. Be sure to includethe contributions of scientists and toevaluate the impact of their contributionson scientific thought and the world outsidethe laboratory.Answers will vary.99. Explain how improved precision inmeasuring time would have led tomore accurate predictions about howan object falls.Answers will vary. For example, studentsmight suggest that improved precisioncan lead to better observations.Challenge Problempage 17An object is suspended from spring 1, and thespring’s elongation (the distance it stretches) is X1.Then the same object is removed from the firstspring and suspended from a second spring. Theelongation of spring 2 is X2. X2 is greater than X1.1. On the same axes, sketch the graphs of themass versus elongation for both springs.2. Is the origin included in the graph? Why orwhy not?Yes; the origin corresponds to0 elongation when the force is 0.3. Which slope is steeper?The slope for X2 is steeper.4. At a given mass, X2 ϭ 1.6 X1.If X2 ϭ 5.3 cm, what is X1?X2 ϭ 1.6X15.3 cm ϭ 1.6X13.3 cm ϭ X114 Solutions Manual Physics: Principles and ProblemsCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 1 continuedX2X1XF
- 19. Physics: Principles and Problems Solutions Manual 15Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.2 Representing MotionCHAPTERSection Review2.1 Picturing Motionpages 31–33page 331. Motion Diagram of a Runner Use theparticle model to draw a motion diagramfor a bike rider riding at a constant pace.2. Motion Diagram of a Bird Use the parti-cle model to draw a simplified motion dia-gram corresponding to the motion diagramin Figure 2-4 for a flying bird. What pointon the bird did you choose to represent it?s Figure 2-43. Motion Diagram of a Car Use the particlemodel to draw a simplified motion diagramcorresponding to the motion diagram inFigure 2-5 for a car coming to a stop at astop sign. What point on the car did youuse to represent it?s Figure 2-54. Critical Thinking Use the particle modelto draw motion diagrams for two runnersin a race, when the first runner crosses thefinish line as the other runner is three-fourths of the way to the finish line.Section Review2.2 Where and When?pages 34–37page 375. Displacement The particle model for a cartraveling on an interstate highway is shownbelow. The starting point is shown.Here ThereMake a copy of the particle model, anddraw a vector to represent the displacementof the car from the starting time to the endof the third time interval.6. Displacement The particle model for a boywalking to school is shown below.Home SchoolMake a copy of the particle model, anddraw vectors to represent the displacementbetween each pair of dots.SchoolHomeHere ThereRunner 2Runner 1FinishStartt0 t1 t2 t3 t4t1 t2 t3 t4t0
- 20. 7. Position Two students compared theposition vectors they each had drawn ona motion diagram to show the position of amoving object at the same time. They foundthat their vectors did not point in the samedirection. Explain.A position vector goes from the originto the object. When the origins are dif-ferent, the position vectors are different.On the other hand, a displacement vec-tor has nothing to do with the origin.8. Critical Thinking A car travels straightalong the street from the grocery store tothe post office. To represent its motion youuse a coordinate system with its origin atthe grocery store and the direction the car ismoving in as the positive direction. Yourfriend uses a coordinate system with its ori-gin at the post office and the oppositedirection as the positive direction. Wouldthe two of you agree on the car’s position?Displacement? Distance? The time intervalthe trip took? Explain.The two students should agree on thedisplacement, distance, and time intervalfor the trip, because these three quanti-ties are independent of where the originof the coordinate system is placed.Thetwo students would not agree on thecar’s position, because the position ismeasured from the origin of the coordi-nate system to the location of the car.Practice Problems2.3 Position-Time Graphspages 38–42page 39For problems 9–11, refer to Figure 2-13.s Figure 2-139. Describe the motion of the car shown bythe graph.The car begins at a position of 125.0 mand moves toward the origin, arriving atthe origin 5.0 s after it begins moving.The car continues beyond the origin.10. Draw a motion diagram that corresponds tothe graph.11. Answer the following questions aboutthe car’s motion. Assume that the positived-direction is east and the negatived-direction is west.a. When was the car 25.0 m east of theorigin?at 4.0 sb. Where was the car at 1.0 s?100.0 m12. Describe, in words, the motion of thetwo pedestrians shown by the lines inFigure 2-14. Assume that the positive direc-tion is east on Broad Street and the origin isthe intersection of Broad and High Streets.t0 ϭ 0.0 s125.0 m 0.0 mt5 ϭ 5.0 sd7.0150.0100.050.00.0Ϫ50.0Position(m)Time (s)1.0 3.0 5.016 Solutions Manual Physics: Principles and ProblemsCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 2 continued
- 21. Physics: Principles and Problems Solutions Manual 17Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.s Figure 2-14Pedestrian A starts west of High Streetand walks east (the positive direction).Pedestrian B begins east of High Streetand walks west (the negative direction).Sometime after B crosses High Street,A and B pass each other. Sometimeafter they pass, Pedestrian A crossesHigh Street.13. Odina walked down the hall at schoolfrom the cafeteria to the band room, adistance of 100.0 m. A class of physicsstudents recorded and graphed herposition every 2.0 s, noting that she moved2.6 m every 2.0 s. When was Odina in thefollowing positions?a. 25.0 m from the cafeteria19 sb. 25.0 m from the band room58 sc. Create a graph showing Odina’smotion.page 41For problems 14–17, refer to the figure inExample Problem 2.s Example Problem 2 Figure14. What event occurred at t ϭ 0.0 s?Runner A passed the origin.15. Which runner was ahead at t ϭ 48.0 s?runner B16. When runner A was at 0.0 m, where wasrunner B?at Ϫ50.0 m17. How far apart were runners A and B att ϭ 20.0 s?approximately 30 m18. Juanita goes for a walk. Sometime later, herfriend Heather starts to walk after her. Theirmotions are represented by the position-time graphs in Figure 2-16.s Figure 2-16a. How long had Juanita been walkingwhen Heather started her walk?6.0 min0.0Position(km)Time (h)1.02.03.04.05.06.01.0 2.01.5JuanitaHeather0.50.0 4.02.0 8.06.0 10.0 12.0200.050.0100.0150.0Position(m)Time (s)Distancefromcafeteria(m)Time (s)10.0 30.0 50.0 70.00.0020.040.060.080.0100.0High St.Broad St.EastWestPosition(m)Time (s)ABChapter 2 continued
- 22. b. Will Heather catch up to Juanita? Howcan you tell?No. The lines representing Juanita’sand Heather’s motions get fartherapart as time increases. The lineswill not intersect.Section Review2.3 Position-Time Graphspages 38–42page 4219. Position-Time Graph From the particlemodel in Figure 2-17 of a baby crawlingacross a kitchen floor, plot a position-timegraph to represent his motion. The timeinterval between successive dots is 1 s.s Figure 2-1720. Motion Diagram Create a particle modelfrom the position-time graph of a hockeypuck gliding across a frozen pond inFigure 2-18.s Figure 2-18For problems 21–23, refer to Figure 2-18.21. Time Use the position-time graph of thehockey puck to determine when it was10.0 m beyond the origin.0.5 s22. Distance Use the position-time graph ofthe hockey puck to determine how far itmoved between 0.0 s and 5.0 s.100 m23. Time Interval Use the position-time graphfor the hockey puck to determine how muchtime it took for the puck to go from 40 mbeyond the origin to 80 m beyond the origin.2.0 s24. Critical Thinking Look at the particlemodel and position-time graph shown inFigure 2-19. Do they describe the samemotion? How do you know? Do notconfuse the position coordinate system inthe particle model with the horizontal axisin the position-time graph. The time inter-vals in the particle model are 2 s.s Figure 2-190Position(m)Time (s)48121 2 3 4 5Position (m)0 100 m 140 mt0 ϭ 0.0 s t7 ϭ 7.0 s0.0Position(m)Time (s)204060801001201407.06.05.04.03.02.01.0Time (s)5 6 7 81 2 3 4160140120100806040200Position(m)Position (cm)0 20 40 60 80 100 120 140 16018 Solutions Manual Physics: Principles and ProblemsCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 2 continued
- 23. Physics: Principles and Problems Solutions Manual 19Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.No, they don’t describe the samemotion. Although both objects are trav-eling in the positive direction, one ismoving more quickly than the other.Students can cite a number of differentspecific examples from the graph andparticle model to back this up.Practice Problems2.4 How Fast?pages 43–47page 4525. The graph in Figure 2-22 describes themotion of a cruise ship during its voyagethrough calm waters. The positived-direction is defined to be south.s Figure 2-22a. What is the ship’s average speed?Using the points (0.0 s, 0.0 m) and(3.0 s, Ϫ1.0 m)vෆϭᎏ⌬⌬dtᎏϭᎏdt22ϪϪdt11ᎏϭᎏϪ31..00smϪϪ00.0.0smᎏϭ Ϫ0.33 m/sϭ 0.33 m/sb. What is its average velocity?The average velocity is the slope ofthe line, including the sign, so it isϪ0.33 m/s or 0.33 m/s north.26. Describe, in words, the motion of the cruiseship in the previous problem.The ship is moving to the north at aspeed of 0.33 m/s.27. The graph in Figure 2-23 represents themotion of a bicycle. Determine the bicycle’saverage speed and average velocity, anddescribe its motion in words.s Figure 2-23Because the bicycle is moving in thepositive direction, the average speedand average velocity are the same.Using the points (0.0 min, 0.0 km) and(15.0 min, 10.0 km),vෆϭᎏ⌬⌬dtᎏϭᎏdt22ϪϪdt11ᎏϭ ϭ 0.67 km/minvෆϭ 0.67 km/min in the positivedirectionThe bicycle is moving in the positivedirection at a speed of 0.67 km/min.10.0 km Ϫ 0.0 kmᎏᎏᎏ15.0 min Ϫ 0.0 minPosition(km)Time (min)20151050 30252015105Position(m)Time (s)1 2 3 4Ϫ2Ϫ10Chapter 2 continued
- 24. 28. When Marilyn takes her pet dog for a walk,the dog walks at a very consistent pace of0.55 m/s. Draw a motion diagram and posi-tion-time graph to represent Marilyn’s dogwalking the 19.8-m distance from in frontof her house to the nearest fire hydrant.Section Review2.4 How Fast?pages 43–47page 47For problems 29–31, refer to Figure 2-25.29. Average Speed Rank the position-timegraphs according to the average speed of theobject, from greatest average speed to leastaverage speed. Specifically indicate any ties.s Figure 2-25For speed use the absolute value, there-fore A, B, C ϭ DSlopeA ϭ Ϫ2SlopeB ϭ ᎏ32ᎏSlopeC ϭ Ϫ1SlopeD ϭ 130. Average Velocity Rank the graphs accord-ing to average velocity, from greatest averagevelocity to least average velocity. Specificallyindicate any ties.B, D, C, ASlopeA ϭ Ϫ2SlopeB ϭ ᎏ32ᎏSlopeC ϭ Ϫ1SlopeD ϭ 131. Initial Position Rank the graphs accordingto the object’s initial position, from mostpositive position to most negative position.Specifically indicate any ties. Would yourranking be different if you had been askedto do the ranking according to initialdistance from the origin?A, C, B, D. Yes, the ranking from greatestto least distance would be A, C, D, B.32. Average Speed and Average VelocityExplain how average speed and averagevelocity are related to each other.Average speed is the absolute value ofthe average velocity. Speed is only amagnitude, while velocity is a magni-tude and a direction.Position(m)Time (s)AB DCt0 ϭ 0 s0.0 m 19.8 mt6 ϭ 36 sMotion DiagramPosition-Time Graph6 12 18 24 30 3605.010.015.0Positionfromhouse(m)Time (s)20.0House Hydrant20 Solutions Manual Physics: Principles and ProblemsCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 2 continued
- 25. Physics: Principles and Problems Solutions Manual 21Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.33. Critical Thinking In solving a physicsproblem, why is it important to createpictorial and physical models before tryingto solve an equation?Answers will vary, but here are some ofthe important points. Drawing the mod-els before writing down the equationhelps you to get the problem situationorganized in your head. It’s difficult towrite down the proper equation if youdon’t have a clear picture of how thingsare situated and/or moving. Also, youchoose the coordinate system in thisstep, and this is essential in makingsure you use the proper signs on thequantities you will substitute into theequation later.Chapter AssessmentConcept Mappingpage 5234. Complete the concept map below using thefollowing terms: words, equivalent representa-tions, position-time graph.Mastering Conceptspage 5235. What is the purpose of drawing a motiondiagram? (2.1)A motion diagram gives you a pictureof motion that helps you visualizedisplacement and velocity.36. Under what circumstances is it legitimate totreat an object as a point particle? (2.1)An object can be treated as a pointparticle if internal motions are notimportant and if the object is small incomparison to the distance it moves.37. The following quantities describe locationor its change: position, distance, and dis-placement. Briefly describe the differencesamong them. (2.2)Position and displacement are differentfrom distance because position and dis-placement both contain informationabout the direction in which an objecthas moved, while distance does not.Distance and displacement are differentfrom position because they describehow an object’s location has changedduring a time interval, where positiontells exactly where an object is locatedat a precise time.38. How can you use a clock to find a timeinterval? (2.2)Read the clock at the beginning andend of the interval and subtract thebeginning time from the ending time.39. In-line Skating How can you use theposition-time graphs for two in-line skatersto determine if and when one in-line skaterwill pass the other one? (2.3)Draw the two graphs on the same setof axes. One inline skater will pass theother if the lines representing each oftheir motions intersect. The positioncoordinate of the point where the linesintersect is the position where thepassing occurs.40. Walking Versus Running A walker and arunner leave your front door at the sametime. They move in the same direction atdifferent constant velocities. Describe theposition-time graphs of each. (2.4)Both are straight lines that start at thesame position, but the slope of therunner’s line is steeper.41. What does the slope of a position-timegraph measure? (2.4)velocityChapter 2 continuedwordsmotiondiagramposition-timegraphdatatableequivalentrepresentations
- 26. 42. If you know the positions of a movingobject at two points along its path, and youalso know the time it took for the object toget from one point to the other, can youdetermine the particle’s instantaneousvelocity? Its average velocity? Explain. (2.4)It is possible to calculate the averagevelocity from the information given, butit is not possible to find the instanta-neous velocity.Applying Conceptspage 5243. Test the following combinations andexplain why each does not have the proper-ties needed to describe the concept of veloc-ity: ⌬d ϩ ⌬t, ⌬d Ϫ ⌬t, ⌬d ϫ ⌬t, ⌬t/⌬d.⌬d ϩ ⌬t increases when either termincreases. The sign of ⌬d Ϫ ⌬t dependsupon the relative sizes of ⌬d and ⌬t.⌬d ϫ ⌬t increases when either increas-es. ⌬t/⌬d decreases with increasingdisplacement and increases withincreasing time interval, which is back-wards from velocity.44. Football When can a football be consid-ered a point particle?A football can be treated as a pointparticle if its rotations are not importantand if it is small in comparison to thedistance it moves — for distances of1 yard or more.45. When can a football player be treated as apoint particle?A football player can be treated as apoint particle if his or her internalmotions are not important and if he orshe is small in comparison to the dis-tance he or she moves — for distancesof several yards or more.46. Figure 2-26 is a graph of two people running.s Figure 2-26a. Describe the position of runner Arelative to runner B at the y-intercept.Runner A has a head start byfour units.b. Which runner is faster?Runner B is faster, as shown bythe steeper slope.c. What occurs at point P and beyond?Runner B passes runner A at pointP.47. The position-time graph in Figure 2-27shows the motion of four cows walkingfrom the pasture back to the barn. Rank thecows according to their average velocity,from slowest to fastest.s Figure 2-27Moolinda, Dolly, Bessie, ElsiePosition(m)Time (s)ElsieBessieDollyMoolindaPosition(m)Time (s)Runner BRunner ACopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 2 continued22 Solutions Manual Physics: Principles and Problems
- 27. Physics: Principles and Problems Solutions Manual 23Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.48. Figure 2-28 is a position-time graph for arabbit running away from a dog.s Figure 2-28a. Describe how this graph would bedifferent if the rabbit ran twice as fast.The only difference is that the slopeof the graph would be twice as steep.b. Describe how this graph would be dif-ferent if the rabbit ran in the oppositedirection.The magnitude of the slope would bethe same, but it would be negative.Mastering Problems2.4 How Fast?page 53Level 149. A bike travels at a constant speed of 4.0 m/sfor 5.0 s. How far does it go?d ϭ vtϭ (4.0 m/s)(5 s)ϭ 20 m50. Astronomy Light from the Sun reachesEarth in 8.3 min. The speed of light is3.00ϫ108 m/s. How far is Earth fromthe Sun?d ϭ vtϭ (3.00ϫ108 m/s)(8.3 min)ᎏ16m0 sinᎏϭ 1.5ϫ1011 mPosition(m)0123Time (s)321Chapter 2 continued
- 28. Level 251. A car is moving down a street at 55 km/h. Achild suddenly runs into the street. If ittakes the driver 0.75 s to react and applythe brakes, how many meters will the carhave moved before it begins to slow down?d ϭ vtϭ (55 km/h)(0.75 s)ᎏ1010k0mmᎏᎏ36100hsᎏϭ 11 m52. Nora jogs several times a week and alwayskeeps track of how much time she runseach time she goes out. One day she forgetsto take her stopwatch with her and wondersif there’s a way she can still have some ideaof her time. As she passes a particular bank,she remembers that it is 4.3 km from herhouse. She knows from her previoustraining that she has a consistent pace of4.0 m/s. How long has Nora been joggingwhen she reaches the bank?d ϭ vtt ϭ ᎏdvᎏ ϭϭ 1075 sϭ (1075 s)ᎏ16m0 sinᎏϭ 18 minLevel 353. Driving You and a friend each drive50.0 km. You travel at 90.0 km/h; yourfriend travels at 95.0 km/h. How long willyour friend have to wait for you at the endof the trip?d ϭ vtt1 ϭ ᎏdvᎏ ϭ ᎏ9500.0.0kkmm/hᎏϭ 0.556 ht2 ϭ ᎏdvᎏ ϭ ᎏ9550.0.0kkmm/hᎏϭ 0.526 ht1 Ϫ t2 ϭ (0.556 h Ϫ 0.526 h)ᎏ601mhinᎏϭ 1.8 minMixed Reviewpages 53–54Level 154. Cycling A cyclist maintains a constantvelocity of ϩ5.0 m/s. At time t ϭ 0.0 s, thecyclist is ϩ250 m from point A.a. Plot a position-time graph of thecyclist’s location from point A at 10.0-sintervals for 60.0 s.b. What is the cyclist’s position from pointA at 60.0 s?550 mc. What is the displacement from thestarting position at 60.0 s?550 m Ϫ 250 m ϭ 3.0ϫ102 m55. Figure 2-29 is a particle model for achicken casually walking across the road.Time intervals are every 0.1 s. Draw thecorresponding position-time graph andequation to describe the chicken’s motion.s Figure 2-2956. Figure 2-30 shows position-time graphs forThis sideThe other side1.9 s0tdThis side The other sideTime intervals are 0.1 s.2000.0 20.010.0 40.030.0 50.0 60.0550250300350400450500Position(m)Time (s)(4.3 km)ᎏ1100k0mmᎏᎏᎏ4.0 m/s24 Solutions Manual Physics: Principles and ProblemsCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 2 continued
- 29. Physics: Principles and Problems Solutions Manual 25Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Joszi and Heike paddling canoes in a localriver.s Figure 2-30a. At what time(s) are Joszi and Heike inthe same place?1.0 hb. How much time does Joszi spend onthe river before he passes Heike?45 minc. Where on the river does it appear thatthere might be a swift current?from 6.0 to 9.0 km from the originLevel 257. Driving Both car A and car B leave schoolwhen a stopwatch reads zero. Car A travelsat a constant 75 km/h, and car B travels at aconstant 85 km/h.a. Draw a position-time graph showingthe motion of both cars. How far arethe two cars from school when the stop-watch reads 2.0 h? Calculate the dis-tances and show them on your graph.dA ϭ vAtϭ (75 km/h)(2.0 h)ϭ 150 kmdB ϭ vBtϭ (85 km/h)(2.0 h)ϭ 170 kmb. Both cars passed a gas station 120 kmfrom the school. When did each carpass the gas station? Calculate the timesand show them on your graph.tA ϭ ᎏdAᎏ ϭ ᎏ71520kmkm/hᎏ ϭ 1.6 htB ϭ ᎏdBᎏ ϭ ᎏ81520kmkm/hᎏ ϭ 1.4 h58. Draw a position-time graph for two carstraveling to the beach, which is 50 km fromschool. At noon, Car A leaves a store that is10 km closer to the beach than the school isand moves at 40 km/h. Car B starts fromschool at 12:30 P.M. and moves at 100 km/h.When does each car get to the beach?Both cars arrive at the beach at 1:00 P.M.Level 359. Two cars travel along a straight road. Whena stopwatch reads t ϭ 0.00 h, car A is atdA ϭ 48.0 km moving at a constant36.0 km/h. Later, when the watch readst ϭ 0.50 h, car B is at dB ϭ 0.00 km moving0Noon 12201210124012301250100PM5010203040Car ACar BPosition(m)Time01.01.41.62.03.025050100120170150200Car BCar APosition(km)Time (h)Position(km)0Time (h)141618246810122.52.01.51.00.5HeikeJosziChapter 2 continued
- 30. at 48.0 km/h. Answer the following ques-tions, first, graphically by creating a posi-tion-time graph, and second, algebraicallyby writing equations for the positionsdA and dB as a function of the stopwatchtime, t.a. What will the watch read when car Bpasses car A?Cars pass when the distances areequal, dA ϭ dBdA ϭ 48.0 km ϩ (36.0 km/h)tand dB ϭ 0 ϩ (48.0 km/h)(t Ϫ 0.50 h)so 48.0 km ϩ (36.0 km/h)tϭ (48.0 km/h)(t Ϫ 0.50 h)(48.0 km) ϩ (36.0 km/h)tϭ (48.0 km/h)t Ϫ 24 km72 km ϭ (12.0 km/h)tt ϭ 6.0 hb. At what position will car B pass car A?dA ϭ 48.0 km ϩ (36.0 km/h)(6.0 h)ϭ 2.6ϫ102 kmc. When the cars pass, how long will ithave been since car A was at thereference point?d ϭ vtso t ϭ ᎏdvᎏ ϭ ᎏ3Ϫ64.08.0kmkm/hᎏ ϭ Ϫ1.33 hCar A has started 1.33 h before theclock started.t ϭ 6.0 h ϩ 1.33 h ϭ 7.3 h60. Figure 2-31 shows the position-time graphdepicting Jim’s movement up and down theaisle at a store. The origin is at one end ofthe aisle.s Figure 2-31a. Write a story describing Jim’s movementsat the store that would correspond to themotion represented by the graph.Answers will vary.b. When does Jim have a position of 6.0 m?from 8.0 to 18.0 s, 53.0 to 56.0 s, andat 43.0 sc. How much time passes between whenJim enters the aisle and when he gets toa position of 12.0 m? What is Jim’s aver-age velocity between 37.0 s and 46.0 s?t ϭ 33.0 sUsing the points (37.0 s, 12.0 m) and(46.0 s, 3.00 m)vෆϭ ϭϭ Ϫ1.00 m/s3.00 m Ϫ 12.0 mᎏᎏ46.0 s Ϫ 37.0 sdf Ϫ diᎏtf Ϫ tiPosition(m)Time (s)14.012.010.08.06.04.02.00.00 10.0 20.0 30.0 40.0 50.0 60.00.00 1.00 2.00Ϫ1.00 7.003.00 4.00 5.00 6.00300.050.0100.0150.0150.0200.0Car ACar BPosition(km)Time (h)26 Solutions Manual Physics: Principles and ProblemsCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 2 continued
- 31. Physics: Principles and Problems Solutions Manual 27Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Thinking Criticallypage 5461. Apply Calculators Members of a physicsclass stood 25 m apart and used stopwatch-es to measure the time which a car travelingon the highway passed each person. Theirdata are shown in Table 2-3.Use a graphing calculator to fit a line to aposition-time graph of the data and to plotthis line. Be sure to set the display range ofthe graph so that all the data fit on it. Findthe slope of the line. What was the speed ofthe car?The slope of the line and the speed ofthe car are 19.7 m/s.62. Apply Concepts You plan a car trip forwhich you want to average 90 km/h. Youcover the first half of the distance at anaverage speed of only 48 km/h. What mustyour average speed be in the second half ofthe trip to meet your goal? Is this reason-able? Note that the velocities are based onhalf the distance, not half the time.720 km/h; NoExplanation:Assume you want to travel 90 km in 1 h.If you cover the first half of the distanceat 48 km/h, then you’ve gone 45 km in0.9375 h (because t ϭ ᎏdvᎏ). This meansyou have used 93.75% of your time forthe first half of the distance leaving6.25% of the time to go the remaining45 km.v ϭ ᎏ04.0562k5mhᎏϭ 720 km/h63. Design an Experiment Every time a par-ticular red motorcycle is driven past yourfriend’s home, his father becomes angrybecause he thinks the motorcycle is goingtoo fast for the posted 25 mph (40 km/h)speed limit. Describe a simple experimentyou could do to determine whether or notthe motorcycle is speeding the next time itis driven past your friend’s house.There are actually several good possibil-ities for answers on this one.Two thatshould be among the most popular arebriefly described here. 1) Get severalpeople together and give everyone awatch. Synchronize the watches andstand along the street separated by aconsistent distance, maybe 10 m or so.When the motorcycle passes, have eachperson record the time (at least to anaccuracy of seconds) that the motorcy-cle crossed in front of them. Plot a posi-tion time graph, and compute the slopeof the best-fit line. If the slope is greaterthan 25 mph, the motorcycle is speed-ing. 2) Get someone with a driver’slicense to drive a car along the street at25 mph in the same direction as youexpect the motorcycle to go. If themotorcycle gets closer to the car (if thedistance between them decreases), themotorcycle is speeding. If the distancebetween them stays the same, themotorcycle is driving at the speed limit.If the distance increases, the motorcycleis driving less than the speed limit.64. Interpret Graphs Is it possible for an0.0 4.02.0 8.06.0 10.0 12.0200.050.0100.0150.0Position(m)Time (s)Table 2-3Position v. TimeTime (s) Position (m)0.0 0.01.3 25.02.7 50.03.6 75.05.1 100.05.9 125.07.0 150.08.6 175.010.3 200.0Chapter 2 continued
- 32. object’s position-time graph to be a hori-zontal line? A vertical line? If you answeryes to either situation, describe the associat-ed motion in words.It is possible to have a horizontal lineas a position-time graph; this wouldindicate that the object’s position is notchanging, or in other words, that it isnot moving. It is not possible to have aposition-time graph that is a verticalline, because this would mean theobject is moving at an infinite speed.Writing in Physicspage 5465. Physicists have determined that the speed oflight is 3.00ϫ108 m/s. How did they arriveat this number? Read about some of theseries of experiments that were done todetermine light’s speed. Describe how theexperimental techniques improved to makethe results of the experiments more accurate.Answers will vary. Galileo attempted todetermine the speed of light but wasunsuccessful. Danish astronomer OlausRoemer successfully measured thespeed of light in 1676 by observing theeclipses of the moons of Jupiter. Hisestimate was 140,000 miles/s (225,308km/s). Many others since have tried tomeasure it more accurately using rotat-ing toothed wheels, rotating mirrors andthe Kerr cell shutter.66. Some species of animals have goodendurance, while others have the ability tomove very quickly, but for only a shortamount of time. Use reference sources tofind two examples of each quality anddescribe how it is helpful to that animal.Answers will vary. Examples of animalswith high endurance to outlast preda-tors or prey include mules, bears, andcoyotes. Animals with the speed toquickly escape predators or captureprey include cheetahs, antelopes anddeer.Cumulative Reviewpage 5467. Convert each of the following time mea-surements to its equivalent in seconds.(Chapter 1)a. 58 ns5.8ϫ10Ϫ8 sb. 0.046 Gs4.6ϫ107 sc. 9270 ms9.27 sd. 12.3 ks1.23ϫ104 s68. State the number of significant digits in thefollowing measurements. (Chapter 1)a. 3218 kg4b. 60.080 kg5c. 801 kg3d. 0.000534 kg369. Using a calculator, Chris obtained the fol-lowing results. Rewrite the answer to eachoperation using the correct number of sig-nificant digits. (Chapter 1)a. 5.32 mm ϩ 2.1 mm ϭ 7.4200000 mm7.4 mmb. 13.597 m ϫ 3.65 m ϭ 49.62905 m249.6 m2c. 83.2 kg Ϫ 12.804 kg ϭ 70.3960000 kg70.4 kg28 Solutions Manual Physics: Principles and ProblemsCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 2 continued
- 33. Physics: Principles and Problems Solutions Manual 29Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.3 Accelerated MotionCHAPTERPractice Problems3.1 Accelerationpages 57–64page 611. A dog runs into a room and sees a cat at theother end of the room. The dog instantlystops running but slides along the woodfloor until he stops, by slowing down with aconstant acceleration. Sketch a motion dia-gram for this situation, and use the velocityvectors to find the acceleration vector.2. Figure 3-5 is a v-t graph for Steven as hewalks along the midway at the state fair.Sketch the corresponding motion diagram,complete with velocity vectors.s Figure 3-53. Refer to the v-t graph of the toy trainin Figure 3-6 to answer the followingquestions.s Figure 3-6a. When is the train’s speed constant?5.0 to 15.0 sb. During which time interval is the train’sacceleration positive?0.0 to 5.0 sc. When is the train’s acceleration mostnegative?15.0 to 20.0 s4. Refer to Figure 3-6 to find the averageacceleration of the train during the follow-ing time intervals.a. 0.0 s to 5.0 saෆϭϭϭ 2.0 m/s2b. 15.0 s to 20.0 saෆϭϭϭ Ϫ1.2 m/s2c. 0.0 s to 40.0 saෆϭv2 Ϫ v1ᎏt2 Ϫ t14.0 m/s Ϫ 10.0 m/sᎏᎏᎏ20.0 s Ϫ 15.0 sv2 Ϫ v1ᎏt2 Ϫ t110.0 m/s Ϫ 0.0 m/sᎏᎏᎏ5.0 s Ϫ 0.0 sv2 Ϫ v1ᎏt2 Ϫ t130.020.010.0 40.00.06.04.02.012.010.08.0Velocity(m/s)Time (s)Time (s) 0 1 2 3 4 5678 109Velocity(m/s)Time (s)5 6 7 8 943210 10StopStart1v12v23v3TimeintervalVelocityPositionv2؊v1a
- 34. ϭϭ 0.0 m/s25. Plot a v-t graph representing the followingmotion. An elevator starts at rest from theground floor of a three-story shoppingmall. It accelerates upward for 2.0 s at arate of 0.5 m/s2, continues up at a con-stant velocity of 1.0 m/s for 12.0 s, andthen experiences a constant downwardacceleration of 0.25 m/s2 for 4.0 s as itreaches the third floor.page 646. A race car’s velocity increases from 4.0 m/sto 36 m/s over a 4.0-s time interval. What isits average acceleration?aෆϭ ᎏ⌬⌬vtᎏ ϭ ϭ 8.0 m/s27. The race car in the previous problem slowsfrom 36 m/s to 15 m/s over 3.0 s. What isits average acceleration?aෆϭ ᎏ⌬⌬vtᎏ ϭ ᎏ15 m/s3.Ϫ0 s36 m/sᎏ ϭ Ϫ7.0 m/s28. A car is coasting backwards downhill at aspeed of 3.0 m/s when the driver gets theengine started. After 2.5 s, the car is movinguphill at 4.5 m/s. If uphill is chosen as thepositive direction, what is the car’s averageacceleration?aෆϭ ᎏ⌬⌬vtᎏ ϭ ϭ 3.0 m/s29. A bus is moving at 25 m/s when the driversteps on the brakes and brings the bus to astop in 3.0 s.a. What is the average acceleration of thebus while braking?aෆϭ ᎏ⌬⌬vtᎏϭ ϭ Ϫ8.3 m/s2b. If the bus took twice as long to stop,how would the acceleration comparewith what you found in part a?half as great (Ϫ4.2 m/s2)10. Rohith has been jogging to the bus stop for2.0 min at 3.5 m/s when he looks at hiswatch and sees that he has plenty of timebefore the bus arrives. Over the next 10.0 s,he slows his pace to a leisurely 0.75 m/s.What was his average acceleration duringthis 10.0 s?aෆϭ ᎏ⌬⌬vtᎏϭϭ Ϫ0.28 m/s211. If the rate of continental drift were toabruptly slow from 1.0 cm/yr to 0.5 cm/yrover the time interval of a year, what wouldbe the average acceleration?aෆϭ ᎏ⌬⌬vtᎏ ϭϭ Ϫ0.5 cm/yr2Section Review3.1 Accelerationpages 57–64page 6412. Velocity-Time Graph What informationcan you obtain from a velocity-time graph?The velocity at any time, the time atwhich the object had a particularvelocity, the sign of the velocity, and thedisplacement.13. Position-Time and Velocity-Time GraphsTwo joggers run at a constant velocity of7.5 m/s toward the east. At time t ϭ 0, one0.5 cm/yr Ϫ 1.0 cm/yrᎏᎏᎏ1.0 yr0.75 m/s Ϫ 3.5 m/sᎏᎏᎏ10.0 s0.0 m/s Ϫ 25 m/sᎏᎏᎏ3.0 s4.5 m/s Ϫ (Ϫ3.0 m/s)ᎏᎏᎏ2.5 s36 m/s Ϫ 4.0 m/sᎏᎏᎏ4.0 sVelocity(m/s)1.0Time (s)15.05.00.0 10.0 20.00.0 m/s Ϫ 0.0 m/sᎏᎏᎏ40.0 s Ϫ 0.0 s30 Solutions Manual Physics: Principles and ProblemsCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 3 continued
- 35. Physics: Principles and Problems Solutions Manual 31Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.is 15 m east of the origin and the other is15 m west.a. What would be the difference(s) in theposition-time graphs of their motion?Both lines would have the sameslope, but they would rise from thed-axis at different points, ϩ15 m,and Ϫ15 m.b. What would be the difference(s) in theirvelocity-time graphs?Their velocity-time graphs would beidentical.14. Velocity Explain how you would use avelocity-time graph to find the time atwhich an object had a specified velocity.Draw or imagine a horizontal line at thespecified velocity. Find the point wherethe graph intersects this line. Drop aline straight down to the t-axis. Thiswould be the required time.15. Velocity-Time Graph Sketch a velocity-timegraph for a car that goes east at 25 m/s for100 s, then west at 25 m/s for another 100 s.16. Average Velocity and Average AccelerationA canoeist paddles upstream at 2 m/s andthen turns around and floats downstream at4 m/s. The turnaround time is 8 s.a. What is the average velocity of the canoe?Choose a coordinate system withthe positive direction upstream.vෆϭϭϭ Ϫ1 m/sb. What is the average acceleration of thecanoe?aෆϭ ᎏ⌬⌬vtᎏϭ ᎏvf⌬Ϫtviᎏϭϭ 0.8 m/s217. Critical Thinking A police officer clockeda driver going 32 km/h over the speed limitjust as the driver passed a slower car. Bothdrivers were issued speeding tickets. Thejudge agreed with the officer that both wereguilty. The judgement was issued based onthe assumption that the cars must havebeen going the same speed because theywere observed next to each other. Are thejudge and the police officer correct? Explainwith a sketch, a motion diagram, and aposition-time graph.No, they had the same position, notvelocity. To have the same velocity, theywould have had to have the same rela-tive position for a length of time.(Ϫ4 m/s) Ϫ (2 m/s)ᎏᎏᎏ8 s2 m/s ϩ (Ϫ4 m/s)ᎏᎏᎏ2vi ϩ vfᎏ225Velocity(m/s)Ϫ25200Time (s)100Chapter 3 continued
- 36. 32 Solutions Manual Physics: Principles and ProblemsCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 3 continuedPractice Problems3.2 Motion with Constant Accelerationpages 65–71page 6518. A golf ball rolls up a hill toward a miniature-golf hole. Assume that thedirection toward the hole is positive.a. If the golf ball starts with a speed of 2.0 m/s and slows at a constant rate of0.50 m/s2, what is its velocity after 2.0 s?vf ϭ vi ϩ atϭ 2.0 m/s ϩ (Ϫ0.50 m/s2)(2.0 s)ϭ 1.0 m/sb. What is the golf ball’s velocity if the constant acceleration continues for 6.0 s?vf ϭ vi ϩ atϭ 2.0 m/s ϩ (Ϫ0.50 m/s2)(6.0 s)ϭ Ϫ1.0 m/sc. Describe the motion of the golf ball in words and with a motion diagram.The ball’s velocity simply decreased in the first case. In the secondcase, the ball slowed to a stop and then began rolling back down thehill.19. A bus that is traveling at 30.0 km/h speeds up at a constant rate of 3.5 m/s2.What velocity does it reach 6.8 s later?vf ϭ vi ϩ atϭ 30.0 km/h ϩ (3.5 m/s2)(6.8 s)ᎏ1100k0mmᎏᎏ36100hsᎏϭ 120 km/hTime interval 1 2 3645VelocityPositionVelocityTime intervalϩdTimePositionPassingpositionPosition-Time Grapht1 t2 t3 t401234t0 t4t3t2t1t0 t4t3t2t1Motion diagramFaster carSlower carSketch
- 37. Physics: Principles and Problems Solutions Manual 33Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.20. If a car accelerates from rest at a constant5.5 m/s2, how long will it take for the car toreach a velocity of 28 m/s?vf ϭ vi ϩ atso t ϭ ᎏvf Ϫaviᎏϭϭ 5.1 s21. A car slows from 22 m/s to 3.0 m/s at aconstant rate of 2.1 m/s2. How manyseconds are required before the car istraveling at 3.0 m/s?vf ϭ vi ϩ atso t ϭ ᎏvf Ϫaviᎏϭϭ 9.0 spage 6722. Use Figure 3-11 to determine the velocityof an airplane that is speeding up at each ofthe following times.s Figure 3-11Graph B represents constant speed. Sograph A should be used for the follow-ing calculations.a. 1.0 sAt 1.0 s, v ϭ 74 m/sb. 2.0 sAt 2.0 s, v ϭ 78 m/sc. 2.5 sAt 2.5 s, v ϭ 80 m/s23. Use dimensional analysis to convert anairplane’s speed of 75 m/s to km/h.(75 m/s)ᎏ36100hsᎏᎏ1100k0mmᎏ ϭ 2.7ϫ102 km/h24. A position-time graph for a pony runningin a field is shown in Figure 3-12. Drawthe corresponding velocity-time graph usingthe same time scale.s Figure 3-1225. A car is driven at a constant velocity of25 m/s for 10.0 min. The car runs out of gasand the driver walks in the same directionat 1.5 m/s for 20.0 min to the nearest gasstation. The driver takes 2.0 min to fill agasoline can, then walks back to the car at1.2 m/s and eventually drives home at25 m/s in the direction opposite that ofthe original trip.a. Draw a v-t graph using seconds as yourtime unit. Calculate the distance the dri-ver walked to the gas station to find thetime it took him to walk back to the car.Time (s)Stops andturns aroundPosition-time graphSlowsdownSpeedsupSpeedsupϩxϩyDisplacement(m)Velocity(m/s)Displacement(m)Time (s) ϩxϩy0.0 3.01.0 2.082807876747270Velocity(m/s)Time (s)3.0 m/s Ϫ 22 m/sᎏᎏᎏϪ2.1 m/s228 m/s Ϫ 0.0 m/sᎏᎏᎏ5.5 m/s2Chapter 3 continued
- 38. distance the driver walked to thegas station:d ϭ vtϭ (1.5 m/s)(20.0 min)(60 s/min)ϭ 1800 mϭ 1.8 kmtime to walk back to the car:t ϭ ᎏdvᎏ ϭ ᎏ118.200mm/sᎏ ϭ 1500 s ϭ 25 minb. Draw a position-time graph for thesituation using the areas under thevelocity-time graph.page 6926. A skateboarder is moving at a constantvelocity of 1.75 m/s when she starts up anincline that causes her to slow down with aconstant acceleration of Ϫ0.20 m/s2. Howmuch time passes from when she begins toslow down until she begins to move backdown the incline?vf ϭ vi ϩ att ϭ ᎏvf Ϫaviᎏ ϭ ϭ 8.8 s27. A race car travels on a racetrack at 44 m/sand slows at a constant rate to a velocityof 22 m/s over 11 s. How far does it moveduring this time?vෆϭ ᎏ⌬2vᎏ ϭ ᎏ(vf Ϫ2vi)ᎏ⌬d ϭ vෆ⌬tϭ ᎏ(vf Ϫ2vi)⌬tᎏϭϭ Ϫ1.2ϫ102 m28. A car accelerates at a constant rate from15 m/s to 25 m/s while it travels a distanceof 125 m. How long does it take to achievethis speed?vෆϭ ᎏ⌬2vᎏ ϭ ᎏ(vf Ϫ2vi)ᎏ⌬d ϭ vෆ⌬tϭ ᎏ(vf Ϫ2vi)⌬tᎏ⌬t ϭϭϭ 25 s29. A bike rider pedals with constant accelera-tion to reach a velocity of 7.5 m/s over atime of 4.5 s. During the period of accelera-tion, the bike’s displacement is 19 m. Whatwas the initial velocity of the bike?vෆϭ ᎏ⌬2vᎏ ϭ ᎏ(vf Ϫ2vi)ᎏ⌬d ϭ vෆ⌬t ϭ ᎏ(vf Ϫ2vi)⌬tᎏso vi ϭ ᎏ2⌬⌬tdᎏ Ϫ vfϭ ᎏ4.5(s2)Ϫ(197.m5)m/sᎏϭ 0.94 m/s(2)(125 m)ᎏᎏ25 m/s Ϫ 15 m/s2⌬dᎏ(vf Ϫ vi)(22 m/s Ϫ 44 m/s)(11 s)ᎏᎏᎏ20.0 m/s Ϫ 1.75 m/sᎏᎏᎏϪ0.20 m/s20500010,00015,00020,000Position(m)1000 2000 3000Time (s)4000 5000Velocity(m/s)Time (s)؊5؊10؊15؊20؊250515202535004000300025002000150010005001034 Solutions Manual Physics: Principles and ProblemsCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 3 continued
- 39. Physics: Principles and Problems Solutions Manual 35Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.page 7130. A man runs at a velocity of 4.5 m/s for 15.0 min. When going up an increasinglysteep hill, he slows down at a constant rate of 0.05 m/s2 for 90.0 s and comes toa stop. How far did he run?d ϭ v1t1 ϩ ᎏ12ᎏ(v2f ϩ v2i)t2ϭ (4.5 m/s)(15.0 min)(60 s/min) ϩ ᎏ12ᎏ(0.0 m/s ϩ 4.5 m/s)(90.0 s)ϭ 4.3ϫ103 m31. Sekazi is learning to ride a bike without training wheels. His father pushes himwith a constant acceleration of 0.50 m/s2 for 6.0 s, and then Sekazi continues at3.0 m/s for another 6.0 s before falling. What is Sekazi’s displacement? Solve thisproblem by constructing a velocity-time graph for Sekazi’s motion and comput-ing the area underneath the graphed line.Part 1: Constant acceleration:d1 ϭ ᎏ12ᎏ(3.0 m/s)(6.0 s)ϭ 9.0 mPart 2: Constant velocity:d2 ϭ (3.0 m/s)(12.0 s Ϫ 6.0 s)ϭ 18 mThus d ϭ d1 ϩ d2 ϭ 9.0 m ϩ 18 m ϭ 27 m32. You start your bicycle ride at the top of a hill. You coast down the hill at a con-stant acceleration of 2.00 m/s2. When you get to the bottom of the hill, you aremoving at 18.0 m/s, and you pedal to maintain that speed. If you continue at thisspeed for 1.00 min, how far will you have gone from the time you left the hilltop?Part 1: Constant acceleration:vf2 ϭ vi2 ϩ 2a(df Ϫ di) and di ϭ 0.00 mso df ϭ ᎏvf22Ϫavi2ᎏsince vi ϭ 0.00 m/sdf ϭ ᎏv2fa2ᎏϭ ᎏ(2()1(82..000mm/s/)s22)ᎏϭ 81.0 mVelocity(m/s)3.0Time (s)6.0 12.01 2Chapter 3 continued
- 40. Part 2: Constant velocity:d2 ϭ vt ϭ (18.0 m/s)(60.0 s) ϭ 1.08ϫ103 mThus d ϭ d1 ϩ d2ϭ 81.0 m ϩ 1.08ϫ103 mϭ 1.16ϫ103 m33. Sunee is training for an upcoming 5.0-km race. She starts out her trainingrun by moving at a constant pace of 4.3 m/s for 19 min. Then she acceleratesat a constant rate until she crosses the finish line, 19.4 s later. What is heracceleration during the last portion of the training run?Part 1: Constant velocity:d ϭ vtϭ (4.3 m/s)(19 min)(60 s/min)ϭ 4902 mPart 2: Constant acceleration:df ϭ di ϩ vit ϩ ᎏ12ᎏat2a ϭ ϭϭ 0.077 m/s2Section Review3.2 Motion with Constant Accelerationpages 65–71page 7134. Acceleration A woman driving at a speed of 23 m/s sees a deer on the roadahead and applies the brakes when she is 210 m from the deer. If the deer doesnot move and the car stops right before it hits the deer, what is the accelerationprovided by the car’s brakes?vf2 ϭ vi2 ϩ 2a(df Ϫ di)a ϭ ᎏ2v(fd2fϪϪvdi2i)ᎏϭϭ Ϫ1.3 m/s235. Displacement If you were given initial and final velocities and the constantacceleration of an object, and you were asked to find the displacement, whatequation would you use?vf2 ϭ vi2 ϩ 2adf0.0 m/s Ϫ (23 m/s)2ᎏᎏᎏ(2)(210 m)(2)(5.0ϫ103 m Ϫ 4902 m Ϫ (4.3 m/s)(19.4 s))ᎏᎏᎏᎏᎏᎏ(19.4 s)22(df Ϫ di Ϫ vit)ᎏᎏt236 Solutions Manual Physics: Principles and ProblemsCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 3 continued
- 41. Physics: Principles and Problems Solutions Manual 37Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.36. Distance An in-line skater first accelerates from 0.0 m/s to 5.0 m/s in 4.5 s, thencontinues at this constant speed for another 4.5 s. What is the total distance trav-eled by the in-line skater?Acceleratingdf ϭ vෆtf ϭ ᎏvi ϩ2vfᎏ(tf)ϭ (4.5 s)ϭ 11.25 mConstant speeddf ϭ vftfϭ (5.0 m/s)(4.5 s)ϭ 22.5 mtotal distance ϭ 11.25 m ϩ 22.5 mϭ 34 m37. Final Velocity A plane travels a distance of 5.0ϫ102 m while being accelerateduniformly from rest at the rate of 5.0 m/s2. What final velocity does it attain?vf2 ϭ vf2 ϩ 2a(df Ϫ di) and di ϭ 0, sovf2 ϭ vf2 ϩ 2adfvf ϭ ͙(0.0 mෆ/s)2 ϩෆ 2(5.0ෆm/s2)(ෆ5.0ϫ1ෆ02 m)ෆϭ 71 m/s38. Final Velocity An airplane accelerated uniformly from rest at the rate of 5.0m/s2 for 14 s. What final velocity did it attain?vf ϭ vi ϩ atfϭ 0 ϩ (5.0 m/s2)(14 s) ϭ 7.0ϫ101 m/s39. Distance An airplane starts from rest and accelerates at a constant 3.00 m/s2 for30.0 s before leaving the ground.a. How far did it move?df ϭ vitf ϩ ᎏ12ᎏatf2ϭ (0.0 m/s)(30.0 s)2 ϩ ᎏ12ᎏ(3.00 m/s2)(30.0 s)2ϭ 1.35ϫ103 mb. How fast was the airplane going when it took off?vf ϭ vi ϩ atfϭ 0.0 m/s ϩ (3.00 m/s2)(30.0 s)ϭ 90.0 m/s0.0 m/s ϩ 5.0 m/sᎏᎏᎏ2Chapter 3 continued
- 42. 40. Graphs A sprinter walks up to the starting blocks at a constant speed andpositions herself for the start of the race. She waits until she hears the startingpistol go off, and then accelerates rapidly until she attains a constant velocity.She maintains this velocity until she crosses the finish line, and then she slowsdown to a walk, taking more time to slow down than she did to speed up atthe beginning of the race. Sketch a velocity-time and a position-time graph torepresent her motion. Draw them one above the other on the same time scale.Indicate on your p-t graph where the starting blocks and finish line are.41. Critical Thinking Describe how you could calculate the acceleration of an auto-mobile. Specify the measuring instruments and the procedures that you would use.One person reads a stopwatch and calls out time intervals. Anotherperson reads the speedometer at each time and records it. Plot speedversus time and find the slope.Practice Problems3.3 Free Fallpages 72–75page 7442. A construction worker accidentally drops a brick from a high scaffold.a. What is the velocity of the brick after 4.0 s?Say upward is the positive direction.vf ϭ vi ϩ at, a ϭ Ϫg ϭ Ϫ9.80 m/s2vf ϭ 0.0 m/s ϩ (Ϫ9.80 m/s2)(4.0 s)ϭ Ϫ39 m/s when the upward direction is positiveb. How far does the brick fall during this time?d ϭ vit ϩ ᎏ12ᎏat2ϭ 0 ϩ ᎏ12ᎏ(Ϫ9.80 m/s2)(4.0 s)2ϭ Ϫ78 mThe brick falls 78 m.43. Suppose for the previous problem you choose your coordinate system so thatthe opposite direction is positive.StartingblocksFinishlinePositionTimeTimeVelocity38 Solutions Manual Physics: Principles and ProblemsCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 3 continued
- 43. Physics: Principles and Problems Solutions Manual 39Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.a. What is the brick’s velocity after 4.0 s?Now the positive direction is downward.vf ϭ vi ϩ at, a ϭ g ϭ 9.80 m/s2vf ϭ 0.0 m/s ϩ (9.80 m/s2)(4.0 s)ϭ ϩ39 m/s when the downward direction is positiveb. How far does the brick fall during this time?d ϭ vit ϩ ᎏ12ᎏat2, a ϭ g ϭ 9.80 m/s2ϭ (0.0 m/s)(4.0 s) ϩᎏ12ᎏ(9.80 m/s2)(4.0 s)2ϭ ϩ78 mThe brick still falls 78 m.44. A student drops a ball from a window 3.5 m above the sidewalk. How fast is itmoving when it hits the sidewalk?vf2 ϭ vi2 ϩ 2ad, a ϭ g and vi ϭ 0so vf ϭ ͙2gdෆϭ ͙(2)(9.8ෆ0 m/sෆ2)(3.5ෆm)ෆϭ 8.3 m/s45. A tennis ball is thrown straight up with an initial speed of 22.5 m/s. It is caughtat the same distance above the ground.a. How high does the ball rise?a ϭ Ϫg, and at the maximum height, vf ϭ 0vf2 ϭ vi2 ϩ 2ad becomesvi2 ϭ 2gdd ϭ ᎏv2ig2ᎏ ϭ ᎏ(2()2(29..580mm/s/)s22)ᎏ ϭ 25.8 mb. How long does the ball remain in the air? Hint: The time it takes the ball to riseequals the time it takes to fall.Calculate time to rise using vf ϭ vi ϩ at, with a ϭ Ϫg and vf ϭ 0t ϭ ᎏvgiᎏ ϭ ᎏ92.28.05mm//ss2ᎏ ϭ 2.30 sThe time to fall equals the time to rise, so the time to remain in the air istair ϭ 2trise ϭ (2)(2.30 s) ϭ 4.60 s46. You decide to flip a coin to determine whether to do your physics or Englishhomework first. The coin is flipped straight up.a. If the coin reaches a high point of 0.25 m above where you released it, whatwas its initial speed?Chapter 3 continued
- 44. vf2 ϭ vi2 ϩ 2a⌬dvi ϭ ͙vf2 ϩෆ2g⌬dෆ where a ϭ Ϫgand vf ϭ 0 at the height of the toss, sovi ϭ ͙(0.0 mෆ/s)2 ϩෆ (2)(9.ෆ80 m/ෆs2)(0.2ෆ5 m)ෆϭ 2.2 m/sb. If you catch it at the same height as you released it, how much time did itspend in the air?vf ϭ vi ϩ at where a ϭ Ϫgvi ϭ 2.2 m/s andvf ϭ Ϫ2.2 m/st ϭ ᎏvfϪϪgviᎏϭϭ 0.45 sSection Review3.3 Free Fallpages 72–75page 7547. Maximum Height and Flight Time Acceleration due to gravity on Mars is aboutone-third that on Earth. Suppose you throw a ball upward with the same velocityon Mars as on Earth.a. How would the ball’s maximum height compare to that on Earth?At maximum height, vf ϭ 0,so df ϭ ᎏv2ig2ᎏ, or three times higher.b. How would its flight time compare?Time is found from df ϭ ᎏ12ᎏgtf2, ortf ϭ Ίᎏ2gdfᎏ. Distance is multiplied by 3 and g is divided by 3,so the flight time would be three times as long.48. Velocity and Acceleration Suppose you throw a ball straight up into the air.Describe the changes in the velocity of the ball. Describe the changes in theacceleration of the ball.Ϫ2.2 m/s Ϫ 2.2 m/sᎏᎏᎏϪ9.80 m/s240 Solutions Manual Physics: Principles and ProblemsCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 3 continued
- 45. Physics: Principles and Problems Solutions Manual 41Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Velocity is reduced at a constant rate as the ball travels upward. At itshighest point, velocity is zero. As the ball begins to drop, the velocitybegins to increase in the negative direction until it reaches the heightfrom which it was initially released. At that point, the ball has the samespeed it had upon release. The acceleration is constant throughout theball’s flight.49. Final Velocity Your sister drops your house keys down to you from the secondfloor window. If you catch them 4.3 m from where your sister dropped them,what is the velocity of the keys when you catch them?Upward is positivev2 ϭ vi2 ϩ 2a⌬d where a ϭ Ϫgv ϭ ͙vi2 Ϫෆ2g⌬dෆϭ ͙(0.0 mෆ/s)2 Ϫෆ (2)(9.ෆ80 m/ෆs2)(Ϫ4ෆ.3 m)ෆϭ 9.2 m/s50. Initial Velocity A student trying out for the football team kicks the footballstraight up in the air. The ball hits him on the way back down. If it took 3.0 sfrom the time when the student punted the ball until he gets hit by the ball,what was the football’s initial velocity?Choose a coordinate system with up as the positive direction and theorigin at the punter. Choose the initial time at the punt and the final timeat the top of the football’s flight.vf ϭ vi ϩ atf where a ϭ Ϫgvi ϭ vf ϩ gtfϭ 0.0 m/s ϩ (9.80 m/s2)(1.5 s)ϭ 15 m/s51. Maximum Height When the student in the previous problem kicked the foot-ball, approximately how high did the football travel?vf2 ϭ vi2 ϩ 2a(⌬d) where a ϭ Ϫg⌬d ϭ ᎏvf2ϪϪ2gvi2ᎏϭϭ 11 m52. Critical Thinking When a ball is thrown vertically upward, it continues upwarduntil it reaches a certain position, and then it falls downward. At that highestpoint, its velocity is instantaneously zero. Is the ball accelerating at the highestpoint? Devise an experiment to prove or disprove your answer.The ball is accelerating; its velocity is changing. Take a strobe photo tomeasure its position. From photos, calculate the ball’s velocity.(0.0 m/s)2 Ϫ (15 m/s)2ᎏᎏᎏ(Ϫ2)(9.80 m/s2)Chapter 3 continued
- 46. Chapter AssessmentConcept Mappingpage 8053. Complete the following concept map usingthe following symbols or terms: d, velocity,m/s2, v, m, acceleration.Mastering Conceptspage 8054. How are velocity and acceleration related?(3.1)Acceleration is the change in velocitydivided by the time interval in which itoccurs: it is the rate of change ofvelocity.55. Give an example of each of the following.(3.1)a. an object that is slowing down, but hasa positive accelerationif forward is the positive direction, acar moving backward at decreasingspeedb. an object that is speeding up, but has anegative accelerationin the same coordinate system, a carmoving backward at increasingspeed56. Figure 3-16 shows the velocity-time graphfor an automobile on a test track. Describehow the velocity changes with time. (3.1)s Figure 3-16The car starts from rest and increasesits speed. As the car’s speed increases,the driver shifts gears.57. What does the slope of the tangent to thecurve on a velocity-time graph measure?(3.1)instantaneous acceleration58. Can a car traveling on an interstate highwayhave a negative velocity and a positive accel-eration at the same time? Explain. Can thecar’s velocity change signs while it is travelingwith constant acceleration? Explain. (3.1)Yes, a car’s velocity is positive or nega-tive with respect to its direction ofmotion from some point of reference.One direction of motion is defined aspositive, and velocities in that directionare considered positive. The oppositedirection of motion is considered nega-tive; all velocities in that direction arenegative. An object undergoing positiveacceleration is either increasing itsvelocity in the positive direction orreducing its velocity in the negativedirection. A car’s velocity can changesigns when experiencing constantacceleration. For example, it can betraveling right, while the acceleration isto the left. The car slows down, stops,and then starts accelerating to the left.59. Can the velocity of an object change whenits acceleration is constant? If so, give anexample. If not, explain. (3.1)Yes, the velocity of an object canchange when its acceleration is con-stant. Example: dropping a book. The5 10 15 20 25 30 35051015202530Velocity(m/s)Time (s)velocityposition accelerationv adm/s m/s2mQuantities of motion42 Solutions Manual Physics: Principles and ProblemsCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 3 continued
- 47. Physics: Principles and Problems Solutions Manual 43Copyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.longer it drops, the faster it goes, butthe acceleration is constant at g.60. If an object’s velocity-time graph is a straightline parallel to the t-axis, what can you con-clude about the object’s acceleration? (3.1)When the velocity-time graph is a lineparallel to the t-axis, the acceleration iszero.61. What quantity is represented by the areaunder a velocity-time graph? (3.2)the change in displacement62. Write a summary of the equations forposition, velocity, and time for an objectexperiencing motion with uniformacceleration. (3.2)tf ϭ ᎏ(vf Ϫavi)ᎏvf ϭ vi ϩ atfvෆϭ ᎏ⌬2vᎏ ϭ ᎏvf Ϫ2viᎏ⌬d ϭ vෆ⌬tϭ ᎏvf Ϫ2viᎏ⌬tassuming ti ϭ 0, then⌬t ϭ tf⌬d ϭ ᎏvf Ϫ2viᎏtf63. Explain why an aluminum ball and a steelball of similar size and shape, droppedfrom the same height, reach the ground atthe same time. (3.3)All objects accelerate toward theground at the same rate.64. Give some examples of falling objects forwhich air resistance cannot be ignored.(3.3)Student answers will vary. Someexamples are sheets of paper,parachutes, leaves, and feathers.65. Give some examples of falling objects forwhich air resistance can be ignored. (3.3)Student answers will vary. Some exam-ples are a steel ball, a rock, and a per-son falling through small distances.Applying Conceptspages 80–8166. Does a car that is slowing down always havea negative acceleration? Explain.No, if the positive axis points in thedirection opposite the velocity, theacceleration will be positive.67. Croquet A croquet ball, after being hit bya mallet, slows down and stops. Do thevelocity and acceleration of the ball havethe same signs?No, they have opposite signs.68. If an object has zero acceleration, does itmean its velocity is zero? Give an example.No, a ϭ 0 when velocity is constant.69. If an object has zero velocity at someinstant, is its acceleration zero? Give anexample.No, a ball rolling uphill has zero velocityat the instant it changes direction, butits acceleration is nonzero.70. If you were given a table of velocities of anobject at various times, how would you findout whether the acceleration was constant?Draw a velocity-time graph and seewhether the curve is a straight line orcalculate accelerations using aෆϭ ᎏ⌬⌬vtᎏand compare the answers to see if theyare the same.71. The three notches in the graph inFigure 3-16 occur where the driver changedgears. Describe the changes in velocity andacceleration of the car while in first gear. Isthe acceleration just before a gear changelarger or smaller than the acceleration justafter the change? Explain your answer.Chapter 3 continued
- 48. Velocity increases rapidly at first, then more slowly. Acceleration is greatestat the beginning but is reduced as velocity increases. Eventually, it is nec-essary for the driver to shift into second gear.The acceleration is smallerjust before the gear change because the slope is less at that point on thegraph. Once the driver shifts and the gears engage, acceleration and theslope of the curve increase.72. Use the graph in Figure 3-16 and determine the time interval during which theacceleration is largest and the time interval during which the acceleration issmallest.The acceleration is largest during an interval starting at t ϭ 0 and lastingabout ᎏ12ᎏ s. It is smallest beyond 33 s.73. Explain how you would walk to produce each of the position-time graphs inFigure 3-17.s Figure 3-17Walk in the positive direction at a constant speed. Walk in the positivedirection at an increasing speed for a short time; keep walking at amoderate speed for twice that amount of time; slow down over a shorttime and stop; remain stopped; and turn around and repeat the procedureuntil the original position is reached.74. Draw a velocity-time graph for each of the graphs in Figure 3-18.s Figure 3-18TimeVelocityVelocityTimeVelocityTimeDisplacementDisplacementDisplacementTime Time TimeDisplacementDisplacementTime TimeA BCD EFG H44 Solutions Manual Physics: Principles and ProblemsCopyright©Glencoe/McGraw-Hill,adivisionofTheMcGraw-HillCompanies,Inc.Chapter 3 continued

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