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Physics110HJournal GeneralPhysicsI‐Fall2013/Spring2014 USAFADepartmentofPhysics,CorePhysicsPublication Name Instructor Section Physics110ConstantsandEquationsSheet AccelerationduetoGravityatEarth'sSurface UniversalGravitationConstant SpeedofLightinVacuum MassofEarth RadiusofEarth 9.81 m s N m kg 6.67 10 3.00 10 m s 5.97 10 kg 6.37 10 m 1in 2.54cm 1mi 1609m 1ft 0.3048 m 1 mi⁄h 0.447 m/s 1lb 4.448N 0.454kg 1 2 2 1 2 2 ∆ 1 2 1 2 ∙ 1 2 cos / ∙ ∆ ∙ Physics 110H Journal General Physics I Fall 2013/Spring 2014 DepartmentofPhysics UnitedStatesAirForceAcademy i PagereservedforPublisher’sCopyrightinformation ii Physics110HJournal‐2013‐2014 Contents Physics 110 Constants and Equations Sheet ................................................. ii Course Description and Policies .................................................................... v IDEA Problem‐Solving Strategy ...................................................................xiv Learning Objectives ..................................................................................... xv Lesson 1 ........................................................................................................ 1 Lesson 2 ........................................................................................................ 9 Lesson 3 ...................................................................................................... 17 Lesson 4 ...................................................................................................... 23 Lesson 5 ...................................................................................................... 31 Lesson 6 ...................................................................................................... 39 Lesson 7 ...................................................................................................... 45 Lesson 8 ...................................................................................................... 53 Lesson 9 ...................................................................................................... 61 Lesson 10 .................................................................................................... 69 Lesson 11 .................................................................................................... 77 Lesson 12 .................................................................................................... 85 Lesson 13 .................................................................................................... 93 Lesson 14 .................................................................................................... 99 Lesson 15 .................................................................................................. 107 Lesson 16 .................................................................................................. 115 Lesson 17 .................................................................................................. 121 Lesson 18 .................................................................................................. 129 Lesson 19 .................................................................................................. 137 Lesson 20 .................................................................................................. 145 Lesson 21 .................................................................................................. 153 Lesson 22 .................................................................................................. 161 Lesson 23 .................................................................................................. 167 Lesson 24 .................................................................................................. 175 Lesson 25 .................................................................................................. 183 Lesson 26 .................................................................................................. 189 Lesson 27 .................................................................................................. 197 Lesson 28 .................................................................................................. 205 Lesson 29 .................................................................................................. 211 Lesson 30 .................................................................................................. 219 Lesson 31 .................................................................................................. 231 Lesson 32 .................................................................................................. 239 Lesson 33 .................................................................................................. 247 Lesson 34 .................................................................................................. 255 Lesson 35 .................................................................................................. 263 Lesson 36 .................................................................................................. 271 Lesson 37 .................................................................................................. 279 Lesson 38 .................................................................................................. 285 iii Lesson 39 ................................................................................................... 291 Lesson 40 ................................................................................................... 299 Block 4 Review........................................................................................... 307 Appendix A: Lab Report Template ............................................................. xix Appendix B: Significant Figures, Uncertainty and Error Propagation ........ xxi Appendix C: Mathematics Reference .......................................................xxvi Appendix D: Equation Dictionary ............................................................. xxx Appendix E: Rotational Inertias and Astrophysical Data ............................. xl Appendix F: Units and Conversions ............................................................ xli Appendix F: Physical Constants ................................................................. xlii Physics 215 Constants and Equations Sheet ............................................. xliii Physics 110H Course Syllabus.................................................................... xliv iv Physics110HJournal‐2013‐2014 CourseDescriptionandPolicies CourseDescriptionandPolicies Overview TheUSAirForceAcademyoffersabroadgeneralphysicscurriculumwithfourspecializedphysics majoroptions:Astronomy,LaserPhysics/Optics,SpacePhysics,andAppliedPhysicstopicssuchas nuclearphysics.Eachphysicsmajoroptionrequires42credithoursofphysicsandmathematics coursesinadditiontocoreacademicrequirements,includingafaculty‐directedcapstonephysics researchproject.AftergraduationphysicsmajorssucceedinawidevarietyofoperationalAir Forceassignmentsorcompleteanadvancedacademicdegreeatgraduateschool. TheUSAFADepartmentofPhysicsofferstwocorecourses,eachwithanhonorsoption.PHYSICS 110/110H(GeneralPhysicsI)isthefirstinatwo‐partseriesofintroductorycalculus‐based physicscourses,whichincludesNewtonianmechanicsandconservationofenergyandmomentum, andisnormallytakenduringthefourth‐classyear.PHYSICS215/215H(GeneralPhysicsII)isthe secondintheseriesofintroductorycalculus‐basedphysicscourseswhichemphasizes electromagnetismandcircuits,andisnormallytakenduringthethird‐classyear. HonorsphysicscoursesaredesignedtobetteraddresstheneedsoftechnicalmajorsattheUSAir ForceAcademyandmeettheneedsofanincreasinglytechnicalAirForce.Cadetsdemonstrating aptitudeincalculusorhavingpreviouslytakenintroductoryphysicscoursesmaybeplacedin honorsphysics.Honorsphysicsincludesenhancedcoverageoftheconceptscoveredintheregular course,withmoreintegrateduseofcalculus,introductiontodifferentialequationsandrigorous dataanalysistechniques. CorePhysicsCourseDescriptions Physics110,GeneralPhysicsI,isacalculus‐basedintroductiontoclassicalphysics,withemphasis oncontemporaryapplications,inwhichyouwilllearntheconceptsandproblem‐solvingskills requiredtounderstandandanalyzethemotionofobjects.Thefirsthalfofthecourseisasolid foundationinkinematicsandNewton’slawsofmotion.Youwillthenbeintroducedtoseveral conservationprinciples,whichareelegantwaysofvisualizingandunderstandingthemotionof objects.Theseincludetheconservationofenergy,momentumandangularmomentum.Alongthe way,youwillbeintroducedtoafewtopicsthatareimportanttoscientistsandengineers,including orbitalmotion,rotationalmotionandoscillations.Labsandsimulationshighlightkeyphysics concepts. Physics215,GeneralPhysicsII,isanintroductorycalculus‐basedphysicscoursewithanemphasis oncontemporaryapplications.Thecoursebeginswithafoundationinthebasicpropertiesof electricchargeandworksuptodealingwiththesophisticatedconceptoftheelectricfield.Then, simplecircuitsareanalyzed,relatingtheprinciplesofpotentialenergyandelectricpotentialtothe electricfield.Next,magneticfieldsandelectromagneticinductionarestudied,culminatingina completedescriptionofelectromagneticfields.Afterthat,lightwaves,thebendingoflightandthe v CourseDescriptionandPolicies Physics110HJournal‐2013‐2014 interferencecausedbythewavenatureoflightarestudied.Finally,modernphysicsisintroduced bystudyingquantizationandquantumuncertainty.Thiscourseutilizesvectorsandcalculusin problemsolvingandincludesin‐classlaboratoriestohighlightkeyconcepts. HonorsCorePhysicsCourses Asa“techie”majorinthePhysicsHonorsCoursesequence,youcanexpectanumberofbenefits comparedtotakingthestandardintroductorycourse.Perhapsthemostsignificantbenefitis learningphysicsmoreefficientlyandmoreenjoyablyamidstudentsofsimilaracademicabilities. Youwillalsoseeenhancedcoverageoftopicsthatareimportantforscientistsandengineers, including amoreintegrateduseofcalculusthroughoutthecourse anintroductiontotheuseofdifferentialequationsinsimpleharmonicmotion enhanceddataanalysistechniques somewhatmoreemphasisongraphicalandnumericaltechniques Theemphasisonthesetopicswillmakeyourphysicsexperiencecomparabletowhatyourpeers wouldreceiveatacivilianuniversitywhentakingaphysicscourseforscientistsandengineers. Toallaypossibleconcernsaboutyourgrade,DFPwillensurethatyouarenotpenalizedfortaking PhysicsHonorsinplaceofstandardPhysicsCourse.ThegradedreviewsforPhysics“regular”and PhysicsHonorswillincludealargepercentageofcommonquestionstoallowagoodstatistical comparisonofthetwocourses,sothatyourfinalgradewillnotdependonwhichversionofthe courseyoutake.Wehavealsobalancedtheoverallworkloadsothatstudentsineithercourse,on average,havethesamenumberofhomeworkproblems,journalquestions,etc.,tocomplete. WhatarethesimilaritiesanddifferencesbetweenPhysics“regular”andPhysicsHonors? Bothcourseswillfollowthesamebasicsyllabusandusethesamecoursepolicies.Withfew exceptions,studentsinbothcourseswillstudythesametextbookexamplesandanswerthesame journalandpreflightquestions.Some(about35%)ofthehomeworkproblemsaredifferentto makebetteruseofcalculusandothermathskillsortohighlightdifferentphysicsconcepts.About halfofthescheduledlabsarecommonbetweenthetwocourses.Theotherlabswillbemoreopen‐ endedforHonorsthanforthestandardcourseandwillrequireashort1‐2pagewrittenreport.To balancetheworkload,Honorsstudentswillbeexcusedfromthelabquizzesforthesethreelabsas wellasallofthecomputersimulationexercisesinPhysics110.Thegradedreviewswillbevery similar;abouttwo‐thirdsofeachGRwillbequestionsandproblemscommontobothcourses. Finally,classtimewillbeusedabitdifferentlyinHonors,withlesstimedevotedtocoveringthe mostbasicmaterial. CorePhysicsCoursePrerequisites ForastudentenrolledinPhysics110,heorshemusthavecompletedorbeenrolledininMath142. Importantmathconceptsrequired: vi Physics110HJournal‐2013‐2014 CourseDescriptionandPolicies Algebraandtrigonometry Vectoroperationsincludingdotproductandcrossproduct Differentiationofpolynomialsandsimplefunctions Integrationofpolynomialsandsimplefunctions StudentsinPhysics215musthavecompletedPhysics110andMath142. USAFAandCorePhysicsCourseOutcomes Physicscorecourses(Physics110andPhysics215)areaprimarycontributortothedevelopment andassessmentofthefollowingUSAFAoutcomes:quantitativeliteracy,criticalthinkingand principlesofscience,andthescientificmethod.Additionally,thesecoursesaredesignedforyouto: 1. Developadeeper,moreintegratedunderstandingofphysicalconcepts,withafocusonthe conceptsofmotion,Newton’sLaws,energy,momentum,electricity,magnetism,and selectedtopicsinmodernphysics. 2. Applythinkingandproblem‐solvingskillstomakeinformedconclusionsaboutthemeaning ofphysicaldataandinformation. 3. Applyexperimentalskillsandreadingcomprehensiontoinvestigateprinciplesofnature. 4. Cultivatehabitsofthemindconsistentwiththatofaneducated,scientificallyliterate person. CorePhysicsLearningGoals Physics110isdesignedtoenhanceyourcriticalthinkingskillsandyourabilityto: 1. Describethemotionofobjectsusingkinematics 2. InterpretandsolvemotionproblemsusingNewton’sthreelaws 3. Analyzethemotionofobjectsusingconservationofenergy,momentumandangular momentum 4. Developvalidphysics‐basedconclusionsaboutreal‐worldproblemsandapplications ThecourselearninggoalsforPhysics215are: 1. Identifyhowthefundamentalphysicalprinciplesofelectricity,magnetismapplyto conceptualorquantitativeproblems. 2. Solveconceptualorquantitativephysicalproblemsinvolvingelectricity,magnetismand modernphysics. 3. Applyexperimentalskillstoinvestigatethephysicalprinciplesgoverningelectricityand magnetism. 4. Analyzeandexplainthephysicalprinciplesthatapplytotheoperationofelectro‐magnetic systemsandcircuits. vii CourseDescriptionandPolicies Physics110HJournal‐2013‐2014 PhysicsCoreCourseAdministration Position PhysicsDepartmentHead DirectorofCorePrograms Physics110CourseDirector Assistant110CourseDir Physics110HCourseDirector Assistant110HCourseDir Physics215CourseDirector Assistant215CourseDir Physics215HCourseDirector Assistant215HCourseDir YourPhysicsInstructor Name ColKiziah LtColNovotny LtColKayser‐Cook CaptSorensen Dr.deLaHarpe MajBuchanan MajLane Mrs.Lickiss Dr.Kontur LtColAnthonyDills Office 2A33 2A27 2A43 2A101 2A219 2A109 2A153 2A149 2A107 2A25 Phone 333‐3510 333‐9248 333‐0357 333‐9733 333‐9719 333‐7707 333‐3615 333‐3412 333‐4224 333‐3272 RequiredCourseMaterials ThefollowingmaterialsarerequiredforthiscourseandmustbeinyourpossessiononLesson1. Failuretopossessyourpersonalcopyofeachofthefollowingisafailuretomeetcourse requirements.QuestionsmaybedirectedtotheDirectorofCoreProgramsorthePhysics DepartmentHead.Inadditiontothefirstdayofclass,youarerequiredtobringthefollowingto eachclassperiod:yourtextbookandyourentireJournal(ina3‐ringbinder). Physics110andPhysics110Honors: TEXTBOOK.Wolfson,Richard,EssentialUniversityPhysics,2nded.,Vol1,SanFrancisco: PearsonEducation,Inc.,2012. JOURNAL.ThePhysics110Journalcontainscourseguidance,syllabus,learningobjectives, questions,andproblems. MASTERINGPHYSICS.MasteringPhysics®istheonlinehomeworksystemthataccompanies thetextbook.Anaccountcanbepurchasedwiththetextbookorseparately,butisrequired forthecourse.TopurchaseMasteringPhysics®separately,goto www.masteringphysics.com,intheREGISTERblockclickontheSTUDENTSbuttonand followtheinstructions.LeaveStudentIDblank.TheCourseIDislistedinthefollowing table: Course MasteringPhysicsCourseID Physics110 FALL2013PHYSICS110 Physics110H FALL2013PHYSICS110H viii Physics110HJournal‐2013‐2014 CourseDescriptionandPolicies SUPPLEMENTALCOURSEMATERIAL.AllothercoursematerialisavailableonthePhysics 110SharePointsites: Course SharepointSites Physics110 https://eis.usafa.edu/academics/physics/110/default.aspx Physics110H https://eis.usafa.edu/academics/physics/110H/default.aspx Physics215andPhysics215Honors: TEXTBOOK.Wolfson,Richard,EssentialUniversityPhysics,2nded.,Vol2,SanFrancisco: PearsonEducation,Inc.,2012. JOURNAL.ThePhysics215Journalcontainscourseguidance,syllabus,learningobjectives, questions,andproblems. MASTERINGPHYSICS.MasteringPhysics®istheonlinehomeworksystemthataccompanies thetextbook.Anaccountcanbepurchasedwiththetextbookorseparately,butisrequired forthecourse.TopurchaseMasteringPhysics®separately,goto www.masteringphysics.com,intheREGISTERblockclickontheSTUDENTSbuttonand followtheinstructions.LeaveStudentIDblank.TheCourseIDislistedinthefollowing table: Course MasteringPhysicsCourseID Physics215 FALL2013PHYSICS215 Physics215H FALL2013PHYSICS215H SUPPLEMENTALCOURSEMATERIAL.AllothercoursematerialisavailableonthePhysics 215SharePointsites: Course SharepointSites Physics215 https://eis.usafa.edu/academics/physics/215/default.aspx Physics215H https://eis.usafa.edu/academics/physics/215H/default.aspx CoursePolicies WORKEDEXAMPLES–CorePhysicsusestheWorkedExamplesapproachtolearning,which requiresstudentstocometoclasspreparedtodiscusslessonmaterial.Forthisreason,class preparationpointsareheavilyweighted(18‐20%)andincludejournalquestions,pre‐class problems,andpreflightquestions. JOURNALQUESTIONS–Journalquestionsareassignedforalllessons,exceptedasnotedoneach lessonpageinyourjournal.Readtheselectionfromthetextbook,studytheassignedexamples,and answerthequestionsbasedonthoseexamples.Givecompleteanswersandjustifyasyouwouldon anexam‐prepquizorgradedreview.YourinstructorwillgradeyourJournaleachlessontoassess yourlevelofpreparationforclass.Thegoalofthisassessmentistoevaluateyourhonest, ix CourseDescriptionandPolicies Physics110HJournal‐2013‐2014 thoughtfuleffortatreasoningthroughtheproblems.Ifyougetstuckonaproblem,reviewthe exampleproblemsinthechapterandnotehowtheconceptsandequationsinthesectionare applied.Ifyouarestillstuck,youcanreceivecreditforyourJournalbywritingdownasmuchof thesolutionasyouareable,listingspecificquestionsyouhaveandidentifyingpointsofconfusion. Journalswillbegradedbasedonthefollowingguidelines: 3/3 GoodeffortwasmadetoanswerallJournalQuestions.Goodeffortwasmadeto solvethePre‐ClassProblem(s)inalogicalformat(IDEAformatisrecommended). 2/3 OneortwoJournalQuestionswerenotansweredorpooreffortwasmadetoanswer severaloftheJournalQuestions.PooreffortwasmadetosolvethePre‐Class Problem(s)oralogicalapproachwasnotused. 1/3 MultipleJournalQuestionswerenotansweredorthePre‐ClassProblemwasmostly orentirelyunfinished. 0/3 Lessthan50%oftheJournalQuestionsforthelessonwerecompleted. Ifyouaremorethan15minuteslateunexcused,youwillreceiveazerofortheJournalgrade. PREFLIGHTQUESTIONS–Preflightquestionsareassignedeachlessonexceptgradedreview lessons.Preflightsareintendedtobedoneafterthejournalquestions.Preflightquestions mustbesubmittedonlinenolaterthan0700beforethestartofeachlesson.Theyaredesignedto assessyourunderstandingofthelessonmaterialandprovidefeedbacktoyourinstructor beforeclass.AnswerthepreflightsinyourJournalthenenteryourresponsesintheJust‐In‐Time Teaching(JiTT)applicationathttp://dfp‐usafas‐computer.usafa.edu/usafa/login.php.Youruser nameisbasedonyoure‐mailaccount,e.g.C14Joe.Smith,andthedefaultpasswordisfall2013. ResponsesaregradedthroughtheJiTTapplication.Yourinstructorwillnotgradewrittenpreflight responsesintheJournal. PRE‐CLASSPROBLEMSandHOMEWORKPROBLEMS–Pre‐classproblemsareselectedfromthe textbookoruniquelydesignedforthelesson.Pre‐classproblemsaregradedaspartofeachlesson’s Journalgrade.Pre‐classproblemsarechosentogiveyoupracticedevelopingessentialskillsto understandthelesson. HOMEWORKPROBLEMS–HomeworkshouldbecompletedinyourJournaltoprovideyou referenceandstudymaterialforclass,quizzes,andexams.(Somequizzesmaybe“openJournal!”) Oncethehomeworkproblemsarecompleted,youshouldenteryouranswerintoMasteringPhysics tobescored. LABSandLABQUIZZES–Onlabdays,youwillcompletethedatacollectionandanalysesasa group,handinthelabworksheetasagroup,andthentakeanindividual‐effortlabquiz.Ifyouare morethan15minuteslateunexcused,youwillreceiveazeroforthelabworksheet.Youmay x Physics110HJournal‐2013‐2014 CourseDescriptionandPolicies participatewithalabgroupandtakethelabquiz.Forexcusedabsences,youmustcompletemissed labswithin3lessons(6classdays).ExemptionstothispolicymustbeapprovedbytheCourse Director.LabworksheetsareavailableontheCourse’sSharePointsite.Additionalinstructionsare onindividuallessonpageswithintheJournal.TheHonorsCoursesmayberequiredtocompletea labreportwhichisfurtherdefinedinAppendixA. EXAM‐PREPQUIZZES–Exam‐prepquizzes(EPQ)consistofworkoutandmultiple‐choiceproblems similartothoseongradedreviewsandthefinalexam.Youshouldusethesequizzestogaugeyour understandingofthematerialbeforetheexams.Additionalresourcesmaybeuseddependingupon coursedirectorpolicyandwillbeannouncedpriortotheEPQ. GRADEDREVIEWADMINISTRATION–GradedReviews(GRs)normallyconsistoftenmultiple‐ choicequestions,andseveralworkoutproblems.Youwillhave80minutestocompletetheexam. GRADING–Physicsisnota“plug‐and‐chug”subject.Submittinganumericallycorrect answerforaworkoutproblemdoesnotguaranteecredit.Itispossibletogettheright numberwiththewrongphysics.Yourscoreisdeterminedbythesoundnessofthe reasoningthatledtoyouranswer.Inordertoreceivefullcredityoumustidentifythemain physicsconceptsandshoweachstepintheproblem‐solvingprocess(IDEAformatis recommended). ABSENCEandTARDINESS– (a)IfyouwillbeabsentduringaGradedReviewduetoaUSAFASchedulingCommittee Action(SCA),youareresponsibletonotifyyourinstructoratleastTHREEDAYS(not includingweekends)PRIORtothefirstofferingoftheexam.Ifyouaremorethan15 minuteslateunexcusedforaGradedReview,youmusttakeamakeupexamwitha25% penalty.Ifyouarelessthan15minuteslate,youmaystilltaketheexamduringthe scheduledtime. (b)Ifyouwillmissalessonforanyreason,completeandturninacopyofthatlesson’s gradedworkbeforeyouleaveorsenditwithanotherstudenttoturninontime. MAKEUPEXAMS(GRsandQuizzes)–Ifyouaretravelingwithanathleticteamorcadetclub,the preferredoptionistotaketheexamontheroad.Ifthisisnotanoptionorifyouhavemissedthe examforanotherreason,workwithyourinstructortoscheduleatimetomakeuptheexamwithin twolessons. FINALEXAMandVALIDATION–TheFinalExamisacomprehensiveexaminationincluding materialfromtheentirecourse.Thefinalexamisyouropportunitytodemonstrateproficiency; therefore,validationoftheFinalExamisnotoffered. DOCUMENTATION–Clearlydocumentallhelpreceivedongradedworkfromsourcesotherthan yourWolfsontextbook.Pleasefeelfreetoseekhelpfromotherinstructors,students,orothertexts atanytime.Forallgradedworkoutsideofclass,youmayusethefollowingAUTHORIZED RESOURCES:Anypublishedorunpublishedsource,websites,andanyindividuals.Forall xi CourseDescriptionandPolicies Physics110HJournal‐2013‐2014 assignments,youmustproperlydocumentallassistanceandsourcesusedaccordingtothePhysics Departmentpolicyletterondocumentationstandards(locatedontheSharePointsite).Thisdoes notallowyoutosimplycopyresourcematerialortheworkofanotherstudent,pastor present,anddocumentthesource.Thereisnoacademiccreditforcopiedwork.Youmust alsoindicatewhethernohelpwasreceived.Documentationforalloutside‐of‐classwork—is accomplishedinthefooteroneachpageoftheJournal. ACADEMICSECURITY–Allexam‐prepquizzesandgradedreviewsremainunderacademic securityuntilreleasedbytheCourseDirector.DONOTdiscussthecontentsorthedifficultyof thematerialwithanyoneexceptyourinstructoruntilafteritisreleasedfromacademicsecurity. CONSTANTSANDEQUATIONSSHEET–YouwillbegivenastandardizedConstantsandEquations Sheetforuseonalllabquizzes,exam‐prepquizzes,gradedreviews,andthefinalexam. Understandingthephysicalconceptsgoverningtheuniversewillnotcomefromscanningan equationsheetinsearchofvariablesthatfittheproblem.Youmustfullycomprehendthenatureof theequations,themeaningsofthevariables,andtheconstraintsforusingeachequation. EXTRAINSTRUCTION–ThesecondhourofclassformostlessonsisdedicatedtoExtraInstruction (EI).Yourinstructorwillnotcovernewmaterialorholdreviewsessionsduringthistime,butheor sheisavailabletohelpyou.Ifyouhaveotherperiodsfree,youmayseekEIinanyofthePhysics classroomsduringsecondhourfromanyinstructorthatisteachingyourcourse.Donotexpect one‐on‐oneEIifyoudonotseekEIduringthesecondhourofyourclass. RE‐GRADES–Re‐gradingofquizzesandlabsisconsideredonanindividualbasisbyyour instructor.Ifyoudesireare‐gradeonagradedreview,firstshowyourinstructoryourworkandhe orshewillletyouknowifare‐gradeiswarranted.Ifitiswarranted,typeaMemoforRecord* (MFR)explainingyourcase,attachittoyourexam,andsubmitittoyourinstructor.TheCourse Directorwillre‐gradeyourwork.Youcouldalsolosepoints,sincetheentireproblemwillbere‐ graded.Youhavesevencalendardaysfromthedateagradedeventisreturnedtorequestare‐ grade. *AMemorandumforRecordistheAirForcestandardforofficialwrittencommunicationsandthe formatisprovidedintheTongueandQuill,availableontheAirForceE‐Publishingwebsite. xii Physics110HJournal‐2013‐2014 CourseDescriptionandPolicies Physics110HonorsCoursePointStructure No.ofEvents/Points GradedEvent JournalQuestions PreflightQuestions Pre‐LabQuestions LabWorksheet LabQuizzes LabReports Exam‐PrepQuizzes CriticalThinking Exercise Homework GradedReviews FinalExam Total Points Percentage 28 @ 30 @ 6@ 3@ 3@ 3@ 4@ 3 pointseach 5 pointseach 5 pointseach 10 pointseach 10 pointseach 25 pointseach 30 pointseach 84 150 30 30 30 75 120 5.6% 10.0% 2.0% 2.0% 2.0% 5.0% 8.0% 3@ 15 pointseach 45 3.0% 37 @ 3 pointseach 3 @ 150 pointseach 1 @ 375 points 111 450 375 1500 7.4% 30.0% 25.0% 100.0% NOTE1:Approximately70%ofthecoursepointsareindividualeffort(labquizzes,exam‐prep quizzes,gradedreviewsandthefinalexam). NOTE2:Asufficientlylowgradeonthefinalexamcouldresultinfailureofthecourseregardlessof theoverallscore,atthediscretionofthePhysicsDepartmentHead. xiii IDEAProblem‐SolvingStrategy Physics110HJournal‐2013‐2014 IDEAProblem‐SolvingStrategy SolvingProblemsUsingtheIDEAFormat Physicsproblemscanbechallenging,butunderlyingallofphysicsisonlyahandfulofbasic principles.Ifyoureallyunderstandthose,youcanapplytheminawidevarietyofsituations.Ifyou approachphysicsasahodgepodgeofunrelatedlawsandequations,you’llmissthepointandmake thingsdifficult.Butifyoulookforthebasicprinciplesandforconnectionsamongseemingly unrelatedphenomena,thenyou’lldiscovertheunderlyingsimplicitythatreflectsthescopeand powerofphysics. Asystematicsolutionmethodhelpsdevelopcriticalthinkingandscientificmethodprinciples.One suchapproachistheIDEAproblem‐solvingstrategy.Solvingaquantitativephysicsproblemalways startswithbasicprinciplesorconceptsandendswithapreciseanswerexpressedaseithera numericalquantityoranalgebraicexpression.Thepathfromprincipletoanswerfollowsfour simplesteps—stepsthatmakeupacomprehensivestrategyfororganizingyourthoughts,clarifying yourconceptualunderstanding,developingandexecutingplansforsolvingproblems,andassessing youranswers. Interpret Identifythemainphysicsconceptusedtosolvetheproblem. Develop Drawadiagramdepictingthesituation.Labelthegiveninformationandidentifythe informationforwhichyouaresolving. Evaluate Solvetheproblemfrombasicprinciplesusingequationsrelatedtothemainphysics concepts.Whenpossible,expressthesolutionsymbolicallybeforesubstituting valuesintotheequations.Includeunitswithallnumericalvalues. Assess Criticallyassessthevalidityofthesolutionbyansweringquestionssimilartothe following: a) Howdoesthesolutioncomparetoknownvalues? b) Howwouldtheanswerchangeifthevalueofoneofthevariableschanged? c) Isthesolutionphysicallypossible?Explain “Even for the physicist the description in plain language will be a criterion of the degree of understanding that has been reached.” Werner Heisenberg, Physics and Philosophy xiv Physics110HJournal‐2013‐2014 LearningObjectives LearningObjectives BlockI–Motion Duringthisblockwewillstartwithstudyingthebasicconceptsofdisplacement,velocityand acceleration.Wewillthenusetheequationsofmotiontoanalyzethemotionofobjects. [Obj9] ConvertphysicalmeasurementsfromvariousunitstothestandardSIunitsofmeters, kilograms,andseconds. Expressquantitiesusingscientificnotationandperformaddition,subtraction, multiplication,division,andexponentiationonthem. Identifythenumberofsignificantfiguresgiveninaproblemstatement,andexpress theanswerusingthecorrectnumberofsignificantfigures. Explaintherelationsbetweenposition,displacement,speed,velocity,andacceleration foranobjectmovinginoneandtwodimensions. Constructandinterpretgraphsofposition,velocity,andaccelerationforanobject movinginoneandtwodimensions. Explainthedifferencebetweeninstantaneousandaveragevelocity,andbetween instantaneousandaverageacceleration. Usemathematicalandgraphicalmethodstocalculateinstantaneousandaverage velocityandinstantaneousandaverageaccelerationinoneandtwodimensions. Useequationsofmotiontosolveproblemsinvolvingmotionwithconstant acceleration. Usecalculustosolveproblemsinvolvingmotionwithnon‐constantacceleration. [Obj10] Solveproblemsinvolvingfree‐fallmotionwithconstantgravitationalacceleration. [Obj11] Expressvectorsbothincomponentformandinmagnitude‐ directionform. [Obj12] Usemathematicalandgraphicalmethodstoperformvectoraddition,vector subtraction,andscalarmultiplication. Usevectorstorepresentposition,velocity,andacceleration. [Obj1] [Obj2] [Obj3] [Obj4] [Obj5] [Obj6] [Obj7] [Obj8] [Obj13] [Obj15] Describehowtheeffectsofaccelerationdependuponthedirectionoftheacceleration vectorrelativetothevelocityvector. Solveproblemsinvolvingprojectilemotionunderconstantgravitationalacceleration. [Obj16] Explainwhyuniformcircularmotioninvolvesacceleration. [Obj17] Solveproblemsinvolvinguniformandnonuniformcircularmotion. [Obj14] xv LearningObjectives Physics110HJournal‐2013‐2014 BlockII–Newton’sLaws Inthisblock,westartbyintroducingNewton’sthreelawsofmotions.Wewillthenusetheselaws tounderstandtheconceptofforce,todescribedifferenttypesofforces,andtoanalyzethemotion ofobjectsinoneandtwodimensions. [Obj18] Explaintheconceptofforceandhowforcescausechangeinmotion. [Obj19] StateNewton’sthreelawsofmotionandgiveexamplesillustratingeachlaw. [Obj20] Explainthedifferencebetweenmassandweight. [Obj21] Constructfree‐bodydiagramsusingvectorstorepresentindividualforcesactingonan object,andevaluatethenetforceusingvectoraddition. UseNewton’slawsofmotiontosolveproblemsinvolvingmultipleforcesactingona singleobject. UseNewton’slawsofmotiontosolveproblemsinvolvingmultipleobjects. [Obj22] [Obj23] [Obj25] Differentiatebetweentheforcesofstaticandkineticfrictionandsolveproblems involvingbothtypesoffriction. Describedragforcesqualitativelyand*quantitatively. [Obj26] Explainthephysicsconceptofwork. [Obj27] Evaluatetheworkdonebyconstantforcesandbyforcesthatvarywithposition. [Obj24] xvi Physics110HJournal‐2013‐2014 LearningObjectives BlockIII–EnergyandMomentum Wewillstartthisblockbyintroducingtheconceptsofenergyandwork.Usingourunderstandingof theseconcepts,wewilldeveloptheprincipleofconservationofenergywhichwillallowusto analyzethecomplexmotionofobjectsincludingthoseinorbits.Wewillfinishthisblockdiscussing collisionsandanotherconservationprinciple:conservationoflinearmomentum. [Obj28] Explaintheconceptofkineticenergyanditsrelationtowork. [Obj29] Explaintherelationbetweenenergyandpower. [Obj30] Explainthedifferencesbetweenconservativeandnonconservativeforces. [Obj31] Evaluatetheworkdonebybothconservativeandnonconservativeforces. [Obj32] Explaintheconceptofpotentialenergy. [Obj33] Evaluatethepotentialenergyassociatedwithaconservativeforce. [Obj34] Solveproblemsbyapplyingthework‐energytheorem,conservationofmechanical energy,orconservationofenergy. [Obj35] Describetherelationbetweenforceandpotentialenergyusingpotential‐energy curves. [Obj36] Explaintheconceptofuniversalgravitation. [Obj37] Solveproblemsinvolvingthegravitationalforcebetweentwoobjects. [Obj38] Determinethespeed,acceleration,andperiodofanobjectincircularorbit. [Obj39] Solveproblemsinvolvingchangesingravitationalpotentialenergyoverlarge distances. [Obj40] Usetheconceptofmechanicalenergytoexplainopenandclosedorbitsandescape speed. [Obj41] Useconservationofmechanicalenergytosolveproblemsinvolvingorbitalmotion. [Obj42] Calculatethecenterofmassforsystemsofdiscreteparticlesandforcontinuousmass distributions. [Obj43] Explaintheconceptoflinearmomentumofasystemofparticlesandexpress Newton'ssecondlawofmotionintermsofthelinearmomentumofthesystem. [Obj44] Explainthelawofconservationoflinearmomentumandtheconditionunderwhichit applies. [Obj45] Explaintheconceptofimpulseanditsrelationtoforce. [Obj46] Applyconservationoflinearmomentumtosolveproblemsinvolvingsystemsof particles. [Obj47] Explainthedifferencesbetweenelastic,inelastic,andtotallyinelasticcollisions. [Obj48] Applyappropriateconservationlawstosolveproblemsinvolvingcollisionsinone‐ andtwo‐dimensions. xvii LearningObjectives Physics110HJournal‐2013‐2014 BlockIV–RotationalMotionandSimpleHarmonicMotion Duringthisblockwewillstudytherotationalandoscillatorymotionofobjects.Wewillstartby exploringtherotationmotionofrigidobjects–discussingconceptsofangulardisplacement, velocity,andacceleration.WewillthenrevisittheconceptsofNewton’sSecondLaw,conservation ofenergy,andconservationofmomentumasappliedtoobjectsundergoingrotationalmotion.We willendthecoursebyintroducingtheconceptofsimpleharmonicmotion. [Obj49] Explaintherelationbetweentherotationalmotionconceptsofangulardisplacement, angularvelocity,andangularacceleration. [Obj50] Useequationsofmotionforconstantangularaccelerationtosolveproblemsinvolving angulardisplacement,angularvelocity,andangularacceleration. [Obj51] Usecalculustosolveproblemsinvolvingmotionwithnon‐constantangularacceleration. [Obj52] Explaintheconceptoftorqueandhowtorquescausechangeinrotationalmotion. [Obj53] Givenforcesactingonarigidobject,determinethenettorquevectorontheobject. [Obj54] Determinetherotationalinertiaforasystemofdiscreteparticles,rigidobjects,ora combinationofboth. [Obj55] Compareandcontrasttheconceptsofmassandrotationalinertia. [Obj56] UseNewton’ssecondlawanditsrotationalanalogtosolveproblemsinvolving translationalmotion,rotationalmotion,orboth. [Obj57] Solveproblemsinvolvingrotationalkineticenergyandexplainitsrelationtotorqueand work. [Obj58] Explaintherelationbetweenlinearandangularspeedinrollingmotion. [Obj59] Useconservationofenergytosolveproblemsinvolvingrotatingorrollingmotion. [Obj60] Determinethedirectionsoftheangulardisplacement,angularvelocityandangular accelerationvectorsforarotatingobject. [Obj61] Determinetheangularmomentumvectorfordiscreteparticlesandrotatingrigid objects. [Obj62] Applyconservationofangularmomentumtosolveproblemsinvolvingrotatingsystems changingrotationalinertiasandrotatingsystemsinvolvingtotallyinelasticcollisions. [Obj63] Definesimpleharmonicmotionandexplainwhyitissoprevalentinthephysicalworld. [Obj64] Determinetheperiodandfrequencyofasimpleharmonicoscillatorfromitsphysical parameters,andcompletelyspecifyitsequationofmotion. [Obj65] Determinethevelocityandaccelerationofasimpleharmonicoscillatorfromits equationofmotion. [Obj66] Determinethepotentialandkineticenergiesofasimpleharmonicoscillatoratanypoint initsmotion,anddescribethetimedependenceoftheseenergies. xviii Physics110HJournal‐2013‐2014 Lesson1 Lesson1 Introduction Reading Chapter1,2.1,2.2 Examples 2.1,2.2 HomeworkProblems 1.16,1.24,2.51 Thereisanon‐gradedPHYSICSKNOWLEDGEASSESSMENTTESTthislesson. LearningObjectives [Obj1] [Obj2] [Obj3] [Obj4] [Obj5] [Obj6] ConvertphysicalmeasurementsfromvariousunitstothestandardSIunitsofmeters, kilograms,andseconds. Expressquantitiesusingscientificnotationandperformaddition,subtraction, multiplication,division,andexponentiationonthem. Identifythenumberofsignificantfiguresgiveninaproblemstatement,andexpress theanswerusingthecorrectnumberofsignificantfigures. Explaintherelationship betweenposition,displacement,speed,velocity,and accelerationforanobjectmovinginoneandtwodimensions. Constructandinterpretgraphsofposition,velocity,andaccelerationforanobject movinginoneandtwodimensions. Explainthedifferencebetweeninstantaneousandaveragevelocity,andbetween instantaneousandaverageacceleration. Notes DocumentationStatement: 1 Lesson1 Physics110HJournal‐2013‐2014 WorkedExample Score(3) Studythegivenproblemandsolution,thenanswerthequestionsregardingthe problem. STATEMENTOFTHEPROBLEM Atliftoff,theaccelerationofaspaceshuttleis29m/s2,anditspositionasafunctionoftimeis definedas , whereaistheaccelerationandtistime.a)Whatisthe(instantaneous) velocity ofthespaceshuttleonesecondafterliftoff?b)Whatistheaveragevelocity ̅ overthe firstminuteafterliftoff? STRATEGY We interpret this as a problem involving the relationship between position, velocity, and acceleration. Additionally, we are interested in the difference between instantaneous velocity and average velocity. IMPLEMENTATION We are given the position equation, so in order to arrive at a value for velocity at one given instant, we will need to take the derivative of the equation with respect to time ( / ). To find the average velocity, we calculate the change in position over a given length of time ( ̅ ∆ /∆ ). CALCULATION a) Velocity 1 second after liftoff ( 1s): 2 29m/s 2 1s b) Average velocity over the first minute after liftoff (∆ ̅ ̅ 58m/s 60s): ∆ ∆ 29m/s DocumentationStatement: 2 60s 1740m/s Physics110HJournal‐2013‐2014 Lesson1 SELF‐EXPLANATIONPROMPTS 1. Whydoes∆ become and∆ become whencalculatingaveragevelocity? 2. Describethemotionoftherocketasshownintheposition versustime graph. 3. Howdoyouexpecttheinstantaneousvelocityafteroneminutetocomparetotheaverage velocitycalculatedinpart(b)?Calculatetheinstantaneousvelocityafteroneminute. DocumentationStatement: 3 Lesson1 Physics110HJournal‐2013‐2014 Pre‐ClassProblem STATEMENTOFTHEPROBLEM Alargemeteoris9700kmawayandheadingstraighttowardstheMoon.Itistravellingataspeed suchthatitwouldimpacttheMoonin15minutes,butinsteaditcollideswithasmallermeteor, knockingitoffitsoriginalpathata26°anglebutmaintainingitsoriginalspeed.Withthisnew trajectory,howmuchlongerwillittakeforthemeteortoimpacttheMoon? Answer:~100seconds DocumentationStatement: 4 Physics110HJournal‐2013‐2014 Lesson1 PreflightQuestions 1. Whattopicsdidyoufindmostchallengingfromthereading? 2. Solvethefollowingsystemofequationsfor and . 2 5 3 6 a) b) c) d) e) 3.40, 2.43, 3.40, 1.48, 1.00, 4.20 1.29 4.20 1.57 3.00 3. Itispossibleforanobjecttohave,atthesametime… a) …bothzerovelocityandnon‐zeroacceleration. b) …bothnon‐zerovelocityandzeroacceleration. c) Both(a)and(b)arepossible. d) Neither(a)nor(b)arepossible. 4. CRITICALTHINKING:Explainthedifferencebetweenaverageandinstantaneous speed/velocity/acceleration.(Hint:Youshouldconsiderthequantityoftime.) DocumentationStatement: 5 Lesson1 Physics110HJournal‐2013‐2014 HomeworkProblems 1.16 DocumentationStatement: 6 Physics110HJournal‐2013‐2014 Lesson1 1.24 DocumentationStatement: 7 Lesson1 Physics110HJournal‐2013‐2014 2.51 DocumentationStatement: 8 Physics110HJournal‐2013‐2014 Lesson2 Lesson2 Displacement,Velocity,andAcceleration Reading 2.3,2.4 Examples 2.1‐ 2.3 HomeworkProblems 2.20,2.35,2.79 ThereisanoptionalEquationDictionaryentryinAppendixDforthislesson(1PFpt). LearningObjectives [Obj4] [Obj5] [Obj6] [Obj7] [Obj8] [Obj9] Explaintherelationship between position,displacement,speed,velocity,and accelerationforanobjectmovinginoneandtwodimensions. Constructandinterpretgraphsofposition,velocity,andaccelerationforanobject movinginoneandtwodimensions. Explainthedifferencebetweeninstantaneousandaveragevelocity,andbetween instantaneousandaverageacceleration. Usemathematicalandgraphicalmethodstocalculateinstantaneousandaverage velocityandinstantaneousandaverageaccelerationinoneandtwodimensions. Useequationsofmotiontosolveproblemsinvolvingmotionwithconstant acceleration. Usecalculustosolveproblemsinvolvingmotionwithnon‐constantacceleration. Notes DocumentationStatement: 9 Lesson2 Physics110HJournal‐2013‐2014 WorkedExample Score(3) Studythegivenproblemandsolution,thenanswerthequestionsregardingthe problem. STATEMENTOFTHEPROBLEM Dragracingisanaccelerationcompetitionthattakesplaceoveralevel¼miletrack.Adragster startsfromrestandhastocompletethe¼mile(402.3m)run.Thetimeisveryshortsothe reactiontime(thetimeittakesthedrivertostartafterthegreenlightcomeson)isimportant.The driverwiththeshortestoveralltime(runtime+reactiontime)isthewinner. Thenationalrecordoveralltimeis4.42seconds. a)Assumingthattheaccelerationwasconstant(togetasimpleestimateoftheacceleration),what wastheaccelerationinthewinningrun? b)Whatwastheaveragespeedofthedragster? c)Againassumingconstantacceleration,whatwasthefinalspeedasthedragstercrossedthefinish line? STRATEGY This problem assumes constant acceleration and asks us to relate the given time to the speed and acceleration of the dragster. We will use the definition of average speed and equations of motion to solve this problem. IMPLEMENTATION For part (a) we apply the relation . For part (b) we apply the relation for average speed ̅ For part (c) we use the equation for average acceleration 0 ∆ DocumentationStatement: 10 Physics110HJournal‐2013‐2014 Lesson2 CALCULATION a) Acceleration of the winning run: The initial velocity is zero, so ̅ ∆ ∙ Solving for acceleration gives . . b) Average speed of the dragster: . simplifies to 41m/s 402.3m 91m/s 4.42s 204mph c) Final speed of the dragster (assuming constant acceleration): Using the acceleration from part (a), Since the dragster starts from rest, 41 ∆ can be written as ∙ 4.42s 181m/s ∆ 405mph Note:Accelerationandfinalspeedarenotmeasuredindragraces;theaveragespeedduringthelast 20metersismeasured.Intherecordrun,theaveragespeedduringthelast20meterswas336mph. SELF‐EXPLANATIONPROMPTS 1. Inyourtextbooklookupthederivationsoftheequationsusedinparts(a)and(b)aboveand summarizeinyourownwordshowtheserelationsareobtained. ifaccelerationisnotconstant?Gotothe 2. Isitvalidtousetherelation assignedreadinginthetextbookandfindwhatassumptionwasmadeinthederivationofthe equation. 3. Whatistherelationbetweeninitialspeedandfinalspeedduringatimeintervalwhenthe accelerationisconstant? DocumentationStatement: 11 Lesson2 Physics110HJournal‐2013‐2014 Pre‐ClassProblem STATEMENTOFTHEPROBLEM OnthewaytotheMoonthefirststageengineoftheSaturnVmoonrocketfiredfor156secondsto liftthecraft38miles(61,155meters).WhatistheaverageaccelerationofSaturnVduringthis stage? TryIt!(1pt):WhatisthespeedoftheSaturnVattheendofthisstage? DocumentationStatement: 12 Answer:5m/s2 Physics110HJournal‐2013‐2014 Lesson2 PreflightQuestions 1. Whattopicfromthereadingwouldyouliketodiscussduringclass? 2. Thefollowinggraphsdepictthevelocitiesoffourobjectsmovinginonedimension.Which objecthasthegreatestdisplacementduringthetimeintervalshown? Velocity, (m/s) Velocity, (m/s) Velocity, (m/s) Velocity, (m/s) 10 10 10 10 5 5 5 5 10 20 10 20 10 20 10 20 Time, (s) Time, (s) Time, (s) Time, (s) a) b) c) d) 3. Whichofthefollowingarrowscorrespondtoatimeatwhichtheinstantaneousvelocityis greaterthantheaveragevelocityoverthetimeintervalshown? B Time, Time, Position, Time, Position, A Position, Position, D C Time, a) b) c) d) 4. CRITICALTHINKING:Doesacarodometermeasuredisplacementordistance?Explain. DocumentationStatement: 13 Lesson2 Physics110HJournal‐2013‐2014 HomeworkProblems 2.20 DocumentationStatement: 14 Physics110HJournal‐2013‐2014 Lesson2 2.35 DocumentationStatement: 15 Lesson2 Physics110HJournal‐2013‐2014 2.79 DocumentationStatement: 16 Physics110HJournal‐2013‐2014 Lesson3 Lesson3 Lab1–AccelerationDuetoGravity Reading 2.5,Lab1Worksheet Examples 2.6 HomeworkProblems 2.38,2.42,2.78 ThereisaLABthislesson. LearningObjectives [Obj10] Solveproblemsinvolvingfree‐fallmotionwithconstantgravitationalacceleration. Notes DocumentationStatement: 17 Lesson3 Physics110HJournal‐2013‐2014 Pre‐LabQuestions Score(5) 1. Brieflydescribethepurposeandgoalsofthislab.(Onetotwocompletesentences) 2. Whataretherelevantconceptsandequationsthatyouwillbeusinginthelab? 3. InthesetupofPart1ofthelab,youareaskedtomeasuretheangleoftheinclinedtrack.How willyoudeterminetheangleoftheincline? 4. InPart1ofthelab,yourgroupwillmeasurethetimeittakesforanun‐weightedairtrackcart totraveldifferentdistancesdownanincline.InPart2,yourgroupwillmeasurethetimeit takesforaweightedairtrackcarttotravelthesamedistancesdownanincline.Howdoyou expectthetimestocomparebetweentheweightedandun‐weightedcarts?Brieflyexplainyour reasoning. 5. WhengraphingthedatainpartIandII,youareaskedtoplot ̅ vs.x.Explainthereasons behindplottingthedatainsuchaway. DocumentationStatement: 18 Physics110HJournal‐2013‐2014 Lesson3 LabNotes DocumentationStatement: 19 Lesson3 Physics110HJournal‐2013‐2014 HomeworkProblems 2.38 DocumentationStatement: 20 Physics110HJournal‐2013‐2014 Lesson3 2.42 DocumentationStatement: 21 Lesson3 Physics110HJournal‐2013‐2014 2.78 DocumentationStatement: 22 Physics110HJournal‐2013‐2014 Lesson4 Lesson4 Two‐Dimensional&ProjectileMotion Reading Examples HomeworkProblems 3.1– 3.5 3.3 3.34,3.53,3.54 LearningObjectives [Obj11] Expressvectorsbothincomponentformandinmagnitude‐directionform. [Obj12] Usemathematicalandgraphicalmethodstoperformvectoraddition,vector subtraction,andscalarmultiplication. Usevectorstorepresentposition,velocity,andacceleration. [Obj13] [Obj14] Describehowtheeffectsofaccelerationdependuponthedirectionoftheacceleration vectorrelativetothevelocityvector. Notes DocumentationStatement: 23 Lesson4 Physics110HJournal‐2013‐2014 WorkedExample Score(3) Studythegivenproblemandsolution,thenanswerthequestionsregardingthe problem. STATEMENTOFTHEPROBLEM Anaircrafthasavelocityof 70 ̂ 50 ̂m/s. Thewindpushestheaircraftwithavelocityof 45 ̂ 40 ̂m/s.Whatistheresultingfinal ? velocityoftheplane, STRATEGY Adding vectors is done by adding the x-components and the y-components to construct the net velocity vector. IMPLEMENTATION Add the components of the two vectors to build the final vector as: (x-component total) ̂+(y-component total) ̂ CALCULATION ̂ ̂ 70 45 ̂m/s 50 40 ̂m/s 115 ̂ 10 ̂ m/s DocumentationStatement: 24 Physics110HJournal‐2013‐2014 Lesson4 SELF‐EXPLANATIONPROMPTS 1. Superpositionofvectorsistheprocessofaddingvectors.Whydoyouaddthex‐andy‐ componentsseparately? 2. Whencomponentsarecombined,aretheabsolutevaluesofthecomponentsusedordothe componentsretaintheirnegativesignsiftheyhavethem? 3. Describea)whatadditionalinformationyouwouldneedtobegiventodeterminethe accelerationoftheplaneinthisproblemandb)whatstepsyouwouldusetocalculatethe accelerationoftheplane. DocumentationStatement: 25 Lesson4 Physics110HJournal‐2013‐2014 Pre‐ClassProblem STATEMENTOFTHEPROBLEM 70 ̂ 50 ̂m/s.Itexperiencesanaccelerationof Anaircrafthasaninitialvelocityof 2.5 ̂ 2 ̂m/s astheresultofastrongwind.After20sinthiswind,whatisthenewvelocityof theaircraft? Answer: DocumentationStatement: 26 120 ̂ 10 ̂ m/s Physics110HJournal‐2013‐2014 Lesson4 PreflightQuestions 1. Whattopicfromthereadingwouldyouliketodiscussduringclass? 2. Anobjectisinitiallymovinginthepositive ‐directionandthenexperiencesaccelerationinthe positive ‐direction.Whichofthegraphsdepictsthe ‐and ‐positionsoftheobjectwhile accelerating? a) b) c) d) 3. Theposition ofaparticleasafunctionoftime is 5 ̂ 2 ̂.Which statementistrueconcerningtheparticle? a) Theparticleislocatedattheoriginat b) 1 5m/s c) d) e) 5 ̂ 4 2 0. 2 ̂m/s 19/2m/s2 √ ̂ 2 ̂m/s f) Accelerationoftheparticleisconstant. 4. CRITICALTHINKING:Cananobjecthaveanorthwardvelocityandsouthwardacceleration? Explain. DocumentationStatement: 27 Lesson4 Physics110HJournal‐2013‐2014 HomeworkProblems 3.34 DocumentationStatement: 28 Physics110HJournal‐2013‐2014 Lesson4 3.53 DocumentationStatement: 29 Lesson4 Physics110HJournal‐2013‐2014 3.54 DocumentationStatement: 30 Physics110HJournal‐2013‐2014 Lesson5 Lesson5 ProjectileMotion Reading 3.5 Examples 3.4 HomeworkProblems 3.55,3.70,MP ThereisanoptionalEquationDictionaryentryinAppendixDforthislesson(1PFpt). ThereisanEXAM‐PREPQUIZthislesson. LearningObjectives [Obj14] [Obj15] Describehowtheeffectsofaccelerationdependuponthedirectionoftheacceleration vectorrelativetothevelocityvector. Solveproblemsinvolvingprojectilemotionunderconstantgravitationalacceleration. Notes DocumentationStatement: 31 Lesson5 Physics110HJournal‐2013‐2014 WorkedExample Score(3) Studythegivenproblemandsolution,thenanswerthequestionsregardingthe problem. STATEMENTOFTHEPROBLEM Avintagebomberisparticipatinginanairshowandplanstoconductabombingrunusingan “explosive”flourbag.Iftheaircraftisflyingat75m/sandreleasestheflourbomb1500meters abovetheground,howfarbackfromthetargetmustthepilotreleasethisflourbomb(therelease distancex)?Howfastisthebombmovinginthehorizontalandverticaldirectionswhenithitsthe ground? STRATEGY This is a projectile motion problem where the only acceleration affecting the motion is assumed to be due to gravity, acting vertically downward. We need to apply the basic kinematics equations separately for the motion in the horizontal, x-direction, and the vertical, y-direction. In this problem there is no horizontal acceleration, so the release distance will be the horizontal velocity times the flight time. The flight time will come from analyzing the vertical motion - knowing the total distance and the bomb’s initial vertical velocity. The kinematics equations we will need are and . These equations can be written for both motion in the x- and y-directions with the flight time t being a common variable. IMPLEMENTATION First, we need to establish an origin and coordinate system. Let’s set the origin at the point of release of the bomb with the x-axis pointed to the right and the y-axis pointed up (in a standard configuration). Now, we will determine the flight time (i.e. the time that the flour bomb travels from release to impact). The aircraft is flying in level flight, so the initial velocity in the y-direction v0y is zero. Also, the only acceleration is due to gravity, acting in a downward direction (g=-9.8 m/s2). We will manipulate and solve for flight time. Note that using our origin set at the point of release, the final position (yf) will be a negative 1500 m. DocumentationStatement: 32 Physics110HJournal‐2013‐2014 Lesson5 Now that we have the flight time, we will use to solve for the to determine the vertical speed of the bomb. There is no release distance and horizontal acceleration, so the horizontal velocity of the bomb is the same as when it was part of the aircraft. CALCULATION First, determine the flight time in the vertical direction. Starting with , we get ∆ 1500m 0m 0 9.8m/s and 2 1500m / 9.8 17.5s.. Next, determine the how far back the bomb is released in the horizontal. , we get ∆ Starting with 75 17.5s 0 1312m. Finally, solve for the final bomb velocity in the vertical: and Starting with In addition, 0 9.8m/s 12.4s 171.5m/s 75m/s since there is no acceleration in the horizontal. SELF‐EXPLANATIONPROMPT 1.Whyisthefinalposition,yf,anegativequantity? 2.Whatwouldbedifferentifweweretodesignatetheoriginatthegroundlevelbelowtherelease point? 3.Whatwouldhappeniftheinitialvelocity,v0y,intheverticalwasnotzero? DocumentationStatement: 33 Lesson5 Physics110HJournal‐2013‐2014 Pre‐ClassProblem STATEMENTOFTHEPROBLEM Acannononaclifffiresatashipinapiratemovie.Theshipis200mfromthecliffandtheinitial velocityofthelaunchedcannonballis 60 ̂ 20 ̂m/s.Ifthecannonballhitstheship,a)how highisthecliff,andb)whatisthefiringangle? Answers:12m,18.4° DocumentationStatement: 34 Physics110HJournal‐2013‐2014 Lesson5 PreflightQuestions 1. Whattopicfromthereadingwouldyouliketodiscussduringclass? 2. Asnowballisthrownverticallyupwardfromamovingsledtravelingonastraight,levelroadat aconstantspeed.Neglectingairresistance,thesnowballwillland a) infrontofthesled. b) onthesled. c) behindthesled. d) Theanswerdependsonthespeedofthesled. 3. Twoidenticalmassesareshotoutofacannonsittingonaflatsurface.Thecannonisadjusted suchthatthehorizontalvelocitycomponentofthecannonballsareequal.Object1,ared cannonball,isshotupwardatanangleof30°withrespecttothehorizontal.Object2,ablue cannonball,isshotupwardsatanangleof60°withrespecttothehorizontal.Whichballwillhit thegroundfurthestfromthecannon? a) Theredcannonball. b) Thebluecannonball. c) Bothcannonballswillhitatthesamespot. d) Thecannonballswillonlygoupanddown. e) Theanswercannotbedeterminedfromthegivendata. 4. CRITICALTHINKING:Ahighjumperandalongjumperarebothhumanprojectiles,butwith slightlydifferentgoals.Thehighjumperwantstotraveloverahighbarwithouttouchingit,and thelongjumperwantstotravelasgreatadistanceaspossiblewithouttouchingtheground. Describehowthex‐andy‐componentsoftheinitialvelocityvectorshoulddifferbetweenthe twotypesofjumpers. DocumentationStatement: 35 Lesson5 Physics110HJournal‐2013‐2014 HomeworkProblems 3.55 DocumentationStatement: 36 Physics110HJournal‐2013‐2014 Lesson5 3.70 DocumentationStatement: 37 Lesson5 Physics110HJournal‐2013‐2014 MP DocumentationStatement: 38 Physics110HJournal‐2013‐2014 Lesson6 Lesson6 Lab2–ProjectileMotion Reading Lab2Worksheet Examples 3.4 HomeworkProblems MP,3.58,MP ThereisaLABthislesson. LearningObjectives [Obj15] Solveproblemsinvolvingprojectilemotionunderconstantgravitationalacceleration. Notes DocumentationStatement: 39 Lesson6 Physics110HJournal‐2013‐2014 Pre‐LabQuestions Score(5) 1. Brieflydescribethepurposeandgoalsofthislab.(Onetotwocompletesentences) 2. Anobjectislaunchedhorizontallyfromaheight withvelocity .Howmuchtime doesittake fortheobjecttoreachthelevelgroundbelow? a b c d) 3. Youwillbelaunchingasmallaircompressionrocketforthislab.First,youwilllaunchthe rocketverticallyandmeasurethetimeofflight.Deriveanequationthatrelatestimeofflight,t, toinitialvelocity,v0,fortherocket. 4. Inthesecondpartofthelab,youwilllaunchtherocketatanangle,θ,andaheight,h,above levelground.Usingθ,h,andinitialvelocityv0asknownquantities,deriveanexpressionforthe horizontalrange,Δ ,thattherocketwilltravel. DocumentationStatement: 40 Physics110HJournal‐2013‐2014 Lesson6 LabNotes DocumentationStatement: 41 Lesson6 Physics110HJournal‐2013‐2014 HomeworkProblems MP DocumentationStatement: 42 Physics110HJournal‐2013‐2014 Lesson6 3.58 DocumentationStatement: 43 Lesson6 Physics110HJournal‐2013‐2014 MP DocumentationStatement: 44 Physics110HJournal‐2013‐2014 Lesson7 Lesson7 AccelerationinCircularMotion Reading Examples HomeworkProblems 3.6 3.7,3.8 MP,MP,3.80 LearningObjectives [Obj16] Explainwhyuniformcircularmotioninvolvesacceleration. [Obj17] Solveproblemsinvolvinguniformandnonuniformcircularmotion. Notes DocumentationStatement: 45 Lesson7 Physics110HJournal‐2013‐2014 WorkedExample Score(3) Studythegivenproblemandsolution,thenanswer thequestionsregardingtheproblem. STATEMENTOFTHEPROBLEM Anaircrafttravelingataconstant150m/smakesa360°turnata constantaltitude(referredtoaslevelflight).Iftheaircraft’s accelerationtowardthecenteroftheturnis1.5g,whatistheradius oftheturn? STRATEGY This is a problem involving uniform circular motion (UCM), where several things in the horizontal are uniform: radius (r), tangential speed (vtan), and the center-directed acceleration (acentripetal). The aircraft experiences NO acceleration in the vertical direction. The center-directed acceleration (acentripetal) is related to the tangential velocity by the UCM basic relationship: IMPLEMENTATION First, we need to determine the magnitude of the center-directed acceleration. We are given that it is 1.5 g. This means 1.5 times the acceleration due to gravity (9.8 m/s2). Next, we will manipulate the UCM basic relationship so that r is alone on the left side of the equation. We then solve for the radius. CALCULATION First, manipulate the UCM basic relationship to solve for r : becomes Now, substitute and solve: 150m/s 1.5 9.8m/s Notice that the units resolve as: / / m DocumentationStatement: 46 1530m Physics110HJournal‐2013‐2014 Lesson7 SELF‐EXPLANATIONPROMPTS 1.Inthisproblem,theaircraftistravelingataconstantspeedof150m/s.Isthisaircraft(orany objectexecutinguniformcircularmotion)undergoingacceleration?Explain. 2.Howdoyouknowthattheaccelerationintheverticaliszero? 3.Whatcausesthecenter‐directedacceleration? DocumentationStatement: 47 Lesson7 Physics110HJournal‐2013‐2014 Pre‐ClassProblem STATEMENTOFTHEPROBLEM A650‐kgFormulaOneracecarexecutesaportionofacircularturnat20m/s.Theradiusofthe turnis50meters.Whataccelerationmustthefrictionofthetiresgenerateinordertoaccomplish thisturn?Whatisthedirectionofthatacceleration? TryIt!(1pt):Describeanddrawtheaccelerationvector ifthecar’sspeedwasincreasingasitexecutedtheturn. DocumentationStatement: 48 Answer:8m/s2,towardsthe centeroftheturn Physics110HJournal‐2013‐2014 Lesson7 PreflightQuestions 1. Whattopicfromthereadingwouldyouliketodiscussduringclass? 2. Whenacartravelingataconstantspeedgoesaroundacurveonalevelroad,whatisthe directionofacceleration? a) Thereisnoacceleration. b) Thecarisacceleratingtowardthecenterofthecurve. c) Thecarisacceleratingawayfromthecenterofthecurve. d) Theaccelerationisinthesamedirectionthecaristraveling. 3. Rankinordertheradialaccelerationsofthefollowingobjectsfromlargesttosmallest. 2 2 2 2 a) b) c) d) 4. CRITICALTHINKING:Whenyourideinavehiclethatismakingaturnyourbodyfeelspushed outward.Reconcilethisfactwiththephysicsstatementthattherealaccelerationofyourbody isinwardtowardsthecenteroftheturn. DocumentationStatement: 49 Lesson7 Physics110HJournal‐2013‐2014 HomeworkProblems MP DocumentationStatement: 50 Physics110HJournal‐2013‐2014 Lesson7 3.58 DocumentationStatement: 51 Lesson7 Physics110HJournal‐2013‐2014 MP DocumentationStatement: 52 Physics110HJournal‐2013‐2014 Lesson8 Lesson8 GRADEDREVIEW1 LearningObjectives [Obj9] ConvertphysicalmeasurementsfromvariousunitstothestandardSIunitsofmeters, kilograms,andseconds. Expressquantitiesusingscientificnotationandperformaddition,subtraction, multiplication,division,andexponentiationonthem. Identifythenumberofsignificantfiguresgiveninaproblemstatement,andexpress theanswerusingthecorrectnumberofsignificantfigures. Explaintherelationship betweenposition,displacement,speed,velocity,and accelerationforanobjectmovinginoneandtwodimensions. Constructandinterpretgraphsofposition,velocity,andaccelerationforanobject movinginoneandtwodimensions. Explainthedifferencebetweeninstantaneousandaveragevelocity,andbetween instantaneousandaverageacceleration. Usemathematicalandgraphicalmethodstocalculateinstantaneousandaverage velocityandinstantaneousandaverageaccelerationinoneandtwodimensions. Useequationsofmotiontosolveproblemsinvolvingmotionwithconstant acceleration. Usecalculustosolveproblemsinvolvingmotionwithnon‐constantacceleration. [Obj10] Solveproblemsinvolvingfree‐fallmotionwithconstantgravitationalacceleration. [Obj11] Expressvectorsbothincomponentformandinmagnitude‐directionform. [Obj12] Usemathematicalandgraphicalmethodstoperformvectoraddition,vector subtraction,andscalarmultiplication. [Obj13] Usevectorstorepresentposition,velocity,andacceleration. [Obj14] [Obj15] Describehowtheeffectsofaccelerationdependuponthedirectionoftheacceleration vectorrelativetothevelocityvector. Solveproblemsinvolvingprojectilemotionunderconstantgravitationalacceleration. [Obj16] Explainwhyuniformcircularmotioninvolvesacceleration. [Obj17] Solveproblemsinvolvinguniformandnonuniformcircularmotion. [Obj1] [Obj2] [Obj3] [Obj4] [Obj5] [Obj6] [Obj7] [Obj8] Notes DocumentationStatement: 53 Lesson8 Physics110HJournal‐2013‐2014 Lesson1:“Areyouready?” Readtheproblembelowandworkthroughtheguidedsolution,thenanswerthequestions regardingtheproblem. STATEMENTOFTHEPROBLEM Susanisdrivingat50mphtopickupherfriendattheairport.Herfriend’sflightlandsin30 minutes,andsheis40miawayfromtheairport.WillSusanbeabletopickupherfriendontime? Ifso,howlongwillittakeforhertoarriveathercurrentspeed?Ifnot,whatwillshehaveto changeherspeedtoinordertoarriveattheairportontime? STRATEGY(Fillintheblanks.) We will need to first determine if Susan’s current speed is sufficient to allow her to arrive within 30 minutes. We can calculate the speed necessary to cover the given remaining distance and compare it to her current speed. If her current speed is greater than the needed speed, then she will be able to arrive on time. If her current speed is less than the needed speed, then she will need to modify her current speed. CALCULATION(Fillintheblanks.) Needed speed based on remaining distance: ∆ ∆ ̅ ̅ If ̅ ̅ ∆ If ̅ ̅ ∆ ̅ ̅ 40mi 0.5hr or ____________mi/hr ̅ (circle one) ̅ , how long will it take to arrive? _____________hr , what will Susan have to change her speed to? SELF‐EXPLANATIONPROMPTS 1.WhatspeedwouldSusanneedtoarriveexactlyontime? OptionalPracticeProblems:2.21,2.43,2.47 DocumentationStatement: 54 Physics110HJournal‐2013‐2014 Lesson8 Lesson2:“Areyouready?” Readtheproblembelowandworkthroughtheguidedsolution,thenanswerthequestions regardingtheproblem. STATEMENTOFTHEPROBLEM Theaccelerationduetogravityinfreefallisabout9.8m/s2.Atypicalspeedforanarrowshotfrom abowis76.2m/s.Ifsuchanarrowisshotstraightup,andairresistanceisneglected,howhigh woulditgo? STRATEGY(Fillintheblanks.) In our case v = _______________, v0 = ________________, a = __________ (watch the sign!), x – x0 is the height. Now, if we eliminate the variable t between we get ½ and 2 CALCULATION(Fillintheblanks.) height = ________________________= 296 m That is almost 0.2 mile and probably unrealistic. SELF‐EXPLANATIONPROMPTS 1.PerformthederivationintheSTRATEGYsection. 2.Whichquantitiesin 2 arepositive,whicharenegative? OptionalPracticeProblems:2.37,2.51,2.61,2.69 DocumentationStatement: 55 Lesson8 Physics110HJournal‐2013‐2014 Lesson4:“Areyouready?” Readtheproblembelowandworkthroughtheguidedsolution,thenanswerthequestions regardingtheproblem. STATEMENTOFTHEPROBLEM Twovectorsare 7̂ 4 ̂ and 3̂ 2 ̂.Whatisthevector ? STRATEGY(Fillintheblanks.) Perform this subtraction by dealing with the x-components and the y-components separately. IMPLEMENTATION(Fillintheblanks.) The Ax and Bx components are: Ax =___________ Bx = ____________ The Ay and By components: Ay =___________ By = ____________ CALCULATION(Supplytheneededsigns,ornumbers) ______3 7and ___________ ̂ 2_______4 ___________ ̂ SELF‐EXPLANATIONPROMPTS 1.Whatisthemagnitudeofthevector ? 2.Howdowehandlethesubtractionofa“negative”component,likethe“ OptionalPracticeProblems:3.11,3.14,3.31 DocumentationStatement: 56 4/3 ̂”? Physics110HJournal‐2013‐2014 Lesson8 Lesson5:“Areyouready?” Readtheproblembelowandworkthroughtheguidedsolution,thenanswerthequestions regardingtheproblem. STATEMENTOFTHEPROBLEM Avintagebomberparticipatinginanairshowwantstodropabombthatstaysintheairfor15 secondsbeforeimpact.Ifthehorizontalvelocityoftheplaneis75m/s,determinetherequired launchaltitude. STRATEGY(Fillintheblanks.) Let’s set the ________ at the vertical point where the bomb is __________. written in the _______ We will use dimension, using _______ for the time of flight. The v0 will still be ______ in the vertical, and the __________ will still be ____ 9.8 m/s2. CALCULATION(Fillintheblanks) 1 2 ______m 0 _____s 1 2 9.8m/s 15s 1103m SELF‐EXPLANATIONPROMPTS 1.Howaretheflighttimesinthehorizontalandtheverticaldirectionsconnected? 2.Howwouldaninitialvelocityintheverticalaffecttheanswerinthisproblem? 3.Howisthenegativedirectionofgravity’seffectaccountedforinordertoresultinapositive valuefory0? OptionalPracticeProblems:3.33,3.62 DocumentationStatement: 57 Lesson8 Physics110HJournal‐2013‐2014 Lesson7:“Areyouready?” Readtheproblembelowandworkthroughtheguidedsolution,thenanswerthequestions regardingtheproblem. STATEMENTOFTHEPROBLEM Thishammerthrowerreleasesthehammerballwitha tangentialspeedof21m/swhentheballis1.8mfromthe centeroftheathlete’srotation.a)Whatisthecentripetal accelerationoftheballattheinstantitisreleased?b)How doesthisaccelerationcomparetotheaccelerationdueto gravity? STRATEGY(Fillintheblanks.) To solve this problem we use the UCM basic relationship acentripetal =___________________. CALCULATION(Fillintheblanks.) acentripetal = _____________________________ = 245 m/s2 acentripetal is directed ________________ and is __________ times larger than the acceleration due to gravity, which is directed _____________________. SELF‐EXPLANATIONPROMPTS 1.Whatobjectprovidestheaccelerationofthehammerball? 2.Whatisthedirectionofthenetaccelerationofthehammerballjustbeforeitisreleased? OptionalPracticeProblems:3.38,3.39,3.40 DocumentationStatement: 58 Physics110HJournal‐2013‐2014 Lesson8 Notes DocumentationStatement: 59 Lesson8 Physics110HJournal‐2013‐2014 Notes DocumentationStatement: 60 Physics110HJournal‐2013‐2014 Lesson9 Lesson9 ForcesandNewton’sLawsofMotion Reading Examples HomeworkProblems 4.1– 4.4 4.1,4.2 4.15,4.26,4.60 LearningObjectives [Obj18] Explaintheconceptofforceandhowforcescausechangeinmotion. [Obj19] StateNewton’sthreelawsofmotionandgiveexamplesillustratingeachlaw. [Obj20] Explainthedifferencebetweenmassandweight. Notes DocumentationStatement: 61 Lesson9 Physics110HJournal‐2013‐2014 WorkedExamples Score(3) Studythegivenproblemandsolution,thenanswerthequestionsregardingthe problem. STATEMENTOFTHEPROBLEM Atowtruckispullingadisabled1200‐kgcaralongalevelroad.Thetow‐ropeisparalleltotheroad. Startingfromrest,thespeedincreasesto2m/sovera20metersdistance.Whatisthetensionin therope?Assumefrictionisnegligible. STRATEGY Newton’s Second Law as applied to the car states that the acceleration of the car given by is . We know the mass of the car, and we can use kinematics to find the acceleration of the car. Newton’s Second Law can then be used to obtain the net force. IMPLEMENTATION To get the net force, we multiply the acceleration of the car, obtained from the kinematics equation 2 , by the mass of the car. CALCULATION 2 1200kg 4 0 m /s 2 20m 120N The force unit kg·m/s2 is called a newton, N, in honor of Isaac Newton. DocumentationStatement: 62 Physics110HJournal‐2013‐2014 Lesson9 SELF‐EXPLANATIONPROMPTS 1.TheunitofforceisanewtonwhichisgiventhesymbolN.Expressthenewtonintermsofthe fundamentalSIunits. 2.Findthedefinitionof“tensioninarope”inyourtextbookandrephraseitinyourownwords. 3.Whatchangewouldyoumakeinthecalculationifthetow‐ropewasdirectedatanangle? DocumentationStatement: 63 Lesson9 Physics110HJournal‐2013‐2014 Pre‐ClassProblem A45‐ggolfballatrestishitbyaclubwithaforceof5.0N.a)Whatistheball’sacceleration immediatelyafteritishit?b)Howfardoestheballtravelinthefirsttenthofasecond? Answer:110m/s2,0.56m DocumentationStatement: 64 Physics110HJournal‐2013‐2014 Lesson9 PreflightQuestions 1. Whattopicsdidyoufindmostchallengingfromthereading? 2. A200‐kgrockisbeingpulledupwardwithanaccelerationof3m/s2.Thenetforceontherock is a) 200Nup b) 200Ndown c) Zero d) Noneoftheabove. 3. Thenetforcevectorforanobjectinmotionis a) alwaysinthesamedirectionastheobject'saccelerationvector. b) sometimesinthesamedirectionastheobject'saccelerationvector. c) alwaysinthesamedirectionastheobject'svelocityvector. d) alwaysinthesamedirectionastheobject'sdisplacementvector. 4. CRITICALTHINKING:Thetake‐offmassofanF‐16is16,875kg.Itsenginecanexertaforceof 105,840N.IfyoumountedtheF‐16engineonacar,whataccelerationwouldyouget?Usea reasonableestimateforthemassofacarandexplainhowyouobtainedyouranswer. DocumentationStatement: 65 Lesson9 Physics110HJournal‐2013‐2014 HomeworkProblems 4.15 DocumentationStatement: 66 Physics110HJournal‐2013‐2014 Lesson9 4.26 DocumentationStatement: 67 Lesson9 Physics110HJournal‐2013‐2014 4.60 DocumentationStatement: 68 Physics110HJournal‐2013‐2014 Lesson10 Lesson10 UsingNewton’sLaws Reading 4.5,4.6 Examples 4.3,4.4,4.5 HomeworkProblems 4.34,4.47,4.49 ThereisanoptionalEquationDictionaryentryinAppendixDforthislesson(1PFpt). LearningObjectives [Obj19] StateNewton’sthreelawsofmotionandgiveexamplesillustratingeachlaw. [Obj20] Explainthedifferencebetweenmassandweight. [Obj21] Constructfree‐bodydiagrams usingvectorstorepresentindividualforcesacting onan object,andevaluatethenetforceusingvectoraddition. UseNewton’slawsofmotiontosolveproblemsinvolvingmultipleforcesactingona singleobject. UseNewton’slawsofmotiontosolveproblemsinvolvingmultipleobjects. [Obj22] [Obj23] Notes DocumentationStatement: 69 Lesson10 Physics110HJournal‐2013‐2014 WorkedExamples Score(3) Studythegivenproblemandsolution,thenanswerthequestionsregardingthe problem. STATEMENTOFTHEPROBLEM Ateamofdogsispullingtwoconnectedsledswithaconstantaccelerationof2.3m/s2.The passengersled,connectedtothedogsinfront,hasamassof96kg.Thecargosled,tiedtothefront sled,hasamassof42kg.Fornow,weassumethattheretardingfrictionismuchsmallerthanthe forceexertedbythedogs. a)Howmuchistheforcethatthedogsexerton thesledtrain? b)Withwhatforceisthecargosledpullingbackonthepassengersled? STRATEGY The accelerating sleds are subject to Newton’s Second Law, which states that the acceleration of an object is proportional to the applied force and inversely proportional to the mass of the accelerating object. To answer part (a), we apply the law to the sled train with the combined mass of 138 kg and solve the resulting equation for the unknown applied force. Newton’s Third Law states that when two objects are connected and the first one exerts a force on the second one, the second one responds with a reaction force of the same magnitude, acting back on the first one. Since we know the mass and the acceleration of the cargo sled, we can determine the applied force exerted on the cargo sled by the passenger sled. It is the passenger sled that pulls the cargo sled, not the dogs directly. The reaction force exerted by the cargo sled on the passenger sled has the same magnitude as the force exerted by the passenger sled on the cargo sled and is pulling back on it. DocumentationStatement: 70 Physics110HJournal‐2013‐2014 Lesson10 IMPLEMENTATION Let’s label the force exerted by the dog team on the sled team. Let’s label the force exerted by the passenger sled on the cargo sled . Let’s label the force exerted by the cargo sled on the passenger sled . CALCULATION For each part we apply Newton’s Second Law a) 2.3m/s b) 2.3m/s . 320 in the forward direction 97 in the forward direction The dogs pull the sled train forward with a force of 320 N. The cargo sled pulls back on the passenger sled with a force of 97N. SELF‐EXPLANATIONPROMPTS 1. RephraseNewton’sSecondLawinyourownwords. 2. Whatisthenetforceonthepassengersled? 3. Ifthecargosledwasremoved,howdoyouexpecttheforceappliedbythedogteamtochange inordertoobtainthesameaccelerationof2.3m/s2forjustthepassengersled?Calculatethe forceexertedbythedogteam forthisscenario. DocumentationStatement: 71 Lesson10 Physics110HJournal‐2013‐2014 Pre‐ClassProblem STATEMENTOFTHEPROBLEM A12‐kgchildisridingina4100‐kgelevatorwhichisacceleratingupwardataconstant1.3m/s2. Whatistheforcethattheelevatorexertsonthechild?Whatistheforcethechildexertsonthe elevator? Free‐BodyDiagram(required) Tryit!(1PFpt):Ifthechildwasstandingonascaleintheelevator, whatwouldthescalereadwhentheelevatorwas(a)stationary and(b)acceleratingupwardat1.3m/s2?Showallyourwork. DocumentationStatement: 72 Answer:133N,‐133N Physics110HJournal‐2013‐2014 Lesson10 PreflightQuestions 1. Whattopicfromthereadingwouldyouliketodiscussduringclass? 2. Twoforcesofequalmagnitudeactonthesameobject.Whichofthefollowingmustbetrue? a) Theobjectismoving. b) Theobjectisaccelerating. c) Iftheobjectisinitiallyatrest,itcannotremainatrest. d) Thetwoforcesformathird‐lawpair. e) Noneoftheabove. 3. Twoblocksarehangingmotionlessfromtheceilingasshowninthe diagram.Whichofthefollowingistrue? a) b) c) onlyif d) 4. CRITICALTHINKING:Theterm”weight”inphysicshasthefollowingveryspecificmeaning: “Theweightofanobjectisthenamegiventoaparticularforce:thegravitationalforceexerted bytheearthontheobject,givingitanaccelerationof9.8m/s2nearthesurfaceofEarth.” Inordinaryspeechtheuseof“weight”isnowherenearlysoprecise.Explainwhetherthe followingusagesarescientificallycorrect. a) A3‐kgobjecthasaweightofabout30NatthesurfaceofEarth. b) A120‐lbpersonweighsabout55kg. c) AnastronautorbitingEarthexperiencesweightlessness d) Ifyoueattoomuchyoumaygainweight. DocumentationStatement: 73 Lesson10 Physics110HJournal‐2013‐2014 HomeworkProblems 4.34 DocumentationStatement: 74 Physics110HJournal‐2013‐2014 Lesson10 4.47 DocumentationStatement: 75 Lesson10 Physics110HJournal‐2013‐2014 4.49 DocumentationStatement: 76 Physics110HJournal‐2013‐2014 Lesson11 Lesson11 Newton’sLawsinTwoDimensions Reading Examples HomeworkProblems 5.1 5.1,5.2 5.16,MP,5.38 LearningObjectives [Obj22] UseNewton’slawsofmotiontosolveproblemsinvolvingmultipleforcesactingona singleobject. Notes DocumentationStatement: 77 Lesson11 Physics110HJournal‐2013‐2014 WorkedExample Score(3) Studythegivenproblemandsolution,thenanswerthequestionsregardingthe problem. STATEMENTOFTHEPROBLEM 50kg A50‐kgblockisonafrictionless30°ramp.Determinetheblock’s accelerationdowntheramp. STRATEGY 30° Newton’s Second Law as applied to the block states that the acceleration of the block given by . In this problem, we have two forces acting on the block: weight is and the normal force . These forces act in the x– and y-directions, so we need to separate each force into its components. Once in component form, we can sum the forces in each direction and apply Newton’s Second Law to find acceleration. Because the motion of the block is along the incline, we “tilt” the coordinate system of our free-body diagram to align with the incline of the ramp and the normal force that is acting on the block. IMPLEMENTATION Let’s draw a free-body diagram for our object of interest: the block. There are two forces acting on the block, weight and normal force, that are included in the diagram. Since the block is moving down the ramp, we use a tilted coordinate system. The net force on the block in the x-direction is: sin The net force on the block in the y-direction is: cos DocumentationStatement: 78 Physics110HJournal‐2013‐2014 Lesson11 CALCULATION The acceleration in the y-direction (perpendicular to the incline as defined by our coordinate system) is zero. To find the acceleration of the block, we need to solve for the acceleration in the x-direction . Cancelling mass in the net force equation above gives: sin 9.8m/s sin 30° 4.9m/s SELF‐EXPLANATIONPROMPTS 1.Explainwhytiltingthecoordinatesystemsimplifiedtheproblem.Thinkabouthowthe procedurewouldhavechangedhadtraditionalx‐ycoordinatesbeenused. 2.Wouldtheanswerhavechangedhadthecoordinatesystembeenswitched,sothepositivex‐axis wasdefinedasbeinguptheramp? 3.Whatwouldhappentothemagnitudeoftheblock’saccelerationiftheangleoftherampwas increased?Whatisthemaximumaccelerationtheblockcanexperience?Whatistheminimum accelerationtheblockcanexperience? DocumentationStatement: 79 Lesson11 Physics110HJournal‐2013‐2014 Pre‐ClassProblem STATEMENTOFTHEPROBLEM CEILING 32° 68° A3.0‐kgboxissuspendedfromaceilingasshown.What arethemagnitudesofthetensionsexertedbytheropes attachedtothebox?Assumetheropeshavenegligible masscomparedtothebox.(Hint:LookatExample5.2in m thetextbook.Whyisiteasiertouseatraditionalx—y coordinatesystemratherthantiltedforthisproblem?) Free‐BodyDiagramofBox(required) Answer:T1=25N T2=11N DocumentationStatement: 80 Physics110HJournal‐2013‐2014 Lesson11 PreflightQuestions 1. Whattopicfromthereadingwouldyouliketodiscussduringclass? 2. A5‐kgblockispushedacrossahorizontalfloorwitha20‐Nforcedirected20°belowthe horizontal.Whatisthemagnitudeofthenormalforceontheblock? a) b) c) d) e) 3. 49N 6.8N 42N 56N 68N 20N 20° 5kg IfRope1remainshorizontalandthepointatwhichRope2istiedis movedfrom to ,whatistrueaboutthetensionintheropes? a) remainsthesameand increases. b) decreasesand increases. Rope1 c) Both and remainthesame. d) Both and increase. 4. CRITICALTHINKING:Refertopreflightquestion3:IsitpossibletoattachRope2atpointCand havebothropesparalleltotheground?Explain. DocumentationStatement: 81 Lesson11 Physics110HJournal‐2013‐2014 HomeworkProblems 5.16 DocumentationStatement: 82 Physics110HJournal‐2013‐2014 Lesson11 MP DocumentationStatement: 83 Lesson11 Physics110HJournal‐2013‐2014 5.38 DocumentationStatement: 84 Physics110HJournal‐2013‐2014 Lesson12 Lesson12 Newton’sLawswithMultipleObjects Reading Examples HomeworkProblems 5.2 5.4 5.19,5.21,5.71 LearningObjectives [Obj23] UseNewton’slawsofmotiontosolveproblemsinvolvingmultipleobjects. Notes DocumentationStatement: 85 Lesson12 Physics110HJournal‐2013‐2014 WorkedExamples Score(3) Studythegivenproblemandsolution,thenanswerthequestionsregardingthe problem. STATEMENTOFTHEPROBLEM A2,500‐kgtractorispullinga750‐kgcowoutofaravine,as shown.Ifthetractorappliesaforceof20kN,determinethe accelerationofthecowoutoftheravine.Assumetheropeand pulleyaremasslessandtheropedoesnotstretch. STRATEGY There are multiple components in this problem (tractor, rope, pulley, and cow), so we need first to determine which objects are of interest. Once we have identified the objects of interest, we will draw free-body diagrams for each and apply Newton’s Second Law (N2L). IMPLEMENTATION For this problem, we are only interested in the tractor and the cow since the rope and pulley are massless. Let’s draw free-body diagrams for each object and apply Newton’s Second Law, summing the forces acting on each object. This operation will give us separate equations that include forces and accelerations. Since the objects are connected by a massless rope that does not stretch, the magnitudes of the tensions and accelerations are the same. We can then solve for the unknown acceleration. CALCULATION The net force on the tractor in the x-direction is: DocumentationStatement: 86 Physics110HJournal‐2013‐2014 Lesson12 The net force on the cow in the y-direction is: Combining these two equations gives: Solving for acceleration: Substituting in values gives an acceleration of: 20000N 750kg 750kg ∙ 9.8 2500kg 3.9m/s SELF‐EXPLANATIONPROMPTS 1. Explainwhytheaccelerationofthetractorinthex‐directionisthesameastheaccelerationof thecowinthey‐direction. 2. Explainwhytheweightofthecowisanegativequantity. 3. Ifthetractorcouldonlyapplya2kNforce,calculatetheaccelerationofthecow.Describethe motionofthecow+tractorsystemforthisscenario. DocumentationStatement: 87 Lesson12 Physics110HJournal‐2013‐2014 Pre‐ClassProblem STATEMENTOFTHEPROBLEM A10‐kgcartisconnectedbyastringtoa10‐kgweightoverapulley. Assumingthatthemassesofthestringandthepulleycanbeneglected, findtheaccelerationofthecartandthetensioninthestring. Free‐BodyDiagramoftheCart(required) Free‐bodyDiagramoftheWeight(required) Answers:4.9m/s2,49N DocumentationStatement: 88 Physics110HJournal‐2013‐2014 Lesson12 PreflightQuestions 1. Whattopicfromthereadingwouldyouliketodiscussduringclass? 2. Abucketattachedtoaropeisraisedoutofawellataconstantspeed.Whatcanbesaidabout thetensionintheropecomparedtotheweightofthebucket? a) Tensionislessthantheweightofthebucket. b) Tensionisequaltotheweightofthebucket. c) Tensionisgreaterthantheweightofthebucket. d) Cannotbedeterminedfromthegiveninformation. 3. InCase1,BlockBacceleratesBlockAacrossafrictionlesstable.InCase2,aforceof98N acceleratesBlockAacrossthesametable.TheaccelerationofBlockAis A A a) zero. 10kg 10kg b) greaterinCase1. c) greaterinCase2. d) thesameinbothcases. Case1 Case2 B 10kg 4. CRITICALTHINKING:Whenyouareinanelevatoryouoftenfeelalittlelighterastheelevator startstomovedownward.ExplainthisfeelingbasedonNewton’sLaws. DocumentationStatement: 89 98 N Lesson12 Physics110HJournal‐2013‐2014 HomeworkProblems 5.19 DocumentationStatement: 90 Physics110HJournal‐2013‐2014 Lesson12 5.21 DocumentationStatement: 91 Lesson12 Physics110HJournal‐2013‐2014 5.71 DocumentationStatement: 92 Physics110HJournal‐2013‐2014 Lesson13 Lesson13 Lab3–Newton’sLaws Reading 5.2,Lab3Handout Examples 5.4 HomeworkProblems MP,MP,MP ThereisaLABthislesson. LearningObjectives [Obj23] UseNewton’slawsofmotiontosolveproblemsinvolvingmultipleobjects. Notes DocumentationStatement: 93 Lesson13 Physics110HJournal‐2013‐2014 Pre‐LabQuestions Score(5) 1. Brieflydescribewithoneortwocompletesentencesthepurposeandgoalsofthis lab. 2. Constructfree‐bodydiagramsform1andm2forthefollowingscenario. Free‐BodyDiagram:Mass1 Free‐BodyDiagram:Mass2 3. UseNewton’ssecondlawtoderiveanexpressionfortheaccelerationofthemassesintermsof m1,m2,θ,andg. DocumentationStatement: 94 Physics110HJournal‐2013‐2014 Lesson13 LabNotes DocumentationStatement: 95 Lesson13 Physics110HJournal‐2013‐2014 HomeworkProblems MP DocumentationStatement: 96 Physics110HJournal‐2013‐2014 Lesson13 MP DocumentationStatement: 97 Lesson13 Physics110HJournal‐2013‐2014 MP DocumentationStatement: 98 Physics110HJournal‐2013‐2014 Lesson14 Lesson14 Newton’sLawsinCircularMotion Reading 5.3 Examples 5.5,5.6,5.7 HomeworkProblems 5.65,5.73,MP ThereisanEXAM‐PREPQUIZthislesson. LearningObjectives [Obj16] Explainwhyuniformcircularmotioninvolvesacceleration. [Obj17] Solveproblemsinvolvinguniformandnonuniformcircularmotion. [Obj22] UseNewton’slawsofmotiontosolveproblemsinvolvingmultipleforcesactingona singleobject. Notes DocumentationStatement: 99 Lesson14 Physics110HJournal‐2013‐2014 WorkedExample Score(3) Studythegivenproblemandsolution,thenanswerthequestionsregardingthe problem. STATEMENTOFTHEPROBLEM Anamusementparkrideconsistsofaverticalloopwhosediameteris 15mandasmall150‐kgcartthatrunsontheinsidetrackintheloop. Therideisdesignedtocarryamaximumloadof320kg. Thecartisgivenaninitialspeedatthebottomofthetrackandisnot propelledfurther.Whenthecartclimbsverticallytothe90°point,its speedis12.4m/s.Whatisthemagnitudeanddirectionofthenetforce onthecartatthispoint? STRATEGY The cart is subject to the force of gravity, which is equal to its mass times the acceleration due to gravity, 9.8 m/s2 vertically down. The cart also is subject to a normal force from the track that is directed towards the center of the loop and acts like a centripetal force. We add the two force vectors to obtain the net force. IMPLEMENTATION Normal force: directed horizontally to the left. Force due to gravity (weight) directed vertically downward. 1. The magnitude of the net force is 2. The direction of the net force is at an angle tan tan below the horizontal. The net force is causing the cart to slow down as it climbs to track. DocumentationStatement: 100 Physics110HJournal‐2013‐2014 Lesson14 CALCULATION 1. 3410 2. θ = 25.4 degrees below horizontal, to the left towards the center of the loop. SELF‐EXPLANATIONPROMPTS 1. Drawfree‐bodydiagramsofthecartwhenitisatthebottomandtopofthetrack. 2. Doesthecarttravelaroundtheloopataconstantspeed?Explain. 3. Describehowtheweight,normalforceandnetforcechangeasthecartmovesaroundthetrack. DocumentationStatement: 101 Lesson14 Physics110HJournal‐2013‐2014 Pre‐ClassProblem STATEMENTOFTHEPROBLEM A50‐kgwrecker’sballishangingonan8‐mropethatcansupportamaximumforceof1000N.If theballisswunginaverticalcircle,whatisfastestspeeditcanhaveatthelowestpointsuchthat theropewon’tbreak? Answer:9.0m/s DocumentationStatement: 102 Physics110HJournal‐2013‐2014 Lesson14 PreflightQuestions 1. Whattopicfromthereadingwouldyouliketodiscussduringclass? 2. Anobjectmovesataconstantspeedinacircularpath.Theinstantaneousvelocityandthe instantaneousaccelerationvectorsare a) bothtangenttothecircularpath. b) bothperpendiculartothecircularpath. c) perpendiculartoeachother. d) oppositetoeachother. e) noneoftheabove. 3. Aballonastringmovesaroundaverticalcircle.Atthebottomofthecircle, thetensioninthestring a) isgreaterthantheweightoftheball. b) islessthantheweightoftheball. c) isequaltotheweightoftheball. d) maybegreaterorlessthantheweightoftheball. 4. CRITICALTHINKING:Thefigureshownisaviewlookingdownonahorizontaltabletop.Aball rollsalongthegraybarrierwhichexertsaforceontheball,guidingitsmotioninacircularpath. Aftertheballceasescontactwiththebarrier,describethemotionoftheballandyour reasoning. DocumentationStatement: 103 Lesson14 Physics110HJournal‐2013‐2014 HomeworkProblems 5.65 DocumentationStatement: 104 Physics110HJournal‐2013‐2014 Lesson14 5.73 DocumentationStatement: 105 Lesson14 Physics110HJournal‐2013‐2014 MP DocumentationStatement: 106 Physics110HJournal‐2013‐2014 Lesson15 Lesson15 Newton’sLawswithFriction Reading Examples HomeworkProblems 5.4,5.5 5.9,5.10,5.11 5.43,MP,5.57 LearningObjectives [Obj24] [Obj25] Differentiatebetweentheforcesofstaticandkineticfrictionandsolveproblems involvingbothtypesoffriction. Describedragforcesqualitatively andquantitatively. Notes DocumentationStatement: 107 Lesson15 Physics110HJournal‐2013‐2014 WorkedExample Score(3) Studythegivenproblemandsolution,thenanswerthequestionsregardingthe problem. STATEMENTOFTHEPROBLEM Ateamofdogsispullingtwoconnectedsledswithanaccelerationof2.3m/s2.Thepassengersled, connectedtothedogsinfront,hasamassof96kg;thecargosled,tiedbehindthepassengersled, hasamassof42kg.Thecoefficientofkinetic frictionbetweenthesteelrunsonthesledsand theiceisμ=0.007.Howmuchforcedoesthe dogteamexertonthesledtrain? STRATEGY The accelerating sleds are subject to Newton’s Second Law (N2L), which states that the acceleration of an object is proportional to the applied force and inversely proportional to the mass of the accelerating object. We apply N2L to the sled train with the combined mass of 138 kg and solve the resulting equation for the unknown applied force, including the frictional force which acts opposite the direction of motion. IMPLEMENTATION Let’s label the force exerted by the dog team d. Let’s label the force exerted on the cargo sled by passenger sled cp. Let’s label the force exerted on the passenger sled by cargo sled pc. Let’s label the force exerted by the kinetic friction k CALCULATION The net force on the sled team in the x-direction is: The net force on the sled team in the y-direction is: DocumentationStatement: 108 on both sleds. Physics110HJournal‐2013‐2014 Lesson15 The acceleration in the y-direction is zero, so the normal force is: The kinetic force is given by: f μn Substituting into the equation of the net force in the x-directions gives: F μw m a 42 kg 96 42 kg 2.3m/s CALCULATION 0.007 96 F F 320N in the forward direction. SELF‐EXPLANATIONPROMPTS 1. InLesson10wesolvedthesameproblem,butwithoutfriction.Explainhowthemethod changeswhenfrictionisincluded. 2. Explainwhykineticfrictionwasusedintheproblemratherthanstaticfriction. 3. Describethestepsusedtodeterminethekineticfriction. DocumentationStatement: 109 Lesson15 Physics110HJournal‐2013‐2014 Pre‐ClassProblem STATEMENTOFTHEPROBLEM A60‐kgblockisreleasedfromrestona45°rampwherethecoefficientoffrictionbetweenthe blockandrampis0.4.Whatistheaccelerationoftheblock? Tryit!(1pt):Determinethespeedoftheblockatthebottomoftheramp ifitstartsfromrestatthetopofthe3‐mlongramp.Showyourwork. DocumentationStatement: 110 Answer:4.2m/s2 Physics110HJournal‐2013‐2014 Lesson15 PreflightQuestions 1. Whattopicfromthereadingwouldyouliketodiscussduringclass? 2. Whichstatementconcerningfrictionistrue? a) Staticfrictionisalwaysoppositethedirectionofmotion. b) Kineticfrictionisalwaysoppositethedirectionofmotion. c) Bothstaticandkineticfrictionarealwaysoppositethedirectionofmotion. d) Neitherisalwaysoppositethedirectionofmotion. 3. Aboxisatrestontheflatbedofamovingtruck.Dawn appliesthebrakesabruptlyandtheboxbeginstoslide. Whichfree‐bodydiagramcorrectlydepictstheforces actingontheboxanditsresultingmotion? a) c) b) d) 4. CRITICALTHINKING:Describe,inyourownwords,thedifferencebetweenstaticfrictionforces andkineticfrictionforces. DocumentationStatement: 111 Lesson15 Physics110HJournal‐2013‐2014 HomeworkProblems 5.43 DocumentationStatement: 112 Physics110HJournal‐2013‐2014 Lesson15 MP DocumentationStatement: 113 Lesson15 Physics110HJournal‐2013‐2014 5.57 DocumentationStatement: 114 Physics110HJournal‐2013‐2014 Lesson16 Lesson16 CriticalThinking:Newton’sLaws withNon‐constantMass Reading Examples HomeworkProblems 9.3Application,Handout None 5.30,5.62,6.54 LearningObjectives [Obj18] Explaintheconceptofforceandhowforcescausechangeinmotion. Notes DocumentationStatement: 115 Lesson16 Physics110HJournal‐2013‐2014 Notes DocumentationStatement: 116 Physics110HJournal‐2013‐2014 Lesson16 PreflightQuestions 1. Whattopicsdidyoufindmostchallengingfromthereading? 2. Arocketliftsofffromthelaunchpadandrisesmajesticallyonitsflight.Thethrustoftherocket resultsfrom a) theexhaustgasespushingagainsttheground. b) theexhaustgasespushingagainsttheair. c) thecombustiongasespushingagainsttherocket. d) theequalandoppositereactiontogravitypullingdown. e) thegravitationalenergyreleasedbyburningfuel. 3. Atsomepointbeyondatmosphericspaceshuttleflight,the3‐mainenginesstopproviding thrustandthentheboostertankSEPARATESfromthecraft.Whentheconnectionbetweenthe twoobjectsissevered,thevelocityoftheshuttle a) increases. b) decreases. c) remainsunchanged. d) Theanswerdependsonthemassofthebooster. 4. CRITICALTHINKING:Thespaceshuttleassemblyonthelaunchpadhasamassofabout2 millionkg.Theexhaustvelocityofthepropellantgasesisabout4000m/s.Thegasesare streamingoutofthenozzlesattherateofabout18,000kg/s.Giventhisinformation,estimate theaccelerationofthespaceshuttleassembly. DocumentationStatement: 117 Lesson16 Physics110HJournal‐2013‐2014 HomeworkProblems 5.30 DocumentationStatement: 118 Physics110HJournal‐2013‐2014 Lesson16 5.62 DocumentationStatement: 119 Lesson16 Physics110HJournal‐2013‐2014 MP DocumentationStatement: 120 Physics110HJournal‐2013‐2014 Lesson17 Lesson17 GRADEDREVIEW2 LearningObjectives [Obj18] Explaintheconceptofforceandhowforcescausechangeinmotion. [Obj19] StateNewton’sthreelawsofmotionandgiveexamplesillustratingeachlaw. [Obj20] Explainthedifferencebetweenmassandweight. [Obj21] Constructfree‐bodydiagrams usingvectorstorepresentindividualforcesacting onan object,andevaluatethenetforceusingvectoraddition. UseNewton’slawsofmotiontosolveproblemsinvolvingmultipleforcesactingona singleobject. UseNewton’slawsofmotiontosolveproblemsinvolvingmultipleobjects. [Obj22] [Obj23] [Obj24] [Obj25] Differentiatebetweentheforcesofstaticandkineticfrictionandsolveproblems involvingbothtypesoffriction. Describedragforcesqualitatively andquantitatively. Notes DocumentationStatement: 121 Lesson17 Physics110HJournal‐2013‐2014 Lesson9:“Areyouready?” Readtheproblembelowandworkthroughtheguidedsolution,thenanswerthequestions regardingtheproblem. STATEMENTOFTHEPROBLEM A1000‐kgcaristravelingat10m/swhenabrakingforceof500Nisapplied.Howmuchtimedoes elapsebeforethecarcomestoacompletestop? STRATEGY(Fillintheblanks.) Newton’s Second Law as applied to the car states that the acceleration of the car by is given . We know the mass of the car and the net force, so we can get the deceleration of the car applying Newton’s Second Law. We can then use kinematics to find the stopping time. CALCULATION(Fillintheblanks.) 0.5 . ___________ 20 SELF‐EXPLANATIONPROMPTS 1.Comparethisexampletothetow‐truckexample,stepbystep. 2.Wecalculatedtheaccelerationtobe–0.5m/s2.Whatdoestheminussignindicateaboutthe car’sacceleration? OptionalPracticeProblems:4.13,4.15,4.23 DocumentationStatement: 122 Physics110HJournal‐2013‐2014 Lesson17 Lesson10:“Areyouready?” Readtheproblembelowandworkthroughtheguidedsolution,thenanswerthequestions regardingtheproblem. STATEMENTOFTHEPROBLEM OnJuly16,1969,aSaturnVrocketliftedoffthepadinFloridaonmankind’sfirsttriptothesurface oftheMoon.Thefully‐loadedrockethadamassof2.8x106kg.Topropelitselfupwardit generated34.5x106Nofthrust.Whatwastheinitialaccelerationoftherocket? STRATEGY(Fillintheblanks.) We calculate the acceleration by dividing the net force on the rocket by its mass, / . There is an upward force on the rocket from the thrust of its engines, and a downward force, the weight of the rocket, from gravity acting on the rocket. The net upward force is therefore thrust minus weight. CALCULATION(Fillintheblanks.) The weight of the rocket is ________ 27,440,000N The net upward force on the rocket is __________ __________ 7,060,000N The initial acceleration of the rocket is 2.52m/s . SELF‐EXPLANATIONPROMPTS 1.Whatwouldbetheaccelerationofarocketofthesamemassifitstartedfromrestinempty space,awayfromobjectsthatexertgravitationalforceslikeEarth? 2.Furtherintothelift‐off,wouldyouexpecttheSaturn’saccelerationtoincrease,decrease,or remainthesame? 3.WhatmagnitudeofthrustwouldmaketheSaturnjusthover,withnoacceleration? OptionalPracticeProblems:4.27,4.37,4.45 DocumentationStatement: 123 Lesson17 Physics110HJournal‐2013‐2014 Lesson11:“Areyouready?” Readtheproblembelowandworkthroughtheguidedsolution,thenanswerthequestions regardingtheproblem. STATEMENTOFTHEPROBLEM 58° A5‐kgballissuspendedfromthreeropesasshowninthepicture.Whatistheforce exertedonthewallbythehorizontalrope? STRATEGY(Fillintheblanks.) Apply Newton’s Second Law to the junction of the three ropes. The system is not accelerating, so the vector sum of the forces is zero. Decompose the forces into components and solve for the unknown force. IMPLEMENTATION(Fillintheblanks.) The forces acting on the vertical rope are: ________, _______, and _______. The net force in the x-direction is: _____________________ The net force in the y-direction is: ____________________ Since _______ = 0, the equation relating the forces _______ ________ , , and the weight of the ball is: 0 CALCULATION Solving the two equations gives us T1 = 8.00 N SELF‐EXPLANATIONPROMPTS 1.IsitpossibletosuspendtheballinthisexampleinsuchawaythatbothforcesT1andT2have horizontalcomponentsonly?Explain. 2.Arethemagnitudesofanyofthetensionsinthethreeropeslargerthantheweightoftheball? OptionalPracticeProblems:5.15,5.33,5.36 DocumentationStatement: 124 Physics110HJournal‐2013‐2014 Lesson17 Lesson12:“Areyouready?” Readtheproblembelowandworkthroughtheguidedsolution,thenanswerthequestions regardingtheproblem. STATEMENTOFTHEPROBLEM Twoballswithmasses,M1andM2,areconnectedbyaropewhichpasses overapulleyasshown.Findtheaccelerationsoftheballsastheyare releasedfromrest.Assumethattheropedoesnotstretchandthemasses oftheropeandthepulleyarenegligiblecomparedtothemassesofthe balls. STRATEGY(Fillintheblanks.) We draw free-body diagrams for the two balls and apply Newton’s Second Law to each. Since the rope does not stretch, the magnitudes of the balls’ accelerations are the same CALCULATION(Fillintheblanks.) The net force in the x-direction is for M1 is : ______________________ The net force in the y-direction for M2 is: ∑ _____________________ 3. The eqns in 1 and 2 above have two unknowns: a and T. Combining these equations and eliminating tensions, gives SELF‐EXPLANATIONPROMPTS 1.Explaininyourownwordswhythemagnitudesoftheaccelerationsofthetwoballsarethesame. 2.Whyisthemagnitudeofthetensionintheropeontheleftsideofthepulleythesameasthe magnitudeontherightsideofthepulley? OptionalPracticeProblems:5.18,5.19,5.20 DocumentationStatement: 125 Lesson17 Physics110HJournal‐2013‐2014 Lesson14:“Areyouready?” Readtheproblembelowandworkthroughtheguidedsolution,thenanswerthequestions regardingtheproblem. STATEMENTOFTHEPROBLEM A1300‐kgcarisroundingacurveonaflathorizontalroadway.Thecaristravelingat13.4m/sand slowingdownat2m/s2.Theradiusofthecurveis30meters.Thecoefficientofstaticfrictionis 0.80,andthecoefficinetofkineticfrictionis 0.40. Whatisthenetforceofthecar,magnitudeanddirection? STRATEGY(Fillintheblanks.) The car is slowing down which means it has a force directed opposite to its motion. Since this direction is tangent to the road, it is called the tangential force . The car is also changing direction which means it has a radial force caused by friction between the tires and the road, . This force is directed towards the center of the curve. . and The net force is the vector sum of . CALCULATION(Fillintheblanks.) 1. Tangential force is 2. Force of friction is 3. Net force is __________ . √_____ ___________ _____ The direction is _____________________________. SELF‐EXPLANATIONPROMPTS 1.Whydidwenotneedcoefficientoffrictionforthisproblem? 2.Whatisthemagnitudeanddirectionofthenetforceifthecarroundsthecurveatconstant speed? OptionalPracticeProblems:5.27,5.37,5.41 DocumentationStatement: 126 Physics110HJournal‐2013‐2014 Lesson17 Lesson15:“Areyouready?” Readtheproblembelowandworkthroughtheguidedsolution,thenanswerthequestions regardingtheproblem. STATEMENTOFTHEPROBLEM Amanispushinga50‐kgcartthatacceleratesat1.3m/s2onlevelgroundwherethecoefficientof frictionbetweenthewheelsandthegroundis0.03.Howmuchresistancefromthecartdoeshe feel? STRATEGY(Fillintheblanks.) First, we apply Newton’s Second Law to determine the force needed to accelerate the cart. Then, we use Newton’s Third Law to determine the frictional force. CALCULATION The net force in the x-direction for the cart is: _____________________ The net force in the y-direction for the cart is: ______________________ The force exerted on the cart by the man = _____________ x _____________ = 79.7 N in the forward direction. The force exerted on the man by the cart = _____________ in the ____________ direction. SELF‐EXPLANATIONPROMPTS 1.Whydon’ttheforceonthecartandtheforceonthemancancelout?Thatis,whydoesthe mathematicallycorrectstatement, 79.7 – 79.7 0,notimplythatthenetforceintheabove scenarioiszero? 2.Whattypeoffrictionalforceactsonthecart:kineticorstatic?Explain. OptionalPracticeProblems:5.29,5.43,5.49 DocumentationStatement: 127 Lesson17 Physics110HJournal‐2013‐2014 Notes DocumentationStatement: 128 Physics110HJournal‐2013‐2014 Lesson18 Lesson18 WorkwithConstantandVaryingForces Reading 6.1,6.2 Examples 6.1– 6.5 HomeworkProblems 6.18,6.20,6.52 ThereisanoptionalEquationDictionaryentryinAppendixDforthislesson(1PFpt). LearningObjectives [Obj26] Explainthephysicsconceptofwork. [Obj27] Evaluatetheworkdonebyconstantforcesandbyforcesthatvarywithposition. Notes DocumentationStatement: 129 Lesson18 Physics110HJournal‐2013‐2014 WorkedExample Score(3) Studythegivenproblemandsolution,thenanswerthequestionsregardingthe problem. STATEMENTOFTHEPROBLEM Amandragsa50‐kgcrate10macrossaroughhorizontalsurface,wherethecoefficientofkinetic friction,μ ,betweenthecrateandthesurfaceis0.3.Hepullsatconstantspeedanddirectshis pullingforce20°upwardfromthehorizontal.Howmuchworkdoesheperform? STRATEGY Work done by a force is defined as the dot product of the applied force and the displacement: ⋅∆ ,where θ is the angle between the direction of the ∆ force vector and the direction of the displacement vector. To find the work done by the man, we find the force he applies to the crate, the displacement, and θ, then compute the dot product between work and displacement. IMPLEMENTATION Free‐BodyDiagramofCrate Since the crate is moving at constant speed, (acceleration is zero), the net force on the crate must be zero. The net force on the crate is the vector sum of the force applied by the man friction and the force of kinetic . Note that the force of friction depends on the direction of the man’s force because the man’s force affects the normal force (unless he pulls horizontally.) The force of kinetic friction = (coefficient of friction) (normal force) Since there is no acceleration, the x-component of Fm must equal fk, Thus, DocumentationStatement: 130 Physics110HJournal‐2013‐2014 Lesson18 Solving for Fm we get cosθ The work done by Fm is then ∙∆ Δ CALCULATION SELF‐EXPLANATIONPROMPTS 1.Startwiththedefinition zero. cosθ ∙∆ Δ 1325J ∆ cos andexplainhowWcanbepositive,negative,or 2.Explainwhatitmeanstohave(a)positiveWand(b)negativeW. 3.Intheexample,youaretoldthatthenormalforceis: neededtoobtainthenormalforceandthenshowthecalculation. DocumentationStatement: 131 .Describethesteps Lesson18 Physics110HJournal‐2013‐2014 Pre‐ClassProblem STATEMENTOFTHEPROBLEM Acranelowersa120‐kgrockatconstantspeedthroughaverticaldistanceof5meters.Howmuch workdoesthecraneperform? Free‐BodyDiagramofRock(required) Answer:‐5880J DocumentationStatement: 132 Physics110HJournal‐2013‐2014 Lesson18 PreflightQuestions 1. Whattopicfromthereadingwouldyouliketodiscussduringclass? 2. Solveforwork andrankorderfromsmallest(negative)tolargest(positive)theworkdonein thefollowingcases: 2m 2m 10N 10N 32° 112° 2m 10 N 10 N 4m CaseA CaseB CaseC CaseD RankOrder:Smallest(1)_____(2)_____(3)_____(4)_____Largest 3. Twoidenticalobjectsareeachdisplacedthesamedistance,oneby aforce pushinginthedirectionofmotionandtheotherbya force2 pushingatanangle relativetothedirectionofmotion. Theworkdonebythetwoforcesisthesame.Whatistheangle ? (Hint:SeeGOTIT?6.1.) 2 a) b) c) d) 0° 30° 45° 60° 4. CRITICALTHINKING:Aweightlifterpicksupabarbelland(1)liftsitchesthigh,(2)holdsitfor 30seconds,and(3)putsitdownslowly(butdoesnotdropit).Rankorderfromsmallestto largestthework theweightlifterperformsduringthesethreeoperations.Labelthe quantitiesas , ,and .Justifyyourrankingorder. DocumentationStatement: 133 Lesson18 Physics110HJournal‐2013‐2014 HomeworkProblems 6.18 DocumentationStatement: 134 Physics110HJournal‐2013‐2014 Lesson18 6.20 DocumentationStatement: 135 Lesson18 Physics110HJournal‐2013‐2014 6.52 DocumentationStatement: 136 Physics110HJournal‐2013‐2014 Lesson19 Lesson19 KineticEnergyandPower Reading Examples HomeworkProblems 6.3,6.4 6.6,6.7,6.9 6.29,6.64,6.71 LearningObjectives [Obj28] Explaintheconceptofkineticenergyanditsrelationtowork. [Obj29] Explaintherelationbetweenenergyandpower. [Obj34] Solveproblemsbyapplyingthework‐energytheorem,conservationofmechanical energy,orconservationofenergy. Notes DocumentationStatement: 137 Lesson19 Physics110HJournal‐2013‐2014 WorkedExample Score(3) Studythegivenproblemandsolution,thenanswerthequestionsregardingthe problem. STATEMENTOFTHEPROBLEM A3,000‐kgsailboatistravellingat25m/swhenaconstantnetforceof1200Nstartsactingonit,in thedirectionofmotion.Whatisthespeedoftheboatafterithastravelled200mundertheaction ofthisforce? STRATEGY When a force acts on a moving object, work is done on the object. The work done on the object results in the change of the object’s kinetic energy K, defined as 1 2 where m is the mass of the object and v is its speed. The net work done on the object and the change in the kinetic energy are related by the work-energy theorem 1 2 ∆ 1 2 To find the answer to the question posed in the problem: 1. we find the net work done on the boat, 2. set it equal to the change in kinetic energy of the boat, and 3. solve the resulting equation for the unknown final speed. IMPLEMENTATION 1. Net work: 2. 3. ∙ Δ ∆ cos DocumentationStatement: 138 Physics110HJournal‐2013‐2014 Lesson19 CALCULATION 1200N 200m cos 0° 240,000Nm 480,000J 240,000J joules 3000kg 25 3000kg m s m 28 s SELF‐EXPLANATIONPROMPTS 1. Statethework‐energytheoreminyourownwords. 2. TheworkdonebyaconstantforceF,actingalongthedirectionofmotionoveradistanceΔx equals .Fromkinematics,weknowthatifanobjectstartsfromrestandaccelerateswith accelerationaoveradistanceΔx,2 ∆ ;andfromNewton’sSecondLaw,weknowthat .Combinethethreeequationsandshowthattheworkdonebytheforceequals . 3. Usethesameprocedureasabovetoshowthattheworkdonetoincreasethespeedofmassm fromv1tov2isequaltothechangeinitskineticenergy. DocumentationStatement: 139 Lesson19 Physics110HJournal‐2013‐2014 Pre‐ClassProblem STATEMENTOFTHEPROBLEM Galileoissaidtohavedroppedtwoobjectsofdifferentmassfromatalltowertoshowthatall objectsfallwiththesamespeed.Ifyoudroptwomasses,m1andm2,fromthesameheighth,do theyreachthegroundwiththesamekineticenergy? CalculatethedifferenceintheirkineticenergiesΔK. Answer: ∆ DocumentationStatement: 140 Physics110HJournal‐2013‐2014 Lesson19 PreflightQuestions 1. Whattopicfromthereadingwouldyouliketodiscussduringclass? 2. Twocars,onefourtimesasheavyastheother,areatrestonafrictionlesshorizontaltrack. Equalforcesactoneachofthesecarsforadistanceofexactly5m.Thekineticenergyofthe lightercarwillbe_______thekineticenergyoftheheaviercar. a) one‐quarter b) one‐half c) equalto d) twice e) fourtimes 4. Whichofthefollowingistrue? a) NeitherΔKnorWnetcaneverbenegative. b) Wnetcanneverbenegative,butΔKcanbenegativeorpositive. c) ΔKcanneverbenegative,butWnetcanbenegativeorpositive. d) ΔKandWnetcanbenegativeorpositive. 5. CRITICALTHINKING:OnMondayyourunupthestairstothetopfloorofatallbuilding.You runataconstantspeed.OnTuesdayyouwalktothetop,alsoatconstantspeed.On Wednesdayyoutakeaconstantspeedelevator.Howdotheamountsofworkyoudidgettingto thetopofthebuildingeachdaycompare?Howdoesthepowercompare? DocumentationStatement: 141 Lesson19 Physics110HJournal‐2013‐2014 HomeworkProblems 6.29 DocumentationStatement: 142 Physics110HJournal‐2013‐2014 Lesson19 6.64 DocumentationStatement: 143 Lesson19 Physics110HJournal‐2013‐2014 6.71 DocumentationStatement: 144 Physics110HJournal‐2013‐2014 Lesson20 Lesson20 PotentialEnergy Reading Examples HomeworkProblems 7.1,7.2 7.1,7.2 7.14,7.31,7.42 LearningObjectives [Obj30] Explainthedifferences betweenconservativeandnonconservativeforces. [Obj31] Evaluatetheworkdonebybothconservativeandnonconservativeforces. [Obj32] Explaintheconceptofpotentialenergy. [Obj33] Evaluatethepotentialenergyassociatedwithaconservativeforce. Notes DocumentationStatement: 145 Lesson20 Physics110HJournal‐2013‐2014 WorkedExample Score(3) Studythegivenproblemandsolution,thenanswerthequestionsregardingthe problem. STATEMENTOFTHEPROBLEM Averticalspringwithaspringconstantk=150N/miscompresseddown1.5m.A2‐kgballis placedonthecompressedspringandreleasedfromrest.Whatheightdoestheballreachafteritis released? STRATEGY This problem involves two examples of potential energy: the elastic energy of a compressed (or stretched) spring and the gravitational potential energy as an object moves from one elevation to another. An object is said to possess potential energy if, because of its condition, it can generate kinetic energy. A ball on a spring, for example, can be propelled by the force of the spring and gain kinetic energy. A ball can be dropped from a height and be propelled by the force of gravity and gain kinetic energy. Potential energy is traditionally denoted by the symbol U. The change in the elastic potential energy as a spring’s vertical extension changes from y1 to y2 is given by 1 2 Δ 1 2 The change in the gravitational potential energy as an object of mass m moves from height y2 to height y3 is given by Δ We solve the problem by comparing the energy imparted to the ball by the compressed spring to the energy lost by the ball as it climbs against the force of gravity. Symbolically Δ ⇒ ⇒Δ IMPLEMENTATION 1 2 1 2 DocumentationStatement: 146 Physics110HJournal‐2013‐2014 Lesson20 CALCULATION First, we are given the following quantities: y1 = 0 m y2 = − 1.5 m m = 2 kg k = 150 N/m g = 9.8 m/s2 Let’s set up a vertical coordinate axis with y1 = 0 at the position of the unstretched spring. Now, we solve for y3 – y2 in 1 2 1 2 8.6m The ball rises 8.6 meters above the top of compressed spring. SELF‐EXPLANATIONPROMPTS 1.Thepotentialenergystoredinacompressedspringcomesfromtheworkdonebycompressing thespringagainstitsrestoringforceF=−ky.Calculatethatworkandverifytheaboveexpression ofthespringpotentialenergyUs. 2.DothesameforthegravitationalpotentialenergyUg. 3.Insolvingtheproblemweignoredthemassofthespring.Includingthemassofthespringis messy,butansweringthefollowingquestionisnot.Howwouldincludingthemassofthespring changetheoutcomeofthecalculation? DocumentationStatement: 147 Lesson20 Physics110HJournal‐2013‐2014 Pre‐ClassProblem STATEMENTOFTHEPROBLEM A2‐kgballisreleasedfromrest3metersaboveanunstretchedspringofwhosespringconstantis 150N/m.Howmuchdoesitcompressthespringbeforeitcomestorest?(Beforeyoustart calculating,carefullydrawthecoordinatesystemandcarefullyidentifyalltherelevantvertical coordinates.Whenyouequatethetwopotentialenergychangesyouwillgetaquadraticequation!) Tryit!(1PFpt):Howhighwouldtheballneedtobereleasedifyou wantedtodoubletheamountthatthespringiscompressed? Showyourwork. DocumentationStatement: 148 Answer:1m Physics110HJournal‐2013‐2014 Lesson20 PreflightQuestions 1. Whattopicfromthereadingwouldyouliketodiscussduringclass? 2. Theenergystoredinacompressedspringdependsontheamountofcompression.Agiven springrequires10.0Jforacompressionof10.0cm.Howmuchtotalenergywouldbestoredifit werecompressedanadditional5.00cm? a) 22.5J b) 12.5J c) 5.00J d) 1.25J e) Cannotbedeterminedfromthegiveninformation. 3. Atrunkofmass isliftedalongacurvedpathoflength toaheight . Anothertrunkwithtwicethemassisslidacrossalevelfloor( 0.5) alongacurvedpathalsohavinglength .Whichisgreater,theworkdone againstfrictionortheworkdoneagainstgravity? a) Moreworkisdoneagainstfriction. b) Moreworkisdoneagainstgravity. c) Theworkdoneagainstfrictionisthesameastheworkdone againstgravity. d) Cannotbedeterminedfromthegiveninformation. 2 4. CRITICALTHINKING:Whycan’twedefinepotentialenergyforfriction?Explain. DocumentationStatement: 149 Lesson20 Physics110HJournal‐2013‐2014 HomeworkProblems 7.14 DocumentationStatement: 150 Physics110HJournal‐2013‐2014 Lesson20 7.31 DocumentationStatement: 151 Lesson20 Physics110HJournal‐2013‐2014 7.42 DocumentationStatement: 152 Physics110HJournal‐2013‐2014 Lesson21 Lesson21 ConservationofMechanicalEnergy Reading 7.3,7.4 Examples 7.4,7.5,7.6 HomeworkProblems 7.24,7.25,7.55 ThereisanoptionalEquationDictionaryentryinAppendixDforthislesson(1PFpt). LearningObjectives [Obj34] [Obj35] Solveproblemsbyapplyingthework‐energytheorem,conservationofmechanical energy,orconservationofenergy. Describetherelationbetweenforceandpotentialenergyusingpotential‐energy curves. Notes DocumentationStatement: 153 Lesson21 Physics110HJournal‐2013‐2014 WorkedExample Score(3) Studythegivenproblemandsolution,thenanswerthequestionsregardingthe problem. STATEMENTOFTHEPROBLEM Note:Beforeworkingwiththisexample,revisitLesson14,whichhasthesameproblemneglecting friction. Anamusementparkrideconsistsofaverticalloopwhosediameteris15mandasmall150‐kgcart thatrunsontheinsidetrackintheloop.Therideisdesignedtocarryamaximumloadof320kg. Ifthecartiscarryingitsmaximumload,howmuchkineticenergymustithaveatthebottomofthe loopifitistonegotiatethetopoftheloopsafely(upsidedown)withoutleavingthetrack? STRATEGY In order not to leave the track at the top of the loop, the cart needs to go fast enough so that its weight provides the centripetal force necessary to just keep it on the track. becomes As the cart climbs up the loop it loses kinetic energy and gains potential energy. The kinetic energies at the bottom and the top are related to the potential energies by Since we know the minimal required kinetic energy at top, we can use the energy conservation equation to find KE at the bottom. DocumentationStatement: 154 Physics110HJournal‐2013‐2014 Lesson21 IMPLEMENTATION 1 2 1 2 If we set the potential energy to be zero at the bottom of the track 2 The energy conservation equation then becomes 1 2 2 0 CALCULATION 1 2 SELF‐EXPLANATIONPROMPTS 2.5 86,000J 1. Stateinyourownwordswhatwemeanby“conservationprinciple.” 2. Whycanthezeropointofpotentialenergybechosenarbitrarily? 3. Sketchanenergybarchart(similartothoseinFigure7.8inyourtextbook)forthecartat(a) thetopofthetrackand(b)atthebottomofthetrack. Energy→ Energy→ 0 0 DocumentationStatement: 155 Lesson21 Physics110HJournal‐2013‐2014 Pre‐ClassProblem STATEMENTOFTHEPROBLEM A50‐kgwrecker’sballishangingonan8‐mropethatcansupportamaximumforceof1000N.If theballisswunginverticalcircle,whatisfastestspeeditcanhaveatthelowestpoint,suchthatthe ropewon’tbreak? Answer:9m/s DocumentationStatement: 156 Physics110HJournal‐2013‐2014 Lesson21 PreflightQuestions 1. Whattopicfromthereadingwouldyouliketodiscussduringclass? 2. Abottledroppedfromabalconystrikesthegroundwithaparticularspeed.To doublethespeedatimpact,youwouldhavetodropthebottlefromabalconythat is a) twiceashigh. b) threetimesashigh. c) fourtimesashigh. d) eighttimesashigh. 3. Atruckinitiallyatrestatthetopofahillisallowedtorolldown.Atthebottom,itsspeedis 14m/s.Next,thetruckisagainrolleddownthehill,butthistimeitdoesnotstartfromrest.It hasaninitialspeedof14m/satthetopbeforeitstartsrollingdownthehill.Howfastisitgoing whenitgetstothebottom? a) b) c) d) e) 14m/s 17m/s 20m/s 24m/s 28m/s 4. CRITICALTHINKING:Askydiverwhoseparachuteisfullydeployedisdescendingatconstant speed.Describewhatishappeningtoherkineticenergy,herpotentialenergyandhertotal mechanicalenergyasshefalls.Isanyworkbeingdone?Ifyes,wheredoesitgo? DocumentationStatement: 157 Lesson21 Physics110HJournal‐2013‐2014 HomeworkProblems 7.24 DocumentationStatement: 158 Physics110HJournal‐2013‐2014 Lesson21 7.25 DocumentationStatement: 159 Lesson21 Physics110HJournal‐2013‐2014 7.55 DocumentationStatement: 160 Physics110HJournal‐2013‐2014 Lesson22 Lesson22 Lab4‐ConservationofEnergy Reading 7.3,Lab4Worksheet Examples 7.5 HomeworkProblems 7.56,7.59,7.63 ThereisaLABthislesson. LearningObjectives [Obj34] Solveproblemsbyapplyingthework‐energytheorem,conservationofmechanical energy,orconservationofenergy. Notes DocumentationStatement: 161 Lesson22 Physics110HJournal‐2013‐2014 Score(5) Pre‐LabQuestions Inthislab,aspringiscompressedadistancexandusedtolaunchacartofmassMalonga perfectlyhorizontalairtrack.Thespeedofthecart,v,ismeasuredsomedistancedowntheair trackandusedtocalculatethespringconstant,k(refertothelabhandoutandExample7.4inthe textbook). 1. Usetheprincipleofconservationofmechanicalenergytofindanexpressionforthespeedof thecartasafunctionofthecompressiondistance. a) b) c) d) 2 2 2. WhengraphingthedatainPartII,youareaskedtoplotvvs.x.Describetheshapeofthe plotandexplainwhyitmakessensetoplotthedatainsuchaway. 3. Afterplottingvvs.x,yourgroupdeterminesthattheslopeofthebest‐fitlinethroughthe datapointsis50s‐1.Iftheaircarthasamassof0.50kg,thespringconstantkis a) 25N/m b) 50N/m c) 1250N/m d) Cannotbedeterminedwiththegiveninformation. DocumentationStatement: 162 Physics110HJournal‐2013‐2014 Lesson22 LabNotes DocumentationStatement: 163 Lesson22 Physics110HJournal‐2013‐2014 HomeworkProblems 7.56 DocumentationStatement: 164 Physics110HJournal‐2013‐2014 Lesson22 7.59 DocumentationStatement: 165 Lesson22 Physics110HJournal‐2013‐2014 7.63 DocumentationStatement: 166 Physics110HJournal‐2013‐2014 Lesson23 Lesson23 OrbitalMotion Reading 8.1– 8.3 Examples 8.1,8.2,8.3 HomeworkProblems 8.17,8.39,MP ThereisanoptionalEquationDictionaryentryinAppendixDforthislesson(1PFpt). LearningObjectives [Obj36] Explaintheconceptofuniversalgravitation. [Obj37] Solveproblemsinvolvingthegravitationalforcebetweentwoobjects. [Obj38] Determinethespeed,acceleration,andperiodofanobjectincircularorbit. Notes DocumentationStatement: 167 Lesson23 Physics110HJournal‐2013‐2014 WorkedExample Score(3) Studythegivenproblemandsolution,thenanswerthequestionsregardingthe problem. STATEMENTOFTHEPROBLEM Aspacecraftisorbiting200kmabovethesurfaceoftheplanetMars.Oneoftheastronautson boarddropsapen.HowfastdoesthepenfallrelativetothesurfaceofMars?Howfastdoesthe penfallrelativetotherestofthespacecraft? STRATEGY The spacecraft is in orbit about mars, meaning that it is traveling in a circular path 200 km above the surface of Mars. Since the orbit is circular, the motion of the spacecraft (and everything on board it including the pen) is undergoing centripetal motion; the acceleration is therefore centripetal acceleration. IMPLEMENTATION 1. What is the orbital radius of the spacecraft? 2. What is the gravitational force? By combining the gravitational force with Newton’s Second Law, we can find the acceleration of the spacecraft and everything on board. CALCULATION 1. 3,389km 200km 3589km 2. Combining the gravitational force, law, ; with Newton’s Second , we find the magnitude acceleration, 3.32 . The entire space craft and everything inside is accelerating at the same rate, so the pen will not appear to fall. DocumentationStatement: 168 Physics110HJournal‐2013‐2014 Lesson23 SELF‐EXPLANATIONPROMPTS 1.Whichdirectionisthespacecraftacceleratingandtowhichobjectsdoesthevalueofacceleration, 3.32 ,apply? 2.Howisthequantity“r”definedintheequationforuniversalgravitation?Useyourdefinitionto intheexample. justifywhy 3.Ifthepenisaccelerating,explainwhyitisconsideredtobein“freefall”. DocumentationStatement: 169 Lesson23 Physics110HJournal‐2013‐2014 Pre‐ClassProblem STATEMENTOFTHEPROBLEM Itiscommonlybelievedthatyouexperienceabrieffeelingofweightlessnesswhenyouareriding anelevator.Consideranelevatorwhichhasafinalspeedof2.3m/s.Inorderforyoutoexperience afeelingof“weightless”,howlongmustittaketheelevatortogofromresttoitsfinalspeed (assumingconstantacceleration)?Doesthishappenwhentheelevatorisgoinguporgoingdown? Free‐BodyDiagram(required) Answer:0.23s, goingdown DocumentationStatement: 170 Physics110HJournal‐2013‐2014 Lesson23 PreflightQuestions 1. Whattopicfromthereadingwouldyouliketodiscussduringclass? 2. What is the approximate force that the Moon exerts on you when it is directly overhead? (Hint:YouwillneeddatafromAppendixEtoanswerthisquestion) a) b) c) d) e) 2 10 2 10 2 10 2 10 2N N N N N 3. Themagnitudeoftheforceofgravitybetweentwoidenticalobjectsis .Ifthemassofeach objectandthedistancearedoubled,whatisthenewforceofgravitybetweentheobjects? a) b)4 c)8 d) e) 4. CRITICALTHINKING:Ageosynchronousorbitisonewheretheorbitalobjectstaysbasically overthesameplaceonearthallthetime.Theobjectstaysrelativelymotionlessinthesky above.ThemassofEarthis5.97x1024kg,andtheperiodisthesameasthatofEarthat T=23hr,56min,4sec.Describehowyouwoulddeterminethealtitudeforgeosynchronous orbit.(Hint:HowareorbitalperiodTandorbitalradiusrelated?) DocumentationStatement: 171 Lesson23 Physics110HJournal‐2013‐2014 HomeworkProblems 8.17 DocumentationStatement: 172 Physics110HJournal‐2013‐2014 Lesson23 8.39 DocumentationStatement: 173 Lesson23 Physics110HJournal‐2013‐2014 MP DocumentationStatement: 174 Physics110HJournal‐2013‐2014 Lesson24 Lesson24 GravitationalEnergy Reading Examples HomeworkProblems 8.4 8.4,8.5 8.27,8.52,MP LearningObjectives [Obj39] [Obj40] [Obj41] Solveproblemsinvolvingchangesingravitationalpotentialenergyoverlarge distances. Usetheconceptofmechanicalenergytoexplainopenandclosedorbitsandescape speed. Useconservationofmechanicalenergytosolveproblemsinvolvingorbitalmotion. Notes DocumentationStatement: 175 Lesson24 Physics110HJournal‐2013‐2014 WorkedExample Score(3) Studythegivenproblemandsolution,thenanswerthequestionsregardingthe problem. STATEMENTOFTHEPROBLEM A120‐kgsatelliteisinacircularorbit100kmabovethesurfaceoftheEarth.Howwouldthetotal energyofthesatellitechangeifitweremovedtoahigherorbit200kmabovethesurfaceofthe Earth? STRATEGY The total energy (potential and kinetic) of a satellite in a circular orbit about the Earth is 1 2 where G = 6.67 x 10-11 Nm2/kg2 is the universal gravitational constant m is the mass of the satellite M is the mass of the Earth = 5.97 x 1024 kg r is the radius of the orbit (radius of the Earth + altitude) IMPLEMENTATION We will calculate the energy in each of the two orbits and subtract to get the change in energy between the orbits. Δ 1 2 – 1 2 6.37 10 100 10 6.37 10 200 10 1 1 2 1 CALCULATION Δ 1 6.67 2 10 Nm /kg 5.97 Δ 6.47 10 m 6.57 10 m 10 kg 120kg 3600 DocumentationStatement: 176 10 J 1 1 6.47 10 m 6.57 10 m Physics110HJournal‐2013‐2014 Lesson24 SELF‐EXPLANATIONPROMPTS 1.Howisthegravitationalenergyformuladerived?Lookinthetextandsummarizethestepsfor thisderivation. 2.Thegravitationalenergyequationincludesgravitationalpotentialenergy.Whereisthe gravitationalpotentialenergyzero? 3.Explainwhyisthetotalenergynegative. DocumentationStatement: 177 Lesson24 Physics110HJournal‐2013‐2014 Pre‐ClassProblem STATEMENTOFTHEPROBLEM A1200‐kgsatelliteisinanellipticalorbitaround theEarth.Atperigee,thealtitudeofthesatellite is1,000kmabovethesurface,andatapogeethe altitudeis10,000kmabovethesurface. perigee apogee Ifthesatelliteistravelingat8.6km/satperigee, whatisitsspeedatapogee? Tryit!(1PFpt):Determinethetotalenergy(kinetic+potential)ofthe satelliteatbothperigeeandapogee.Showyourwork. DocumentationStatement: 178 Answer:3.89m/s Physics110HJournal‐2013‐2014 Lesson24 PreflightQuestions 1. Whattopicfromthereadingwouldyouliketodiscussduringclass? 2. ConsideraspacecraftorbitingtheSuninacircularorbit.The spacecraftfiresitsenginesaddingenergyuntilitescapesthe Sun’sgravity. Comparethetotalenergy forthecircularorbit ,elliptical orbit ,andparabolictrajectory . a) b) c) 3. Supposeanobjectismovingalonganyoneofthegivenorbitalpaths.Whatistrueregardingthe orbitsdepicted? a) Thekineticenergyisconstantinalltheorbits,whilethepotentialenergychangeswith distancefromtheSun. b) Thepotentialenergyisconstantforallpointsinanyoneoftheorbits. c) Totalenergydecreasesfromthecircularorbit untilitequalszerofortheparabolic trajectory . d) Totalenergyisconstantforanypointalonganyoneoftheorbits. 4. CRITICALTHINKING:Aphysicsbookclaimsthat,“Moon‐boundspacecrafthavespeedsjust ,sothatifanythinggoeswrong(aswithApollo13),theywillreturntoEarth.” under Explainwhythisstatementiscorrectorincorrect.Thinkaboutthederivationoftheescape velocityequationandwhetheraspacecraftcangettotheMoonwithoutescapingtheEarth. DocumentationStatement: 179 Lesson24 Physics110HJournal‐2013‐2014 HomeworkProblems 8.27 DocumentationStatement: 180 Physics110HJournal‐2013‐2014 Lesson24 8.52 DocumentationStatement: 181 Lesson24 Physics110HJournal‐2013‐2014 MP DocumentationStatement: 182 Physics110HJournal‐2013‐2014 Lesson25 Lesson25 CriticalThinking:OrbitalEnergies Reading 8.4 Examples 8.5 HomeworkProblems MP,8.61,8.67 ThereisanEXAM‐PREPQUIZthislesson. LearningObjectives [Obj39] Solveproblemsinvolvingchangesingravitationalpotentialenergyoverlarge distances. [Obj40] Usetheconceptofmechanicalenergytoexplainopenandclosedorbitsandescape speed. Notes DocumentationStatement: 183 Lesson25 Physics110HJournal‐2013‐2014 PreflightQuestions 1. Whattopicfromthereadingwouldyouliketodiscussduringclass? 2. Thetotalenergyofasatelliteinaparticularboundorbit a) variesdependingonthesatellite’spositioninthatorbit. b) isalwayspositive. c) isalwaysnegative. d) isalwaysexactlyzero. 3. Fortwoobjectsseparatedbyadistance ,themagnitudeofthegravitationalpotentialenergyis .Ifthedistanceisdoubled,whatisthenewgravitationalpotentialenergy? a) b)4 c)8 d) e) 4. CRITICALTHINKING:TheInternationalSpaceStation(ISS) (http://www.nasa.gov/mission_pages/station/main/index.html) orbitsEarthatanaltitudeof350km.Sincethestationandthe astronautsinsideareinfreefalltogether,theyfloataroundinsidethe ISSmodules.Ifthestationwerestationaryatthataltitude,howwould theastronauts’weightscomparetotheirweightsatthesurfaceof Earth? DocumentationStatement: 184 Physics110HJournal‐2013‐2014 Lesson25 HomeworkProblems MP DocumentationStatement: 185 Lesson25 Physics110HJournal‐2013‐2014 8.61 DocumentationStatement: 186 Physics110HJournal‐2013‐2014 Lesson25 8.67 DocumentationStatement: 187 Lesson25 Physics110HJournal‐2013‐2014 Notes DocumentationStatement: 188 Physics110HJournal‐2013‐2014 Lesson26 Lesson26 CenterofMass Reading Examples HomeworkProblems 9.1 9.1,9.2,9.3 9.16,9.37,9.89 LearningObjectives [Obj42] Calculatethecenterofmassforsystemsofdiscreteparticlesandforcontinuousmass distributions. Notes DocumentationStatement: 189 Lesson26 Physics110HJournal‐2013‐2014 WorkedExample Score(3) Studythegivenproblemandsolution,thenanswerthequestionsregardingthe problem. 1kg STATEMENTOFTHEPROBLEM 1m Foursmallmassesm1,m2,m3,andm4aretiedtogetherwithrigidrods sothattheyformasquareofside1m,asshowninthefigure.Wewant towriteNewton’sSecondLawfortheentiresystemasifallthemass wereconcentratedatasinglepoint,thatis 1kg ,where isthenetexternalforceonthesystem(i.e.the vectorsumofalltheexternalforces)and istheaccelerationofthe system.Whatisthelocationofsuchapoint?Considerthemassofthe connectingrodstobeverysmallcomparedtothemassesonthe corners. STRATEGY 2kg The point described above is called the center-ofmass of the system. Under the action of external forces the assembly of the masses moves as if it were a single mass. For example, in projectile motion the center of mass of the four masses will follow a parabola. The location of the center of mass point is given by ⋯ ⋯ IMPLEMENTATION We choose a coordinate system for the assembly of the four masses and apply the centerof-mass equation. Any coordinate system will work. We choose the origin of our system to be the center of the square. DocumentationStatement: 190 2kg Physics110HJournal‐2013‐2014 Lesson26 CALCULATION 1kg 1kg 0.5m 0.5m 1kg 1kg 0.5m 0.5m 2kg 6kg 2kg 6kg 0.5m 0.5m 2kg 2kg 0.5m 0.5m 0 1 m 6 The center of mass is 1/6 meters under the origin on the y-axis. SELF‐EXPLANATIONPROMPTS 1.Intuitively,thecenterofmasscanbethoughtofasthepointatwhichtheassemblycouldbe stablysupported.Usingthisapproach,wherewouldyouexpectthecenterofmassofthetwo1‐kg massestobe? 2.Whataboutthecenterofmassofthetwo2‐kgmasses? 3.Justify,usingsymmetry,whythecenterofmassisonthey‐axisandbelowthex‐axis? DocumentationStatement: 191 Lesson26 Physics110HJournal‐2013‐2014 Pre‐ClassProblem STATEMENTOFTHEPROBLEM Findthelocationofthecenter‐of‐massofasystemcomprisedofthree1‐kgmasseslocatedatthree cornersofasquarewhosesideis1m.(Hint:Drawapictureandmarkthecenter‐of‐mass.) Answer:x=−0.17m,y=−0.17mina coordinatesystemwiththeoriginat thecenterofthesquare DocumentationStatement: 192 Physics110HJournal‐2013‐2014 Lesson26 PreflightQuestions 1. Whattopicfromthereadingwouldyouliketodiscussduringclass? 2. (True/False)A4.8tonelephantisstandingina15tonrailcarthatisatrestonafrictionless track.Theelephantbeginstowalktowardstheotherendofthecar.Foreverymeterthe elephantmoves,thecarmoves1meterintheoppositedirection. a) True b) False 3. (True/False)Accordingtotheequationsofmotionforaprojectile,afirecrackerfollowsa parabolicpath,neglectingairresistance.Afteritexplodes,thecenterofmassofthepiecesstill followsaparabolictrajectory. a) True b) False 4. CRITICALTHINKING:Afully‐loadedcanoeisattachedtoanemptycanoewithabungeecord. Thecanoesareatrestonaplacidlake.Apassengerintheheaviercanoepushesthecanoes apart,stretchingthebungeecord.Describewhathappenstothecenterofmassofthesystem andexplainyourreasoning. DocumentationStatement: 193 Lesson26 Physics110HJournal‐2013‐2014 HomeworkProblems 9.16 DocumentationStatement: 194 Physics110HJournal‐2013‐2014 Lesson26 9.37 DocumentationStatement: 195 Lesson26 Physics110HJournal‐2013‐2014 9.89 DocumentationStatement: 196 Physics110HJournal‐2013‐2014 Lesson27 Lesson27 ConservationofLinearMomentum&Collisions Reading Examples HomeworkProblems 9.1– 9.5 CE9.1,9.4,9.5, 9.7 9.38,MP,MP LearningObjectives [Obj46] ExplaintheconceptoflinearmomentumofasystemofparticlesandexpressNewton's secondlawofmotionintermsofthelinearmomentumofthesystem. Explainthelawofconservationoflinearmomentumandtheconditionunderwhichit applies. Applyconservationoflinearmomentumtosolveproblemsinvolvingsystems of particles. Explaintheconceptofimpulseanditsrelationtoforce. [Obj47] Explainthedifferencesbetweenelastic,inelastic,andtotallyinelasticcollisions. [Obj48] Applyappropriateconservationlawstosolveproblemsinvolvingcollisionsinone‐ and two‐dimensions. [Obj43] [Obj44] [Obj45] Notes DocumentationStatement: 197 Lesson27 Physics110HJournal‐2013‐2014 WorkedExample Score(3) Studythegivenproblemandsolution,thenanswerthequestionsregardingthe problem. STATEMENTOFTHEPROBLEM A1‐kgball,m1,collideswitha3‐kgball,m2,asshown.The 3m/sand ballshaveinitialvelocitiesof 3m/s.Immediatelyafterthecollision 2m/s,whatisv1final? STRATEGY This is a one-dimensional Conservation of Linear Momentum problem. To use the concept of conservation of momentum, we must ensure that there is no net external force acting on the system. Since 1) we are only interested in what happens immediately before and after the collision, and 2) the collision is brief, we can assume that any external forces acting on the balls are negligible. Because of these conditions, we say that linear momentum is conserved in collisions. (Note that linear momentum can be conserved during other interactions as long as the condition of no net external forces is met.) The Conservation of Linear Momentum equation is ∑ specific to this problem, ,and, ∑ .As the figure shows it is possible for one of the balls to have a negative velocity (oppositely directed) after or prior to the collision. IMPLEMENTATION We will designate a standard x-y coordinate system as shown. We will use the conservation of linear momentum equation and solve it for v1final. DocumentationStatement: 198 Physics110HJournal‐2013‐2014 Lesson27 CALCULATION Starting with: It becomes: m s Now substituting: 1kg 3 m s 3kg 3 3kg m s 3kg 2 4m/s SELF‐EXPLANATIONPROMPTS 1.Whyisitimportanttoensurethatnonetexternalforceactsontheobjects? 2.Whycanyounotusetheabsolutevaluesofthevelocitiesintheabovecalculations? 3.Usingthecalculatedfinalvelocityofball1,showthatlinearmomentumwasindeedconservedin thecollision. DocumentationStatement: 199 Lesson27 Physics110HJournal‐2013‐2014 Pre‐ClassProblem Thediagramontheleftshowsacollisionbetweenaseriesof railroadcars.Ifthecars,eachhavingamassof3000kg, departthecollisionsasonecoupledgroup,whatwillbethe finalvelocityoftheassembly? Answer:2.5m/s DocumentationStatement: 200 Physics110HJournal‐2013‐2014 Lesson27 PreflightQuestions 1. Whattopicfromthereadingwouldyouliketodiscussduringclass? 2. Linearmomentumofasystemisconservedif a) b) c) d) thenetexternalforceiszero. theenergyofthesystemisconserved. thenetworkdoneispositive. onlyconservativeforcesaredoingwork. 3. A500‐gfireworkrocketismovingat60m/sstraightupwardwhenitexplodes.Thesumofall themomentumvectorsoftherocketfragmentsimmediatelyaftertheexplosionis a) zero. b) 30kgm/sstraightup. c) 30kgm/sinmultipledirections. d) morethan30kgm/sbecauseoftheenergyaddedbytheexplosion. 4. CRITICALTHINKING:Considerarubberbulletandanaluminumbullet;bothhavethesamesize, speedandmass.Eachbulletisfiredatablockofwood.Therubberbulletbouncesback,the aluminumbulletpenetratestheblock.Whichismostlikelytoknocktheblockover?Explain. DocumentationStatement: 201 Lesson27 Physics110HJournal‐2013‐2014 HomeworkProblems 9.38 DocumentationStatement: 202 Physics110HJournal‐2013‐2014 Lesson27 MP DocumentationStatement: 203 Lesson27 Physics110HJournal‐2013‐2014 MP DocumentationStatement: 204 Physics110HJournal‐2013‐2014 Lesson28 Lesson28 Lab5–1‐DCollisions Reading 9.5,9.6,Lab5Worksheet Examples None HomeworkProblems 9.28,9.44,9.61 ThereisaLABthislesson. LearningObjectives [Obj46] Explaintheconceptofimpulseanditsrelationtoforce. [Obj47] Explainthedifferencesbetweenelastic,inelastic,andtotallyinelasticcollisions. [Obj48] Applyappropriateconservationlawstosolveproblemsinvolvingcollisionsinone‐ and two‐dimensions. Notes DocumentationStatement: 205 Lesson28 Physics110HJournal‐2013‐2014 JournalQuestions Score(5) 1. Brieflydescribethepurposeandgoalsofthislab.(Onetotwocompletesentences) 2. InPartIofthelab,aheavycart(massm1)andastationarylightcart(massm2)willundergoa one‐dimensionalcollisiononafrictionlessairtrack.Assumingthecollisioniselastic,writethe expressionforthefinalvelocityofcart2,v2f,intermsoftheinitialvelocityofcart1,v1i. 3. InPartIIofthelab,aheavycart(massm1)andastationarylightcart(massm2)willundergoa totallyinelasticone‐dimensionalcollisiononafrictionlessairtrack.Deriveasimilar expressionforthefinalvelocityofthejoinedcarts(massesm1+m2),vf,intermsoftheinitial velocityofcart1,v1i,startingfromtheequationforconservationofmomentum. 4. Supposeyoumakeaplotofthefinalvelocityofcart2,v2f,versustheinitialvelocityofcart1,v1i, fortheelasticcollision.Whatwouldtheplotlooklike?Writeanexpression,intermsofm1and m2,fortheslopeassociatedwiththisplot. 5. Ifyouplottedthefinalvelocityofthejoinedcarts,vf,versustheinitialvelocityofcart1,v1i,for thetotallyinelasticcollisioninstead,howwouldtheslopeforthetotallyinelasticcollision comparetotheslopefortheelasticcollision?Explain. DocumentationStatement: 206 Physics110HJournal‐2013‐2014 Lesson28 LabNotes DocumentationStatement: 207 Lesson28 Physics110HJournal‐2013‐2014 HomeworkProblems 9.28 DocumentationStatement: 208 Physics110HJournal‐2013‐2014 Lesson28 9.44 DocumentationStatement: 209 Lesson28 Physics110HJournal‐2013‐2014 9.61 DocumentationStatement: 210 Physics110HJournal‐2013‐2014 Lesson29 Lesson29 CollisionsandConservationofEnergy: WheredoestheEnergyGo? Reading Examples HomeworkProblems 9.3,9.4 9.10 MP,9.68,9.78 LearningObjectives [Obj46] Explaintheconceptofimpulseanditsrelationtoforce. [Obj47] Explainthedifferencesbetweenelastic,inelastic,andtotallyinelasticcollisions. [Obj48] Applyappropriateconservationlawstosolveproblemsinvolvingcollisionsinone‐ and two‐dimensions. Notes DocumentationStatement: 211 Lesson29 Physics110HJournal‐2013‐2014 WorkedExample Score(3) Studythegivenproblemandsolution,thenanswerthequestionsregardingthe problem. STATEMENTOFTHEPROBLEM A1.0‐kgpuck(puck1)isslidingat45°abovethex‐axis withaspeedof1.0m/s.Another1.0‐kgpuck(puck2)is slidingwithaspeedof0.50m/sat45°belowthex‐axis. Thepuckscollide,andpuck2fliesoffat45°belowthex‐ axis,at0.80m/s. 1 m1=1.0kg v1i=1.0m/s x a)Whatisthevelocityofpuck1afterthecollision? m2=1.0kg v2i=0.5m/s b)Wasthiscollisionelastic? 2 STRATEGY Since total linear momentum ( ) is conserved in any collision, we can use the ∑ conservation of linear momentum to obtain the set of equations we need to solve for the velocity of puck 1. We can then compare the kinetic energies before and after the collision. If the kinetic energies before and after the collision are the same (conserved), the collision was elastic. IMPLEMENTATION Since total momentum is conserved we have: = Writing this expression in terms of x- and ycomponents gives us two equations with two unknowns – the magnitude and direction of the velocity of the first puck –which we will solve. To see if the collision was elastic we compare the kinetic energies before and after the collision 1 2 1 2 ? 1 2 1 2 DocumentationStatement: 212 Physics110HJournal‐2013‐2014 Lesson29 CALCULATION a) Before the collision, the x- and y- components of the total momentum are: 1.0kg 1.0 1.0kg 1.0 m ∙ cos45° s m ∙ sin45° s 1.0kg 0.50 m ∙ cos45° s 1.0kg ∙ 0.50 ∙ sin45° 1.06 kg ∙ m s 0.354 kg ∙ m s and after collision they are: 1.0kg 1.0kg 1.0kg 0.80 1.0kg 0.80 m ∙ cos45° s m ∙ sin45° s 1.06 kg ∙ m s 0.354 Solving for the speed of the puck 1 and the direction angle θ we get: kg ∙ m s 0.54 and 23°, above the positive x-axis. b) Calculating the total kinetic energy of the two pucks before the collision, we get 0.62 J; after the collision the kinetic energy is 0.46 J. The collision was not elastic, but it was not totally inelastic. SELF‐EXPLANATIONPROMPTS 1. Solvethemomentumequationsforthespeedanddirectionofmotionofpuck1(i.e.,fillinthe stepsomittedabove). 2. Calculatethetotalkineticenergyofthetwopucksbeforeandafterthecollision(i.e.,fillinthe stepsomittedabove),andconfirmthatthecollisionisinelastic. 3. Wheredidtheenergygoduringtheinelasticcollision? DocumentationStatement: 213 Lesson29 Physics110HJournal‐2013‐2014 Pre‐ClassProblem Twomasses,m1andm2,moveatrightangles,meetattheoriginandflyof,stickingtogether.Their initialspeedsarethesame.Ifm1=3m2,whataretheirspeedanddirectionaftercollision? Answer:0.79v,18.4° DocumentationStatement: 214 Physics110HJournal‐2013‐2014 Lesson29 PreflightQuestions 1. Whattopicfromthereadingwouldyouliketodiscussduringclass? 2. Ifthenetexternalforceactingonanobjectisconstant,whatistrueaboutitsmomentum ? a) Themagnitudeanddirectionof maychange. b) Themagnitudeof remainsconstantbutthedirectionmaychange. c) Themagnitudeof maychangebutthedirectionremainsconstant. d) Themagnitudeanddirectionof remainconstant. 3. Matchthediagramtothetypeofcollisionbetweenobjectsofequalmass. CaseA _____ _____ _____ CaseC CaseB Elasticcollision Inelasticcollision Totallyinelasticcollision 4. CRITICALTHINKING:Birdstrikesareasignificantflightsafety hazard.ConsideranF‐16birdstrikewhereagooseimpactsthe canopy.TheF‐16canopydeformsduringthecollisionandthe birdpartsdeflectawayfromtheaircraft.Whattypeofcollisionis this?Explain. DocumentationStatement: 215 CaseD Lesson29 Physics110HJournal‐2013‐2014 HomeworkProblems MP DocumentationStatement: 216 Physics110HJournal‐2013‐2014 Lesson29 9.68 DocumentationStatement: 217 Lesson29 Physics110HJournal‐2013‐2014 9.78 DocumentationStatement: 218 Physics110HJournal‐2013‐2014 Lesson30 Lesson30 GRADEDREVIEW3 LearningObjectives [Obj26] Explainthephysicsconceptofwork. [Obj27] Evaluatetheworkdonebyconstantforcesandbyforcesthatvarywithposition. [Obj28] Explaintheconceptofkineticenergyanditsrelationtowork. [Obj29] Explaintherelationbetweenenergyandpower. [Obj30] Explainthedifferencesbetweenconservativeandnonconservativeforces. [Obj31] Evaluatetheworkdonebybothconservativeandnonconservativeforces. [Obj32] Explaintheconceptofpotentialenergy. [Obj33] Evaluatethepotentialenergyassociated withaconservativeforce. [Obj34] [Obj36] Solveproblemsbyapplyingthework‐energytheorem,conservationofmechanical energy,orconservationofenergy. Describetherelationbetweenforceandpotentialenergyusingpotential‐energy curves. Explaintheconceptofuniversalgravitation. [Obj37] Solveproblemsinvolvingthegravitationalforcebetweentwoobjects. [Obj38] Determinethespeed,acceleration,andperiodofanobjectincircularorbit. [Obj39] Solveproblemsinvolvingchangesingravitationalpotentialenergyoverlarge distances. Usetheconceptofmechanicalenergytoexplainopenandclosedorbitsandescape speed. Useconservationofmechanicalenergytosolveproblemsinvolvingorbitalmotion. [Obj35] [Obj40] [Obj41] [Obj46] Calculatethecenterofmassforsystemsofdiscreteparticlesandforcontinuousmass distributions. ExplaintheconceptoflinearmomentumofasystemofparticlesandexpressNewton's secondlawofmotionintermsofthelinearmomentumofthesystem. Explainthelawofconservationoflinearmomentumandtheconditionunderwhichit applies. Applyconservationoflinearmomentumtosolveproblemsinvolvingsystemsof particles. Explaintheconceptofimpulseanditsrelationtoforce. [Obj47] Explainthedifferencesbetweenelastic,inelastic,andtotallyinelasticcollisions. [Obj48] Applyappropriateconservationlawstosolveproblemsinvolvingcollisionsinone‐ and two‐dimensions. [Obj42] [Obj43] [Obj44] [Obj45] Notes DocumentationStatement: 219 Lesson30 Physics110HJournal‐2013‐2014 Lesson18:“Areyouready?” Readtheproblembelowandworkthroughtheguidedsolution,thenanswerthequestions regardingtheproblem. STATEMENTOFTHEPROBLEM Amandragsa50‐kgcrate10macrossaroughhorizontalsurface,wherethecoefficientoffriction betweenthecrateandsurfaceis0.3.Hepullsataconstantspeedandhedirectshispullingforce 20°downwardfromthehorizontal.Howmuchworkdoesheperform? STRATEGY(Fillintheblanks.) The strategy is the same as used for the worked example in Lesson 18, the only difference is that the force of friction is now The force exerted by the man is now ____________ CALCULATION(Fillintheblanks.) cosθ Δ 1328J SELF‐EXPLANATIONPROMPTS 1.Theworkdoneinthiscaseis3JmorethanintheworkedexampleforLesson18.Explainwhy theworkincreased. 2.Whatworkdoesfrictiondo? 3.Howwouldtheanswerchangeifthesurfacewasfrictionlessinstead? OptionalPracticeProblems:6.13,6.19,6.21 DocumentationStatement: 220 Physics110HJournal‐2013‐2014 Lesson30 Lesson19:“Areyouready?” Readtheproblembelowandworkthroughtheguidedsolution,thenanswerthequestions regardingtheproblem. STATEMENTOFTHEPROBLEM A1500‐kgcaristravellingat26.8m/s.Thedriverappliesasmallbrakingforceof800N.Howfar doesthecartravelbeforeitslowsdownto13.4m/s? STRATEGY(Fillintheblanks.) Apply the __________________ theorem and solve the resulting equation for the unknown displacement. CALCULATION(Fillintheblanks.) ∙ Δ _________________ _____________ Δ 505m SELF‐EXPLANATIONPROMPTS 1. Whathappenstothestoppingdistanceifthespeedofthecarisdoubled,assumingthesame brakingforce? 2. Wheredoesthe“brakingforce”comefrom? OptionalPracticeProblems:6.27,6.39 DocumentationStatement: 221 Lesson30 Physics110HJournal‐2013‐2014 Lesson20:“Areyouready?” Readtheproblembelowandworkthroughtheguidedsolution,thenanswerthequestions regardingtheproblem. STATEMENTOFTHEPROBLEM Anobjectofmassmisreleasedatrestfromaheighthaboveground.Whatisthespeedoftheobject justbeforeitreachestheground? STRATEGY(Fillintheblanks.) The object has positive potential energy relative to the ground. As it falls, that energy gets converted into kinetic. Symbolically, ∆ ⇒ _____________ CALCULATION(Fillintheblanks.) _____________ ½mv2 Setting the kinetic energy equal to ΔUg and solving for the speed v we get 2 SELF‐EXPLANATIONPROMPTS 1.Whyistherenomassminthefinalanswer?Reviewthecalculationandshowwherethemass dropsout. 2.Doesthefactthatthereisnomassminthefinalanswertellusthatthegravitationalpotential energydoesnotdependonthemass? 3.Thisproblemcanalsobesolvedusing1‐Dkinematics.Usethismethodandcomparetheresults. OptionalPracticeProblems:7.13,7.17,7.30 DocumentationStatement: 222 Physics110HJournal‐2013‐2014 Lesson30 Lesson21:“Areyouready?” Readtheproblembelowandworkthroughtheguidedsolution,thenanswerthequestions regardingtheproblem. STATEMENTOFTHEPROBLEM A60‐kgskierstartsfromrestandskisdownazig‐zagtrail.Whenshereachesthebottomofthetrail shehasdescendedaverticalelevationof600m.Ifsheloses12%ofherenergytofriction,whatis herspeedatthebottomofthetrail? STRATEGY(Fillintheblanks.) We apply a modified energy conservation equation, accounting for the energy lost to friction 0.88 And taking PE to be zero at the bottom of the trail. CALCULATION(Fillintheblanks.) ___________ ___________ 310,464J ___________ 101m/s SELF‐EXPLANATIONPROMPTS 1. Inyourownwordsdescribethemodifiedconservationequationweused. 2. Whydoesthecontouroftheterrainnotmatterinthiscalculation? 3. Howwouldtheproblemneedtobechangedsothatwecouldusetheforceoffrictionformula, ? OptionalPracticeProblems:7.19,7.53,7.57 DocumentationStatement: 223 Lesson30 Physics110HJournal‐2013‐2014 Lesson23:“Areyouready?” Readtheproblembelowandworkthroughtheguidedsolution,thenanswerthequestions regardingtheproblem. STATEMENTOFTHEPROBLEM Manymoviescontainsceneswheretheactorsexperienceweightlessness.Thesescenesareusually filmedinanairplanethatisundergoingcarefullychoreographedmaneuverswhichsimulate weightlessness.Considerthefollowingflightpath:Fromthestartofthemaneuvertot=120s,the airplane’sheightisdescribedby 225 .Duringthenextpartofthemaneuver,whichlasts60 seconds,theairplanesheightisgivenby 4.9 1176 43560.Forthefinal15secondsof 23000.Duringwhattimeperiodisthe themaneuver,theairplane’saltitudeisgivenby airplane“weightless”? STRATEGY(Fillintheblanks.) The back of the airplane will appear to be weightless (aka “free fall”) when the airplane accelerates at same rate as all the objects in the plane. We will use the derivative to find the times when the acceleration is 9.8 m/s2. CALCULATION 1. During the first part of the maneuver, we take the derivative of position to find the velocity, which is ____________. By taking the derivative of velocity, we find the acceleration to be 0 m/s2. The plane is not in free fall. 2. During the second part of the maneuver, find that the velocity is given by __________. We take the derivative of velocity to find that the acceleration is given by ____________. The plane is therefore in free fall. 3. During the third part of the maneuver, we find that the velocity is _________ and the acceleration is ___________. The plane is not in free fall. SELF‐EXPLANATIONPROMPTS 1.Whatpartofthepositionequationdeterminestheplaneisfreefallinthe2ndpartofthe maneuver?Whatpartsoftheequationdoesnotmatter? 2.Howcouldyoumodifythepositionequationforthethirdpartofthemaneuvertomaketheplane beinfreefall? OptionalPracticeProblems:8.35,8.19, DocumentationStatement: 224 Physics110HJournal‐2013‐2014 Lesson30 Lesson24:“Areyouready?” Readtheproblembelowandworkthroughtheguidedsolution,thenanswerthequestions regardingtheproblem. STATEMENTOFTHEPROBLEM Ifa300‐kgsatellite,inacircularorbit150kmabovethesurfaceoftheEarthcrashestotheground (orburnsup),howmuchenergyislost? STRATEGY(Fillintheblanks.) The total energy (potential and kinetic) of a satellite in a circular orbit about the Earth is 1 2 where G = 6.67 x 10-11 Nm2/kg2 is the universal gravitational constant m is the mass of the satellite M is the mass of the Earth = 5.97 x 1024 kg r is the radius of the orbit, i.e. radius of the Earth + altitude CALCULATION(Fillintheblanks.) Δ _____________________ 6.37 10 1 1 2 150 10 1 6.52 10 m __________________________ 216 10 J SELF‐EXPLANATIONPROMPTS 1.Thegravitationalenergyequationincludesthegravitationalpotentialenergy.Whereisthe gravitationalpotentialenergyzero? 2.Completethecalculation. OptionalPracticeProblems:8.30,8.58 DocumentationStatement: 225 Lesson30 Physics110HJournal‐2013‐2014 Lesson26:“Areyouready?” Readtheproblembelowandworkthroughtheguidedsolution,thenanswerthequestions regardingtheproblem. STATEMENTOFTHEPROBLEM Whereisthecenterofmassofa2‐mbarbellwitha1‐kgmassontheleftanda3‐kgmassonthe right?Considerthemassofthebartobeverysmall(negligible)comparedtothemassesonthe corners. 3kg 1kg 2m STRATEGY(Fillintheblanks.) Choose a coordinate system with the origin at the center of the bar. Apply the center-of-mass equation and solve for the x-coordinate. CALCULATION(Fillintheblanks.) 1kg 3kg 0.5m SELF‐EXPLANATIONPROMPTS 1.Doestheresultagreewithyourintuition? 2.Convinceyourselfthatthechoiceofthecoordinatesystemdoesnotmatter.Choosetheoriginof thecoordinatesystemattheleftend,atthelocationofthe1kgmass,andshowthatyougetthe sameresult.(Drawadiagramandmarkthelocationofthecenter‐of‐massascalculatedoriginally andagainascalculatedusingthenewcoordinatesystem. OptionalPracticeProblems:9.12,9.38,9.49 DocumentationStatement: 226 Physics110HJournal‐2013‐2014 Lesson30 Lesson27:“Areyouready?” Readtheproblembelowandworkthroughtheguidedsolution,thenanswerthequestions regardingtheproblem. STATEMENTOFTHEPROBLEM A100‐kgclownislaunchedfroma500‐kgcircuscannon.AfterthefiringofBozo,hehasaspeedof 15m/s.Assumingthathisshoesandcostumearesohighlypolishedthatthereisnofrictionashe movesoutofthecannonbarrelandthatthecannonandclowninitiallyareatrest,whatisthefinal velocityofthecannon? STRATEGY(Fillintheblanks.) We will use a standard x-y orientation for this _______ dimensional problem involving conservation of linear ____________. The statement “that there is no friction” allows us to meet the condition of no ______ _______ acting on the objects during the event. The event in which momentum is conserved in this case is an explosion where the cannon and the clown are considered initially as _________ stationary object that then becomes two objects with individual __________. We will start with the Conservation of Momentum relation and solve for the ____________________. CALCULATION(Fillintheblanks.) First:∑ Now: ∑_____________ _______ With numbers: _____ _____ 100kg _____m/s ___ 500kg _____100kg ___ 100kg ____m/s /_____kg _______m/s 3m/s SELF‐EXPLANATIONPROMPTS 1. Whatdoes“atrest”implyabouttheinitialvelocitiesofthecannonandtheclown? 2. Istheinitialcondition(clowninsidecannon)thesameasifthetwoweresittingatrestnextto oneanother?Explain. OptionalPracticeProblems:9.18,9.19,9.20,9.42 DocumentationStatement: 227 Lesson30 Physics110HJournal‐2013‐2014 Lesson29:“Areyouready?” Readtheproblembelowandworkthroughtheguidedsolution,thenanswerthequestions regardingtheproblem. STATEMENTOFTHEPROBLEM Twoidenticalmasses,M,approachtheoriginwiththesamespeed v,at45degreesfromthehorizontal. Theycollideandsticktogether.Whatarethespeedanddirectionof motionaftercollision? STRATEGY(Fillintheblanks.) We apply the conservation of _______________________ to determine the motion after collision. The y-component of the momentum after collision must be zero because __________. The x-component of the momentum before collision is _____________ CALCULATION(Fillintheblanks.) 2 45 ________________ 45 inthepositivex‐direction. SELF‐EXPLANATIONPROMPTS 1.Isthiscollisionelastic? Ifyouranswerisyes,explainyourreasoning?Ifyouanswerisno,calculatethechangeinkinetic energy. OptionalPracticeProblems:9.43,9.68,9.77 DocumentationStatement: 228 Physics110HJournal‐2013‐2014 Lesson30 Notes DocumentationStatement: 229 Lesson30 Physics110HJournal‐2013‐2014 Notes DocumentationStatement: 230 Physics110HJournal‐2013‐2014 Lesson31 Lesson31 RotationalMotion Reading 10.1,10.2 Examples 10.1,10.2,10.3 HomeworkProblems 10.19,10.23,10.45 ThereisanoptionalEquationDictionaryentryinAppendixDforthislesson(1PFpt). LearningObjectives [Obj49] [Obj50] [Obj51] Explaintherelationbetweentherotationalmotionconceptsofangulardisplacement, angularvelocity,andangularacceleration. Useequationsofmotionforconstantangularaccelerationtosolveproblemsinvolving angulardisplacement,angularvelocity,andangularacceleration. Usecalculustosolveproblemsinvolvingmotionwithnon‐constantangular acceleration. Notes DocumentationStatement: 231 Lesson31 Physics110HJournal‐2013‐2014 WorkedExamples Score(3) Studythegivenproblemandsolution,thenanswerthequestionsregardingtheproblem. STATEMENTOFTHEPROBLEM TheSmokyHillsWindFarmnearSalina,Kansasemploy140,000poundVestasV801.8‐megawatt windturbines.Thethree‐bladeturbineshaveadiameterof80mandoperateat15.5to16.8rpm (revolutionsperminute.) a)Whatisthelinearspeedofthebladetipatmaximumrotationalspeed? b)Whatisthecentripetalaccelerationatthetipofthebladeatthemaximumspeed? c)Ifthebladeslowsdownfrommaximumspeedtorestin30seconds,throughhowmany revolutionsdoesitturn? STRATEGY We use the relation:linearquantity=(radius)times(correspondingangularquantity). arclength=(radius)times(anglesubtended) linearspeedalongthearc=(radius)times(angularspeed) tangentialacceleration=(radius)times(angularacceleration) The above relations are valid if the angles are measured in radians. The tangential acceleration at is non-zero if the angular speed is changing. Whenever the angular speed is non-zero, there is always a centripetal acceleration, , responsible for changing the direction of the tangential velocity. IMPLEMENTATION The angular speed is given in revolutions per minute. Since there are 2π radians in a revolution and 60 seconds in a minute, we multiply rpms by 2π/60 to get the angular speed in radians per second. To obtain the tangential speed, we use 2 centripetal acceleration is then . The . The kinematics equations for angular quantities mimic kinematics equations for linear motion. For constant angular acceleration α, the relation between θ, ω, α, and time is: 2 DocumentationStatement: 232 . Physics110HJournal‐2013‐2014 Lesson31 CALCULATION a) Maximum angular velocity: . 1.76rad/sec b) Maximum linear speed of the tip: 40m 1.76rad/ sec 70.4m/s c) Centripetal acceleration at the tip: 123.9m/s d) During the 30 seconds slow-down the blade undergoes an angular deceleration Note: Compare 0.06rad/s and it turns through 25.8radians for rotational motion to 2 4revolutions 2 for linear motion. SELF‐EXPLANATIONPROMPTS 1.Showtheconversionof15.5rpmtorad/s. 2.Theangularmeasureradianisdefinedastheratioofthearclengthtotheradius.Convert1 degreetoradians.Convert1radiantodegrees. 3.Ifanobjectisrotatingwithanon‐zeroangularvelocityωandzeroangularaccelerationα,isthere acentripetalacceleration?Ifanobjectisrotatingwithanon‐zeroangularvelocityωandnon‐zero angularaccelerationα,whatisthetotallinearacceleration? DocumentationStatement: 233 Lesson31 Physics110HJournal‐2013‐2014 Pre‐ClassProblem STATEMENTOFTHEPROBLEM A3‐mdiameterflywheelisspinningupwithanangularaccelerationof3rad/s2.Howlongdoesit taketheflywheeltoreach12rpm(revolutionsperminute)ifitstartsfromrest? Answer:0.4seconds DocumentationStatement: 234 Physics110HJournal‐2013‐2014 Lesson31 PreflightQuestions 2. Whattopicfromthereadingwouldyouliketodiscussduringclass? 2. Whichofthefollowingistheclosesttooneradian? a) 30° b) 60° c) 90° d) 180° 3. Twoantscrawlontothesurfaceofacompactdisc.AntAisfartherfromthecenterofthedisc thanAntB.Thecompactdiscbeginstospin.Whichofthefollowingstatementsistrue? a) b) c) d) AntAexperiencesagreatertangentialaccelerationthanAntB. AntAexperiencesagreaterangularaccelerationthanAntB. Neitherstatementistrue. Bothstatementsaretrue. 4. CRITICALTHINKING:Whatistheapproximateangularspeedoftheearthrevolvingaroundthe Sun,inrad/day? Explainthereasoningyouusedindeterminingyouranswer. DocumentationStatement: 235 Lesson31 Physics110HJournal‐2013‐2014 HomeworkProblems 10.19 DocumentationStatement: 236 Physics110HJournal‐2013‐2014 Lesson31 10.32 DocumentationStatement: 237 Lesson31 Physics110HJournal‐2013‐2014 10.45 DocumentationStatement: 238 Physics110HJournal‐2013‐2014 Lesson32 Lesson32 RotationalInertia&Torque Reading 10.2,10.3 Examples 10.4,10.5 HomeworkProblems 10.30,10.28,10.52 Thereisanon‐gradedPHYSICSKNOWLEDGEASSESSMENTTESTthislesson. LearningObjectives [Obj52] Explaintheconceptoftorqueandhowtorquescausechangeinrotationalmotion. [Obj53] Givenforcesactingonarigidobject,determinethenettorquevectorontheobject. [Obj54] Determinetherotationalinertiaforasystemofdiscreteparticles,rigidobjects,ora combinationofboth. Compareandcontrasttheconceptsofmassandrotationalinertia. [Obj55] Notes DocumentationStatement: 239 Lesson32 Physics110HJournal‐2013‐2014 WorkedExamples Score(3) Studythegivenproblemandsolution,thenanswerthequestionsregardingthe problem. STATEMENTOFTHEPROBLEM Youhaveaflattireonyourcarand,inordertochangethetire,youneedtoremovethelugnutsthat securethewheeltothecar.Ifthe30‐cmlongwrenchyouareusingtoremovethenutsisata55° angletothehorizontalandyouapplyaforceof120Ndirectlydownontheendofthewrench,what isthemagnitudeofthetorqueyouexertonthelugnut? STRATEGY For this problem, we are interested in the applied torque τ. Torque is the rotational analog to force; it is the effectiveness of a force to cause an object to rotate about a pivot point. To solve for torque, we need to consider 1) the magnitude of the applied force F, 2) how far from the pivot point the force is applied r, and 3) the angle that the force is applied θ. IMPLEMENTATION Let’s draw a diagram and label the applied force vector the vector , that goes from the pivot point to the where the force is applied, and the angle θ between and . Note that the angle θ is not 55°, but (180° - 55°) = 125°. The relation between τ, r, F, and θ is: sin CALCULATION The magnitude of the torque exerted on the lug nuts is sin 0.30m 120N 125 29Nm. The units of torque are newton-meters (N m). DocumentationStatement: 240 Physics110HJournal‐2013‐2014 Lesson32 SELF‐EXPLANATIONPROMPTS 1.Inyourownwords,explainhowtorquediffersfromforce. 2.Whydidweuse125°fortheangleoftheappliedforceandnot55°? 3.Explainhowthemagnitudeofthetorqueexertedonthelugnutswouldchangeiftheforcewas appliedinthemiddleofthehandleratherthantheend. DocumentationStatement: 241 Lesson32 Physics110HJournal‐2013‐2014 Pre‐ClassProblem STATEMENTOFTHEPROBLEM Ifyouapplya45‐Nforceperpendicularlytoadooratdistancesof1m,a)determinethemagnitude ofthetorque,andb)themagnitudeoftheangularaccelerationifthedoor’srotationalinertia,I,is 30kgm2. Tryit!(1PFpt):Calculatethemagnitudeofthe torqueiftheforcewasappliedatanangleof25° instead. DocumentationStatement: 242 Answer:(a)45Nm;(b)1.5rad/s2 Physics110HJournal‐2013‐2014 Lesson32 PreflightQuestions 1. Whattopicfromthereadingwouldyouliketodiscussduringclass? 2. Rankorderthemagnitudeofthetorquesfromsmallesttolargest.Eachrodis50‐cmlongfrom thepivot(). 2N 2N (A) (B) (C) 4N 45° 2N (D) (E) 4N RankOrder:Smallest(1)_____(2)_____(3)_____(4)_____(5)_____Largest 3. Inordertospinfasteraboutaverticalaxis,aniceskaterneedstodecreaseherrotational inertia.Shecouldachievethatby a) stretchingherarmsfartherawayfromtheverticalrotationaxis. b) bringingherarmsclosertoherbody. c) loweringherbodybybendingherkneesandsquattingdown. d) bendingforwardatherwaistsoherbodyisL‐shaped. e) Rotationalinertiacanonlydecreaseifhermassdecreases. 4. CRITICALTHINKING:Abookcanberotatedaboutmanydifferentaxes.Themomentofinertia ofthebookwilldependupontheaxischosen.RankthechoicesAtoCaboveinorderof increasingmomentsofinertiaandexplainyourranking. DocumentationStatement: 243 Lesson32 Physics110HJournal‐2013‐2014 HomeworkProblems 10.30 DocumentationStatement: 244 Physics110HJournal‐2013‐2014 Lesson32 10.28 DocumentationStatement: 245 Lesson32 Physics110HJournal‐2013‐2014 10.52 DocumentationStatement: 246 Physics110HJournal‐2013‐2014 Lesson33 Lesson33 RotationalAnalogtoNewton’sSecondLaw Reading 10.3 Examples 10.8,10.9 HomeworkProblems 10.56,10.57,MP ThereisanoptionalEquationDictionaryentryinAppendixDforthislesson(1PFpt). LearningObjectives [Obj55] Compareandcontrasttheconceptsof massandrotationalinertia. [Obj56] UseNewton’ssecondlawanditsrotationalanalogtosolveproblemsinvolving translationalmotion,rotationalmotion,orboth. Notes DocumentationStatement: 247 Lesson33 Physics110HJournal‐2013‐2014 WorkedExample Score(3) Studythegivenproblemandsolution,thenanswerthequestionsregardingtheproblem. STATEMENTOFTHEPROBLEM A50‐kgblockanda100‐kgweightareconnectedwitharope, passingoverapulleyasshown.The50‐kgblockisona30°ramp wherefrictionisnegligible.Thepulleyisasoliddiscwhoseradius is0.2mandwhosemomentofinertiais2kgm2.Theropedoes notstretch. Whenreleasedfromrest,whatistheaccelerationofthesystem, includingdirection? STRATEGY First, we draw free-body diagrams and apply Newton’s Second Law for each of the two masses and Newton’s Law for rotational motion for the pulley. We then solve the system of three equations for the common acceleration. The system of equations has three unknowns, the acceleration and the two tensions. Since the inertia of the pulley is not negligible, the tension on the left side of the pulley is not the same as the tension on the right side of the pulley. IMPLEMENTATION The 50-kg block, m: The net force on the block is: The normal force – 30° . equals the component of the weight perpendicular to the ramp, The 100-kg block, M: The net force on the block is: – . The lengths of the arrows do not indicate the magnitudes of the forces since we don’t know those until we make the calculations. Note the negative sign for the acceleration, to be consistent with the direction chosen for the 50-kg mass. The pulley: Newton’s Law for rotation states that . I is the moment of inertia, α is the angular acceleration and τ is the DocumentationStatement: 248 Physics110HJournal‐2013‐2014 Lesson33 torque, defined as the applied force multiplied by the perpendicular distance to the axis of rotation from the application point of the force. The net torque on the pulley is: – The Newton’s Law equation for the pulley reads: – CALCULATION The three equations now read: – 30° – – The angular acceleration and the linear acceleration are related by a = αr. Solving for the acceleration we get: – 30° 2.2 / The sign of the calculated acceleration is positive. That means that the 50-kg mass is accelerating up the ramp and the 100-kg weight is accelerating down. SELF‐EXPLANATIONPROMPTS 1.Justifywhyeachcoordinatesystemonthefree‐bodydiagramswasused. 2.Justifythenegativesignusedfortheaccelerationintheequationofmotionforthe100‐kgweight. 3.Explaininyourownwordswhythetensionsonthetwosidesofthepulleyaredifferent. DocumentationStatement: 249 Lesson33 Physics110HJournal‐2013‐2014 Pre‐ClassProblem STATEMENTOFTHEPROBLEM Whatmagnitudeoftorquehastobeappliedtoa2.3‐kg,18‐cmdiameter,soliddiskrotatingat 800rpmtostopitin10seconds? Answer:0.078Nm DocumentationStatement: 250 Physics110HJournal‐2013‐2014 Lesson33 PreflightQuestions 1. Whattopicfromthereadingwouldyouliketodiscussduringclass? 2. Whichstatementiscorrect? a) Iftorqueincreases,rotationalinertiamustincrease. b) Therotationalinertiaofanobjectdoesnotdependonthelocationofitsaxisofrotation. c) Anobjectwithmoremasshasahigherrotationalinertiathananobjectwithlessmass. d) Rotationalinertiameasuresanobject'sresistancetochangesinitsrotationalmotion. 1N 2kg 2m CaseA 3. Rankordertheangularacceleration ofeachcase. 2kg 1N Theobjectsareconnectedwithmasslessrodsof lengthsshown.Theforcesshownaretheonlyforces 2N 2kg 2m actingontheobjectscausingrotationaboutthepivot CaseB 2kg point(). 2N a) 4kg 1N 4m CaseC b) 1N 4kg c) 2N 2kg d) 4m 30° CaseD 30° 2kg 2N 4. CRITICALTHINKING:Thetwoblocksfromtheworkedexampleproblem,mand M,arenowhungdirectlydownfromthepulleyasshown.Describehowthe equationfortheaccelerationoftheblockswouldchangeforthisscenario. DocumentationStatement: 251 Lesson33 Physics110HJournal‐2013‐2014 HomeworkProblems 10.56 DocumentationStatement: 252 Physics110HJournal‐2013‐2014 Lesson33 10.57 DocumentationStatement: 253 Lesson33 Physics110HJournal‐2013‐2014 MP DocumentationStatement: 254 Physics110HJournal‐2013‐2014 Lesson34 Lesson34 RotationalEnergyandRollingMotion Reading Examples HomeworkProblems 10.4,10.5 10.10‐10.12,CE10.1 10.60,10.62,10.68 LearningObjectives [Obj58] Solveproblemsinvolvingrotationalkineticenergyandexplainitsrelationtotorque andwork. Explaintherelationbetweenlinearandangularspeedinrollingmotion. [Obj59] Useconservationofenergytosolveproblemsinvolvingrotatingorrollingmotion. [Obj57] Notes DocumentationStatement: 255 Lesson34 Physics110HJournal‐2013‐2014 WorkedExample Score(3) Studythegivenproblemandsolution,thenanswerthequestionsregardingtheproblem. Aboulderontopofahillbreaksfreeandbeginstorolldownthehillwithoutslipping. Approximatingtheboulderasasolidspherewithradius3m,whatisthespeedoftheboulderatthe bottomofthehillafterithasundergoneaverticaldisplacementof100m? STRATEGY We will use the principle of conservation of mechanical energy to solve for the speed of the boulder at the bottom of the hill. Conservation of mechanical energy applies to this problem, because, although frictional force is acting on the boulder causing it to roll, no work is done by friction on the boulder. IMPLEMENTATION First, we need to determine the types of mechanical energy in both the initial (top of the hill) and the final (bottom of the hill) states. Since the boulder is initially at rest, it has only gravitational potential energy. The total mechanical energy at the top of the hill is given by After the boulder has undergone a vertical displacement of 100 m, the gravitational potential energy has been converted to translational and rotational kinetic energy. In the final state, the boulder will have a combination of gravitational potential energy, translational kinetic energy and rotational kinetic energy. If we take the bottom of the hill to be where the gravitational potential energy is zero, the total mechanic energy final state becomes 1 2 in the 1 2 The total mechanical energy at the top and at the bottom of the hill is the same (conserved), so our conservation of mechanical energy equation becomes 1 2 1 2 Now we can solve for the translational speed of the boulder at the bottom of the hill. The rotational kinetic energy is dependent on the rotational inertia and angular velocity of the DocumentationStatement: 256 Physics110HJournal‐2013‐2014 Lesson34 boulder. We are told that the boulder is (a) a solid sphere and (b) that is not slipping as it rolls – this means that we can use the rotational inertia of a solid sphere relationship between angular speed and translational speed and the to put rotational kinetic energy in terms of the mass, radius, and translational speed of the boulder. This equation can be simplified further as mass of the boulder appears on both sides of the equation and can be cancelled. CALCULATION Solving for the translational speed of the boulder at the bottom of the hill becomes: 10 7 10 ∙ 9.8 m s 7 ∙ 100m 37 m⁄s Note: The speed of the boulder is independent of both the mass and the radius of the boulder. SELF‐EXPLANATIONPROMPTS 1.Frictionalforceisneededforthebouldertoroll,andnotslide,downthehill.Explainwhy“no workisdonebyfrictionontheboulder”. 2.Explainwhytheboulderhasonlyrotationandtranslationkineticenergyatthebottomofthehill. 3.Howwouldthefinalspeedchangeiftheboulderwasslidingdownthehillinsteadofrolling? Deriveanexpressionforthespeedoftheboulderatthebottomofthehillifitwasslidinginsteadof rolling. DocumentationStatement: 257 Lesson34 Physics110HJournal‐2013‐2014 Pre‐ClassProblem STATEMENTOFTHEPROBLEM Inapinballmachine,asolidmetal0.050‐kgballisreleasedfromaspringandrollsaroundthe machinehittingvarioustargets.Ifthespringhasaspringconstantkof410N/mandiscompressed adistancexof22cm,a)whatistherotationalkineticenergyoftheballimmediatelyafterrelease? b)Whatisthetranslationalkineticenergyoftheballimmediatelyafterrelease? Tryit!(1PFpt):Calculatethetranslationkineticenergyofthe ballifitwasslidinginsteadofrolling.Showyouwork. DocumentationStatement: 258 Answer:0.047J;0.12J Physics110HJournal‐2013‐2014 Lesson34 PreflightQuestions 1. Whattopicfromthereadingwouldyouliketodiscussduringclass? 2. Asolidaluminumcylinder(mass ,radius ,rotationalinertia cylinder(mass2 ,radius ,rotationalinertia )andasolidsteel )startfromthesamepositionandroll downarampwithoutsliding.Atthebottomoftheramp, a) thealuminumcylinderhasgreatertotalkineticenergy. b) thesteelcylinderhasgreatertotalkineticenergy. c) thecylindershavethesametotalkineticenergy. 3. A4.5‐kgbicycletire( 0.6kgm , 37cm)isspinningonamechanic’sstandatthesame rateasifitwererollingatalinearspeed 10m/s.Themechanicappliesthebrake 5m/srollingspeed.Whatisthework supplyingaforcetoslowtherotationequivalentto donebythebrake? a) 16.4mJ b) 164J c) 164J d) 16.4mJ 4. CRITICALTHINKING:An8‐kgwheelhasamomentofinertiaIof0.1kgm2.Thewheelisrolling alongwithoutslipping.Whatistheratioofitstranslationalkineticenergytoitsrotational kineticenergy?Explainhowyouobtainedyouranswer. DocumentationStatement: 259 Lesson34 Physics110HJournal‐2013‐2014 HomeworkProblems 10.60 DocumentationStatement: 260 Physics110HJournal‐2013‐2014 Lesson34 10.62 DocumentationStatement: 261 Lesson34 Physics110HJournal‐2013‐2014 MP DocumentationStatement: 262 Physics110HJournal‐2013‐2014 Lesson35 Lesson35 RotationalVectorsandAngularMomentum Reading Examples HomeworkProblems 11.1– 11.3 11.1 11.16,11.17,11.21 LearningObjectives [Obj60] [Obj61] Determinethedirectionsoftheangulardisplacement,angularvelocityandangular accelerationvectorsforarotatingobject. Determinetheangularmomentumvectorfordiscreteparticlesandrotatingrigid objects. Notes DocumentationStatement: 263 Lesson35 Physics110HJournal‐2013‐2014 WorkedExample Score(3) Studythegivenproblemandsolution,thenanswerthequestionsregardingtheproblem. Acarisdrivingclockwisearoundacircularracetrack.Thetiresonthecarrotate50timesevery second.a)Whatisthecar’sangularvelocityasitasittravelsduenorthanddueeast?b)Whatis theaverageangularaccelerationofthecarduringthe10secondsittakestogofromtravelingdue northtotravelingdueeast. STRATEGY The problem asks about vector quantities, thus the answers have both a magnitude and a direction component which can be considered separately. First, we find the magnitude of the angular velocity and use this to find the magnitude of the average acceleration. To find the direction of the angular velocity and acceleration, we will use the right hand rule to find the velocity direction and from that, deduce the direction of the angular acceleration. IMPLEMENTATION To find the magnitude of the velocity, we apply unit analysis. We find the magnitude of ∆ the angular acceleration using the relation: ∆ velocity, we apply the right hand rule. . To find the direction of the angular CALCULATION a) Angular velocity: 50 rotations second 2 radians rotation 314 rad s b) Average angular acceleration: 314radians s 1 10s 31.4 rad s c) The wheel is rotating forward, so if the fingers of our right hand point wrap forward and down – mimicking the motion of the wheel - then our thumb points to the left (west) which is the direction of the angular velocity. When the car is traveling east, the righthand rule gives us a thumb pointing towards the top of the page (north). To find the direction of the acceleration vector, we draw a vector going from the tip of the west arrow to the tip of the north velocity vector. Thus the acceleration vector is to the north east. DocumentationStatement: 264 Physics110HJournal‐2013‐2014 Lesson35 SELF‐EXPLANATIONPROMPTS 1. Vectorscanbeaddedpictoriallybydrawingthevectorssuchthatthetailofonevectorconnects tothetailofanothervector.Explainhowthisapproachisconsistentwiththeabovestatement thattheaverageaccelerationvectorgoesfromthetipofinitialvectortothetipofthefinal vector. 2. Whichdirectionisthevelocityvectorwhenthecaristravelingwest?South? 3. Howwouldyoudescribethedisplacementvectorofthecar? DocumentationStatement: 265 Lesson35 Physics110HJournal‐2013‐2014 Pre‐ClassProblem STATEMENTOFTHEPROBLEM Achildisdoingtrickswitharemote‐controlledairplane.Initiallythepropellersontheairplaneare spinningat1200rpmastheplanedivesstraighttowardtheground.Threesecondslater,the airplaneisinlevel‐flight,flyingnorthandthepropellersarespinningat1800rpm.Whatwasthe averageangularaccelerationofthepropellers? Answer: 20.9 , 34°abovelevelflight DocumentationStatement: 266 Physics110HJournal‐2013‐2014 Lesson35 PreflightQuestions 1. Whattopicfromthereadingwouldyouliketodiscussduringclass? 2. (True/False)Thenettorque andangularacceleration alwayspointinthesamedirection. a) True b) False 3. (True/False)Theangularacceleration andangularvelocity alwayspointinthesame direction. a) True b) False 4. CRITICALTHINKING:Howcanaparticlewithlinearvelocityhaveangularmomentum? Explain. DocumentationStatement: 267 Lesson35 Physics110HJournal‐2013‐2014 HomeworkProblems 11.16 DocumentationStatement: 268 Physics110HJournal‐2013‐2014 Lesson35 11.17 DocumentationStatement: 269 Lesson35 Physics110HJournal‐2013‐2014 11.21 DocumentationStatement: 270 Physics110HJournal‐2013‐2014 Lesson36 Lesson36 ConservationofAngularMomentum Reading Examples HomeworkProblems 11.4 CE11.1 11.26,11.27,11.43 LearningObjectives [Obj62] Applyconservationofangularmomentumtosolveproblemsinvolvingrotating systemschangingrotationalinertiasandrotatingsystemsinvolvingtotallyinelastic collisions. Notes DocumentationStatement: 271 Lesson36 Physics110HJournal‐2013‐2014 Score(3) WorkedExample Studythegivenproblemandsolution,thenanswerthequestionsregardingtheproblem. STATEMENTOFTHEPROBLEM A2.0‐kgprojectilewithaspeedof5.0m/sstrikesafinonawheel asshownthefigure.Theprojectilestrikesatapoint1.48mtothe rightoftheaxisofrotation.Aftertheprojectilecollideswiththe wheelitstickstothefinatthepointofimpact.Ifthewheelhasa rotationalinertiaofI=100kgm2,whatwillbetheangularvelocity ofthewheel+projectilecombinationafterwards? STRATEGY This problem is an example of a rotational collision. If the wheel spins freely, there is no net torque acting on the system as a whole, so long as the system includes both the wheel and the projectile. In this case, the total angular momentum cannot change (see N2LRot). IMPLEMENTATION The initial angular momentum is that of the projectile: The final angular momentum is that of the wheel plus the projectile attached to the fin: Solving for the final angular velocity we get: CALCULATION 1.48m 2kg 5m/s 100kgm 2kg 1.48m 0.14rad/s Notice that the result depends on the positioning of the launcher relative to the axle of the wheel. DocumentationStatement: 272 Physics110HJournal‐2013‐2014 Lesson36 SELF‐EXPLANATIONPROMPTS 1.Howdoestheresultchangeifyoumovelaunchersothatthepointofimpactisatagreater distancefromtheaxleofthewheel? 2.Canyoutellifthecollisioniselasticorinelastic?Explainhowyouknow,orwhyyoucannottell. 3.Ifyouthinkit'sinelastic,howmuchenergyislostinthecollision?Ifyouthinkit'selasticcheckto seeifyou'recorrect. DocumentationStatement: 273 Lesson36 Physics110HJournal‐2013‐2014 Pre‐ClassProblem STATEMENTOFTHEPROBLEM A12‐kgpotter’swheelisspinningat5.0rpmandhasaradiusof0.5m.Thepotterthrowsa2.0‐kg blockofclayontothewheelwithavelocityof0.75m/sinthesamedirectionasthewheel.How fastisthewheelspinningimmediatelyaftertheclaylandsonthepotter’swheel,inrpm? Answer:0.77rad/s or7.33rpm DocumentationStatement: 274 Physics110HJournal‐2013‐2014 Lesson36 PreflightQuestions 1. Whattopicfromthereadingwouldyouliketodiscussduringclass? 2. Ifanettorqueisappliedtoarigidobject,whichofthefollowingisnottrue? a) b) c) d) Theangularmomentumoftheobjectwillchange. Thekineticenergyoftheobjectwillchange. Theobjectwillexperienceanangularacceleration. Therotationalinertiaoftheobjectwillchange. 3. Aniceskaterisspinningat2rad/secwithherarmsoutstretched.Ifshenowpullsherarmsin closetoherbody,her a) angularmomentumremainsthesame. b) angularvelocityincreases. c) kineticenergyincreases. d) Alloftheabovearetrue. 4. CRITICALTHINKING:Explainwhyhelicoptersmusthavetworotorstofunctionproperly.Your explanationshouldinvolveangularmomentumconcepts. DocumentationStatement: 275 Lesson36 Physics110HJournal‐2013‐2014 HomeworkProblems 11.26 DocumentationStatement: 276 Physics110HJournal‐2013‐2014 Lesson36 11.27 DocumentationStatement: 277 Lesson36 Physics110HJournal‐2013‐2014 11.43 DocumentationStatement: 278 Physics110HJournal‐2013‐2014 Lesson37 Lesson37 CriticalThinking:Energy&AngularMomentum Reading Chapter10&11 Examples None HomeworkProblems 11.46,11.49,MP ThereisanEXAM‐PREPQUIZthislesson. LearningObjectives [Obj62] Applyconservationofangularmomentumtosolveproblemsinvolvingrotating systemschangingrotationalinertiasandrotatingsystemsinvolvingtotallyinelastic collisions. Notes DocumentationStatement: 279 Lesson37 Physics110HJournal‐2013‐2014 PreflightQuestions 1. Whattopicfromthereadingwouldyouliketodiscussduringclass? 2. Aplatformdiverjumpsoffthedivingtowerandperformsatwistmaneuver.Whileintheair,he cannotchangehis a) rotationalenergy. b) rotationalspeed. c) rotationalinertia. d) angularmomentum. 3. Whatconditionmustbetrueinorderfortheangularmomentumofanobjecttobeconserved? a) Nonetexternalforceactsontheobject. b) Nonetexternaltorqueactsontheobject. c) Both(a)and(b)aretrue. 4. CRITICALTHINKING: Attheendofitslife,astargoessupernova.Itscore(radius=20Mm) collapsestoformaneutronstar(radius=6.0km).Iftheinitialrotationrateofthestarwas1 rev/45days,whatistherotationrateoftheneutronstar?(Treatthestarasasolidspherewith .) DocumentationStatement: 280 Physics110HJournal‐2013‐2014 Lesson37 HomeworkProblems 11.46 DocumentationStatement: 281 Lesson37 Physics110HJournal‐2013‐2014 11.49 DocumentationStatement: 282 Physics110HJournal‐2013‐2014 Lesson37 MP DocumentationStatement: 283 Lesson37 Physics110HJournal‐2013‐2014 Notes DocumentationStatement: 284 Physics110HJournal‐2013‐2014 Lesson38 Lesson38 Lab6–ConservationofAngularMomentum Reading 11.4,Lab6Worksheet Examples 11.2 HomeworkProblems 11.45,12.69,12.87 ThereisaLABthislesson. LearningObjectives [Obj62] Applyconservationofangularmomentumtosolveproblemsinvolvingrotating systemschangingrotationalinertiasandrotatingsystemsinvolvingtotallyinelastic collisions. Notes DocumentationStatement: 285 Lesson38 Physics110HJournal‐2013‐2014 JournalQuestions Score(5) 1. Brieflydescribethepurposeandgoalsofthislab.(Onetotwocompletesentences) RefertoConceptualExample11.1inyourtextbookforthefollowingquestions. 2. Whentheboyjumpsontothemerry‐go‐round, a) b) c) d) thetotalrotationalinertiaoftheplatformchanges. thetotalangularmomentumoftheplatformchanges. Both(a)and(b)arecorrect. Neither(a)nor(b)iscorrect. 3. Whenthegirljumpsontothemerry‐go‐round, a) b) c) d) thetotalrotationalinertiaoftheplatformchanges. thetotalangularmomentumoftheplatformchanges. Both(a)and(b)arecorrect. Neither(a)nor(b)iscorrect. 4. Intheexample,thegirljumpsinthesamedirectionastheplatformisrotating.Suppose, instead,thatshejumpsintheoppositedirection,sothathervelocityjustbeforelandingonthe platformiscountertoitsrotation.Describehowyouwouldmathematicallyaccountforthis changewhensolvingforthefinalangularspeedofthemerry‐go‐round. 5. Supposethegirldoesnotjumpdirectlyinthetangentialdirection,butatanangleθtothe tangentialdirection.Describehowyouwouldmathematicallyaccountforthischangewhen solvingforthefinalangularspeedofthemerry‐go‐round. DocumentationStatement: 286 Physics110HJournal‐2013‐2014 Lesson38 LabNotes DocumentationStatement: 287 Lesson38 Physics110HJournal‐2013‐2014 HomeworkProblems 11.45 DocumentationStatement: 288 Physics110HJournal‐2013‐2014 Lesson38 12.69 DocumentationStatement: 289 Lesson38 Physics110HJournal‐2013‐2014 12.87 DocumentationStatement: 290 Physics110HJournal‐2013‐2014 Lesson39 Lesson39 SimpleHarmonicMotion Reading 13.1,13.2,13.3 Example 13.3 HomeworkProblems 13.22,13.67,13.43 ThereisanoptionalEquationDictionaryentryinAppendixDforthislesson(1PFpt). LearningObjectives [Obj63] [Obj64] [Obj65] Definesimpleharmonicmotionandexplainwhyitissoprevalentinthephysical world. Determinetheperiodand frequencyofasimpleharmonicoscillatorfromitsphysical parameters,andcompletelyspecifyitsequationofmotion. Determinethevelocityandaccelerationofasimpleharmonicoscillatorfromits equationofmotion. Notes DocumentationStatement: 291 Lesson39 Physics110HJournal‐2013‐2014 WorkedExample Score(3) Studythegivenproblemandsolution,thenanswerthequestionsregardingtheproblem. STATEMENTOFTHEPROBLEM Anidealgrandfatherclockconsistsofasimplependulumwhichswingsbackandforthonceevery second.Whatisa)theoscillationfrequency,b)theangularfrequencyandc)howfarfromtheend oftherodshouldthemasssit? STRATEGY First, connect the period to the frequency and angular frequency; then we can find the length of the pendulum associated with that angular frequency. IMPLEMENTATION 1. In order to answer part (a) and (b), we need to consider how the frequency of simple harmonic motion relates to the period and also how the oscillation frequency of the pendulum depends on the angular frequency. 2. How does the length of the pendulum relate to the frequency of the pendulum? CALCULATION 1. The period of the spring is inversely related to the oscillation frequency of the spring by 1Hz. The angular frequency is related to the oscillation frequency by 2 2 radians/s. 2. The angular frequency of the pendulum is given by is length is 0.248m. DocumentationStatement: 292 / . Therefore the pendulum Physics110HJournal‐2013‐2014 Lesson39 SELF‐EXPLANATIONPROMPTS 1.Inyourownwords,describethedifferencebetweentheoscillationfrequencyandtheangular frequency. 2.Inyourownwords,explainwhytheperiodofthependulumisnotdependentonthemassofthe pendulum. 3.Inyourownwords,describewhytheperiodofthependulumisinverselyproportionaltothe lengthofthependulum. DocumentationStatement: 293 Lesson39 Physics110HJournal‐2013‐2014 Pre‐ClassProblem STATEMENTOFTHEPROBLEM Aspaceprobeissenttoadistantplanettodetermineifitissuitableforcolonization.Afterhaving successfullymetalltheothercriteria,thereisoneremainingtest:isthegravitationalpullofthe planetwithin30%ofEarth’snormalgravity?Theprobecontainsasimplependulumwhichituses todeterminethegravitationalconstantofthatplanet.Thecompactpendulumisonly5.0cmlong andtakes0.33secondstomovefromtheleftmostpartofitsswingtothecenterofitsswing.Isthe planetsuitableforcolonization? Answer:No,since gnew=1.14m/s2 DocumentationStatement: 294 Physics110HJournal‐2013‐2014 Lesson39 PreflightQuestions 1. Whattopicfromthereadingwouldyouliketodiscussduringclass? 2. Astronauts in space took a coiled spring of known spring constant k, attached a bob (small mass) to it, and set it oscillating. Measuring the period, they could determine a) the time of day the acceleration due to gravity b) the mass of the bob c) the weight of the bob 3. Anadultandachildaresittingonadjacentidenticalswings.Oncetheygetmoving,theadult,by comparisontothechild,willnecessarilyswingwith a) amuchgreaterperiod b) amuchgreaterfrequency c) thesameperiod d) thesameamplitude 4. CRITICALTHINKING:Anoscillationisaphysicalphenomenoncharacterizedbythefactthatthe configurationofthephysicalsystemrepeatsitselfoverandoveragain.Simpleharmonic oscillationsareaspecialcase.An oscillation is simple harmonic if the period does not depend on the amplitude. In the following set, identify the oscillations that are simple harmonic, the ones that are approximately simple harmonic, and the ones that are not simple harmonic. Briefly explain your reasoning for each. a) Thependuluminagrandfatherclock. b) Aboatinwaterpusheddownandreleased. c) Achildonaswing. d) Amasshangingfromanidealspring. e) Apingpongbouncingonthefloor. DocumentationStatement: 295 Lesson39 Physics110HJournal‐2013‐2014 HomeworkProblems 13.22 DocumentationStatement: 296 Physics110HJournal‐2013‐2014 Lesson39 13.67 DocumentationStatement: 297 Lesson39 Physics110HJournal‐2013‐2014 13.43 DocumentationStatement: 298 Physics110HJournal‐2013‐2014 Lesson40 Lesson40 EnergyinSimpleHarmonicMotion Reading Examples HomeworkProblems 13.5 13.5 13.29,13.63,13.73 LearningObjectives [Obj66] Determinethepotentialandkineticenergiesofasimpleharmonicoscillatoratany pointinitsmotion,anddescribethetimedependenceoftheseenergies. Notes DocumentationStatement: 299 Lesson40 Physics110HJournal‐2013‐2014 WorkedExample Score(3) Studythegivenproblemandsolution,thenanswerthequestions regardingtheproblem. STATEMENTOFTHEPROBLEM Amotionlessmassisconnectedtoaspring(withaspringconstantof85N/m) whichiscompressed30cmfromitsequilibriumposition.Themass,whichis restingonafrictionlesssurface,isthenreleased.Atwhatpositionwillthe kineticenergyofthesystembeequaltoexactlyhalfthepotentialenergyofthe system? STRATEGY 30cm Since the spring starts at rest, the system has potential energy, but no kinetic energy. When the spring is released, the total mechanical energy of the system is conserved. This means that when the initial potential energy is equal to 2/3 of it’s initial value, the kinetic energy will be half the potential energy of the system. IMPLEMENTATION 1. What is the spring potential energy of the system as a function of position? 2. What is the total mechanical energy of the system? 3. We then solve for the position where the potential energy is equal to 2/3 of its initial value. CALCULATION 1. ∆ 3.83J 2.Since the system is initially at rest, the total mechanical energy is equal to the initial potential energy. 3. 2.55J position gives ∆ ∆ / / . Solving for 24.5cm. DocumentationStatement: 300 Physics110HJournal‐2013‐2014 Lesson40 SELF‐EXPLANATIONPROMPTS 1.Whydon’tyouneedtoexplicitlycalculatethekineticenergyofthesystem? 2.Whatpointisthefinalanswerfordisplacementrelativeto? 3.Whydoesthepointwherethepotentialenergyisequalto2/3itsinitialvaluecorrespondtothe pointwherethekineticenergyishalfthepotentialenergy? DocumentationStatement: 301 Lesson40 Physics110HJournal‐2013‐2014 Pre‐ClassProblem STATEMENTOFTHEPROBLEM Amotionlessmassisconnectedtoaspringwhichisstretched45cmfromitsequilibriumposition. Themass,whichisrestingonafrictionlesssurface,isthenreleased.Themaximumkineticenergy ofthesystemis10.6J.Whatisthespringconstantofthespring? Answer:132N/m DocumentationStatement: 302 Physics110HJournal‐2013‐2014 Lesson40 PreflightQuestions 1. Whattopicfromthereadingwouldyouliketodiscussduringclass? 2. For thesimpleharmonicmotionofamassonaspringwithoutfriction,itistruethat a) theenergyisindependentoftheamplitude b) theenergyisindependentoftheperiod c) both(a)and(b) d) neither(a)nor(b) 3. The position x(t) of a simple harmonic oscillator is shown to the right as a function of time. Which of the graph sets below correctly represent the kinetic and potential energies of the oscillator ? A B C D a) b) c) d) GraphAisthepotentialenergy,graphCisthekineticenergy. GraphCisthepotentialenergy,graphAisthekineticenergy. GraphBisthepotentialenergy,graphDisthekineticenergy. GraphDisthepotentialenergy,graphBisthekineticenergy. 4. CRITICALTHINKING:Foragivenharmonicoscillator,ifthespringconstantandthemassare bothdoubledbuttheamplituderemainsthesame,explainwhathappenstothemechanical energyoftheoscillator. DocumentationStatement: 303 Lesson40 Physics110HJournal‐2013‐2014 HomeworkProblems 13.29 DocumentationStatement: 304 Physics110HJournal‐2013‐2014 Lesson40 13.63 DocumentationStatement: 305 Lesson40 Physics110HJournal‐2013‐2014 13.73 DocumentationStatement: 306 Physics110HJournal‐2013‐2014 Block4Review Block4Review LearningObjectives [Obj49] Explaintherelationbetweentherotationalmotionconceptsofangulardisplacement, angularvelocity,andangularacceleration. [Obj50] Useequationsofmotionforconstantangularaccelerationtosolveproblemsinvolving angulardisplacement,angularvelocity,andangularacceleration. [Obj51] Usecalculustosolveproblemsinvolvingmotionwithnon‐constantangular acceleration. [Obj52] Explaintheconceptoftorqueandhowtorquescausechangeinrotationalmotion. [Obj53] Givenforcesactingonarigidobject,determinethenettorquevectorontheobject. [Obj54] Determinetherotationalinertiaforasystemofdiscreteparticles,rigidobjects,ora combinationofboth. [Obj55] Compareandcontrasttheconceptsofmassandrotationalinertia. [Obj56] UseNewton’ssecondlawanditsrotationalanalogtosolveproblemsinvolving translationalmotion,rotationalmotion,orboth. [Obj57] Solveproblemsinvolvingrotationalkineticenergyandexplainitsrelationtotorque andwork. [Obj58] Explaintherelationbetweenlinearandangularspeedinrollingmotion. [Obj59] Useconservationofenergytosolveproblemsinvolvingrotatingorrollingmotion. [Obj60] Determinethedirectionsoftheangulardisplacement,angularvelocityandangular accelerationvectorsforarotatingobject. [Obj61] Determinetheangularmomentumvectorfordiscreteparticlesandrotatingrigid objects. [Obj62] Applyconservationofangularmomentumtosolveproblemsinvolvingrotating systemschangingrotationalinertiasandrotatingsystemsinvolvingtotallyinelastic collisions. [Obj63] Definesimpleharmonicmotionandexplainwhyitissoprevalentinthephysical world. [Obj64] Determinetheperiodandfrequencyofasimpleharmonicoscillatorfromitsphysical parameters,andcompletelyspecifyitsequationofmotion. [Obj65] Determinethevelocityandaccelerationofasimpleharmonicoscillatorfromits equationofmotion. [Obj66] Determinethepotentialandkineticenergiesofasimpleharmonicoscillatoratany pointinitsmotion,anddescribethetimedependenceoftheseenergies. Notes DocumentationStatement: 307 Block4Review Physics110HJournal‐2013‐2014 Lesson31:“Areyouready?” Readtheproblembelowandworkthroughtheguidedsolution,thenanswerthequestions regardingtheproblem. STATEMENTOFTHEPROBLEM A3‐mdiameterflywheelisspinningupwithanangularaccelerationof3rad/s2.Whatisthetotal linearaccelerationattherimofthewheelattheinstantwhenitsangularvelocityis12rpm? STRATEGY(Fillintheblank) Since the wheel has an angular acceleration, there is tangential linear acceleration . We note that the linear acceleration depends on the radius, i.e. points farther from the center have larger linear accelerations (as well as larger linear velocities.) The rotating points also have a centripetal acceleration, directed at the center of rotation. We calculate both accelerations and add the two vectors, which are perpendicular to each other. CALCULATION The tangential acceleration at = _____ x _____ = 4.5 m/s2 The centripetal acceleration is equal to For the equation / . In terms of angular velocity to be valid, the angular velocity has to be in radians. To convert 120 rpm into radians we write 12 The centripetal acceleration is then _______x ________ = 2.5 m/s2. 1.3 . / . The magnitude of the total acceleration is 5.1 m/s2. The direction of the total acceleration is 60.9 degrees. SELF‐EXPLANATIONPROMPTS 1.Explaininyourownwordswhytheangularspeedofarigidrotatingobjectisthesameforall partsoftheobjectwhilethelinearspeedsofdifferentpartsoftheobjectvarywiththeradius. 2.Justifytherelationac=ω2r. 3.Isthecentripetalaccelerationinanywayrelatedtotheangularacceleration? OptionalPracticeProblems:10.13,10.18,10.41 DocumentationStatement: 308 Physics110HJournal‐2013‐2014 Block4Review Lesson32:“Areyouready?” Readtheproblembelowandworkthroughtheguidedsolution,thenanswerthequestions regardingtheproblem. STATEMENTOFTHEPROBLEM Twoweightsofmasses2mandmareattachedtoeitherendofathinrodoflengthL.Calculatethe rotationalinertiaofthemass‐rodsystemaboutaperpendicularrotationalaxisthroughthecenter oftherod.Assumethethinrodhasnegligiblemass. STRATEGY(Fillintheblanks.) The rotational inertia of an object that consists of multiple discrete masses depends on how those discrete masses are spatially distributed relative to the axis of rotation. For this problem, the object consists of three components: _______________, _______________, and ___________ connecting the two weights. The thin rod has negligible mass, so it does not contribute to the rotational inertia of the system. To determine the rotational inertia of the system, we will sum the rotational inertia of each component. CALCULATION(Fillintheblanks.) The rotational inertia of the object is determined by summing the individual rotational inertias for each discrete mass. When the rotation axis is through the center of the rod, the rotational inertia is: ∑ ____________+ ___________ 3 4 SELF‐EXPLANATIONPROMPTS 1.Inyourownwords,explainrotationalinertiaofanobject. 2.Inthisproblem,whywasthedistancefromtherotationaxisrequaltoL/2forbothweights? 3.Wouldtherotationalinertiaoftheobjectincrease,decrease,orstaythesameiftherotationaxis wasatoneendinsteadofthroughthecenteroftherod? OptionalPracticeProblems:10.22,10.24,10.29 DocumentationStatement: 309 Block4Review Physics110HJournal‐2013‐2014 Lesson33:“Areyouready?” Readtheproblembelowandworkthroughtheguidedsolution,thenanswerthequestions regardingtheproblem. STATEMENTOFTHEPROBLEM A50‐kgbucketishangingfromarope,whichiswoundarounda20‐kgsoliddisc.Thediameterof thediskis50cm.Themassoftheropeisnegligiblecomparedtotheothermassesintheproblem. Whatistheaccelerationofthefallingbucket? STRATEGY(Fillintheblanks.) We will draw free-body diagrams for the two objects of interest: the bucket and disk. We will then apply Newton’s Second Law to each object and the system of two equations for the unknown acceleration. CALCULATION(Fillintheblanks.) Newton’sLawforthefallingbucket: _____________ Newton’sLawfortherotatingdisc: _______________ Eliminating ½ from the two equations and solving for the acceleration we get 8.2m/s 1 2 SELF‐EXPLANATIONPROMPTS 1.Supplythemissingalgebra.Writedownthetwoequationsofmotion,eliminatethetensionand solvefortheacceleration. 2.Inafewsentencestrytoexplainwhytheradiusofthediscdoesnotaffectthefinalresult. OptionalPracticeProblems:10.32,10.59 DocumentationStatement: 310 Physics110HJournal‐2013‐2014 Block4Review Lesson34:“Areyouready?” Readtheproblembelowandworkthroughtheguidedsolution,thenanswerthequestions regardingtheproblem. STATEMENTOFTHEPROBLEM YouarehelpingtounloadcargooffaC‐130Herculesaircraft.Thecargoispackedinbarrels,soyou decideitwillbeeasiertorollthebarrelsdowntherampatthebackoftheaircraftandofftheplane. Ifabarrelhasaspeedof0.5m/swhenitreachestheramp,whatisitsspeedafterithasrolled downtherampwithoutslippingandofftheplane?Theverticalheightoftherampis1.5meters. STRATEGY(Fillintheblanks.) We will use the principle of conservation of _________________ to solve for the speed of the barrel at the end of the ramp. CALCULATION(Fillintheblanks.) Starting with conservation of _________________, we substitute in the types of energy in the initial (at the top of the ramp) and final (at the bottom of the ramp) states. ______ + (______ + _______)0 =( )f because the barrel is not Now, we replace ω with ____________ and put rotational inertia in terms of mass and radius of the barrel. (Approximating the barrel as a solid cylinder, its rotational inertia is 1 2 1 2 1 2 ) Solving for the final speed of the barrel at the end of the ramp gives: √_______________ 4.5 / SELF‐EXPLANATIONPROMPTS 1.Comparetherotationalinertiaofahollowcylindertoasolidcylinder.Ifthebarrelwereinstead hollow,woulditreachthebottomoftherampearlierorlaterthanifitwassolid?Assumethesame initialspeed. 2.Doesthefinalanswerdependonthemassortheradiusofthebarrel?Explain. OptionalPracticeProblems:10.38,10.36,10.61 DocumentationStatement: 311 Block4Review Physics110HJournal‐2013‐2014 Lesson35:“Areyouready?” Readtheproblembelowandworkthroughtheguidedsolution,thenanswerthequestions regardingtheproblem. STATEMENTOFTHEPROBLEM Whatisthemagnitudeanddirectionoftheangularmomentumofa10‐kgsoliddisc,60cmin diameter,rotatingcounter‐clockwiseat120rpmarounditscentralaxis? STRATEGY(Fillintheblanks.) We will use the relation, ___ , and the ____________ rule to find the answer. CALCULATION(Fillintheblanks.) First, we need to convert rotational speed from rpm to rad/s ______ For a solid disc rotating around it central axis _____ _______ 0.45kgm Now substitute to get: 5.66kg m s The direction, from the right-hand rule, is __________________________. SELF‐EXPLANATIONPROMPTS 1.Howwouldtheanswerchangeisthediscwasahoop? 2.Whyaretherenounitsofradiansinthefinalanswer? OptionalPracticeProblems:11.15,11.19,11.22 DocumentationStatement: 312 Physics110HJournal‐2013‐2014 Block4Review Lesson36:“Areyouready?” Readtheproblembelowandworkthroughtheguidedsolution,thenanswerthequestions regardingtheproblem. STATEMENTOFTHEPROBLEM Twodisksarerotatingatdifferentspeedsalongthesameaxisasshown.The topdiskis5kgandrotatingat1.0rad/s;thebottomdiskis10kgandrotating at2.0rad/s.Ifthetopdiskisreleasedandlandsonthebottomdisk,whatisthe finalangularspeedofthecombineddisks? STRATEGY(Fillintheblanks.) This problem is an example of a _______________________. There is no net torque acting on the system, so the total angular momentum does not change (conserved). CALCULATION(Fillintheblanks.) The initial angular momentum of the top disk is: I ___________________ The initial angular momentum of the bottom disk is: I ___________________ The final angular momentum of the combined disks can be determined by ___________________________________. Solving for the final angular velocity, we get: _________________; _________________ SELF‐EXPLANATIONPROMPTS 1.Showthatkineticenergyisnotconversedintheexample. 2.Examplewhyangularmomentumisconversedbutkineticenergyisnot. OptionalPracticeProblems:11.25,11.28 DocumentationStatement: 313 Block4Review Physics110HJournal‐2013‐2014 Lesson39:“Areyouready?” Readtheproblembelowandworkthroughtheguidedsolution,thenanswerthequestions regardingtheproblem. STATEMENTOFTHEPROBLEM Ayounggirldecidestobuildasimplependulumtoknockoveratoycar.Todoso,shetiesoneend ofa40‐cmstringtotherailingandarubberballtotheotherendofthestring.Thesetupis designedsothattheballwillhitthetoycarwhenthependulumisatthelowestpointofitsarc.The girlpositionsthependulumsothatthestringistightandtheballis10cmofftheground.Howlong doesittakefortheballstrikethetoycar? STRATEGY(Fillintheblanks.) First, we find the period of the pendulum. The time it takes the ball to swing from its initial position to the collision point is ¼ the period. CALCULATION(Fillintheblanks.) ______ The time it takes the pendulum to strike the car is 0.32s. SELF‐EXPLANATIONPROMPTS 1.Whyisthefinalansweronly¼oftheperiod? 2.Whydoesn’ttheinitialheightofthependulumaffecttheperiodoftheswing? OptionalPracticeProblems:13.31,13.22,13.25 DocumentationStatement: 314 Physics110HJournal‐2013‐2014 Block4Review Lesson40:“Areyouready?” Readtheproblembelowandworkthroughtheguidedsolution,thenanswerthequestions regardingtheproblem. STATEMENTOFTHEPROBLEM A2.0‐kgmassisattachedtoaverticallyorientedspringwhichhasaspringconstantof25N/m.The springiscompressed31cmrelativetoitsequilibriumpoint.Whatisthespeedofthemassatthe equilibriumpointofthespring? STRATEGY(Fillintheblanks.) This is a conservation of energy problem. The mass initially has both gravitation potential energy and spring potential energy. At the equilibrium point, all of this energy is converted to kinetic energy. CALCULATION(Fillintheblanks.) For convenience, we choose the equilibrium point of the spring to be the reference point. ______=6.99J The gravitational potential energy is The spring potential energy is At the equilibrium point, ______= Solving for velocity we find that _______=2.40 J . 3.1 m/s. SELF‐EXPLANATIONPROMPTS 1.Whyistheequilibriumpointaconvenientchoiceoforigin? 2.Explain,inyourownwords,howyoufoundthekineticenergyattheequilibriumpoint. 3.Whycanthespringenergybecombinedwiththegravitationalenergy? OptionalPracticeProblems:13.41,13.43,13.77 DocumentationStatement: 315 Block4Review Physics110HJournal‐2013‐2014 Notes DocumentationStatement: 316 Physics110HJournal‐2013‐2014 Block4Review Notes DocumentationStatement: 317 Block4Review Physics110HJournal‐2013‐2014 Notes DocumentationStatement: 318 Physics110HJournal‐2013‐2014 Block4Review Notes DocumentationStatement: 319 Block4Review Physics110HJournal‐2013‐2014 Notes DocumentationStatement: 320 Physics110HJournal‐2013‐2014 AppendixA:LabReportTemplate AppendixA:LabReportTemplate Purpose Aformallabreportisessentialtothescientificprocess.Itisthemostcommonwaythattheresults ofascientificstudyarecommunicatedtothescientificcommunity.Youmayassumeyouraudience isscientificallyliteratebuthasnotperformedtheexperimentinquestion. Format Usethefollowingguidancetoformatyourreport: Useaclearlyreadable12‐pointfont Setthepagebordersto1” Spacelineswithinthesameparagraphat1.0or1.15 Separateparagraphswithadoublespace Usesectionheadingstoidentifytransitionsbetweensections Refertoyourexperimentand/orcalculationsinthepasttense Usethethird‐person(i.e.,avoidusing“I”or“we”) Usescientificnotationwhereappropriateandincludeallunits(e.g.,1.1 10 m) Citeanyoutsidesources(otherthanyourtextbook)usingMLAformat Ifyouincludeafigure,centeritinthepageandensureithasadescriptivecaption underneathit.Youmayneatlyhand‐drawfigures. Graphsorplotsmaybeusedtosummarizedataandshowanalysis.Theymustincludea titleandlabeledaxesandmustnotbedonebyhand.Ensurethegraphorplotislarge enoughtobeclearlyreadandinterpretedbyyourreader.Forclarity,youmaychooseto cross‐referencethegraphorplotandincludeitasanattachmentattheendofyourreport. Yourinstructormayprovideadditionalguidance. Sections Usethefollowingformattocreateyourlabreport.Rememberthereisabalancebetweentoolittle informationandtoomuchinformation.Youwantyourreporttoincludewhatisrelevantwithout becomingtoolong,complicated,orconfusing.Yourreaderwilllikelynotstrugglethroughapoorly writtendocument,whichmeansheorshewillneverlearnofyourresultsorfindings. TitlePage Useaseparatetitlepage.Ensurethetitleofyourreportiscenterednearthetopofthefirstpage. Listallcontributorstothelabreportunderneaththetitle.Alsoincludethecoursenameand numberandthedate.Atthebottomofthetitlepage,neatlyincludeyourdocumentationstatement foranyoutsidehelpyouobtained(butnotoutsidereferences). xix AppendixA:LabReportTemplate Physics110HJournal‐2013‐2014 Introduction Inthissection,youwillprovideabriefintroductiontoyourreaderaboutyourpurposeandthe importanceofyourwork.Youshouldalsobrieflysummarizeanypertinentmaterial,including relevantequationsorconcepts. ExperimentalMethods Inthissection,youmustsuccinctlydescribethemethodsyouusedtoobtainyourdata.Ingeneral, readerswillbemostinterestedinreadingaboutyourdata,results,andconclusions,butifyour resultsareinteresting,areaderwillalsobeinterestedinhowyouobtainedyourdata.Focuson keepingthissectioncompletebutconcise.Graphicsandfiguresshouldbeusedsparinglyinthis section. ResultsandDiscussion Thisisanextremelyimportantsectionofyourreport.Hereyoushouldcommunicatewhatyou foundanddrawpertinentconclusionsbasedoninterpretationofyourdata.Graphics,figuresand Excelplotsmaybeusedtoeffectivelycommunicateyourresults.FollowtheguidanceintheFormat section.Makesureyourresultsarecorroboratedorjustifiedbythedatayouobtained.Keepin mindthatnotalldataisnumerical.Forthelabsinthiscourse,youmaybeabletomakesome powerfulconclusionsbasedonqualitativeobservations. Conclusion Hereyouwillsummarizeyourresults.Ensureyoudonotintroduceanynewinformationinthis section. References Ifyoucitedanyreferences,includethemhereusingMLAformat. Appendixes(ifneeded) Usethissectiontoplaceanylargeorcomplicatedgraphsordataplots. Grading Seetheindividuallablessonsfortherubricyourinstructorwillusetogradeyourreport.Youwill begradedontheappearanceandqualityofyourlabreport. xx Physics110HJournal‐2013‐2014 AppendixB:SignificantFigures,UncertaintyandErrorPropagation AppendixB:SignificantFigures,Uncertaintyand ErrorPropagation References: [1] P.R.Bevington,andD.K.Robinson,DataReductionandErrorAnalysis,3rded.,McGraw‐Hill,NewYork,2003. [2] USAirForceAcademy,CoreChemistry/PhysicsLaboratoryDataAnalysisGuide. Numericcalculationsandexperimentalmeasurementsareonlyasaccurate(orreliable)astheleast precisemeasurement.Everyphysicalmeasurementhasuncertaintyandlaboratorymeasurements donotyieldexactresults.Errorsanduncertaintiesinphysicalexperimentsmustbereduced throughexperimentaltechniquesandrepeatedmeasurements–remaininguncertaintymustbe estimatedandreportedtoestablishthevalidityoftheresult. Thetermerrorisdefinedasthedifferencebetweenobserved(orcalculated)valueandthe“true” value.Inlaboratorymeasurementswerarelyknowthetruevalue,thereforewemustestablish systematicmeansofdeterminingthevalidityofourexperimentalresults.Errorsthatoriginatefrom mistakesinmeasurementareknownasillegitimate(gross)errors,andarecorrectedthrough attentionandcarefulrepeatedmeasurements.Inourexperimentsweareconcernedwith uncertaintiesintroducedbyrandomfluctuationsinmeasurementsandsystematicerrorsthatlimit theprecisionandaccuracyofourresults.Randomerrorsarefluctuationsthatoccurinobservations eachtimeameasurementisrepeated.Randomerrormaybereduced throughlaboratorytechniqueorrepeatedobservations.Systemic errorsaredifficulttodetectandmaymakeallourresultsvarywith reproduciblediscrepancy.Systemicerrormayresultfrompoorly calibratedequipmentorbiasbytheobserver. (a)(b) Accuracyisameasureofhowclosetheresultistothetruevalue. Precisionisameasureofhowwelltheresulthasbeendetermined (withoutregardtoagreementwithtruevalue).Precisionisalsoa measureofanexperiment’sreproducibility.FigureB1illustratesthe differencebetweenaccuracyandprecision. xxi FIG.B1.Accuracyand precisiondemonstrated throughtargetpractice. Target(a)isaccurate,butnot precise,while(b)isprecise butnotparticularlyaccurate. AppendixB:SignificantFigures,UncertaintyandErrorPropagation Physics110HJournal‐2013‐2014 SignificantFigures Thenumberofdigitsinreportinganexperimentalresultimpliestheprecisionofameasurement anduncertaintyshouldbereportedspecificallywitheachnumericresult. Rulesfornumberofsignificantfigures: 1. 2. 3. 4. Leftmostnonzerodigitisthemostsignificantdigit. Ifthereisnodecimalpoint,therightmostnonzerodigitistheleastsignificantdigit. Ifthereisadecimalpoint,therightmostdigitistheleastsignificantdigit,evenifitisazero. Thenumberofdigitsbetweenthemostandleastsignificantdigitcountareknownastheas significantfigures. Rulesforsignificantfiguresincalculatingnumbers: 1. Multiplication/division.Thenumericresultcannothavemoresignificantfiguresthananyof theoriginalnumbers. 2. Addition/subtraction.Theresultcannothavemoresignificantdigitstotherightofthe decimalpointthananyoftheoriginalnumbers. 3. Roundingresults.Insignificantdigitsaredroppedfromtheresultandthelastdigitis roundedforbestaccuracy. Uncertainty Everyphysicalmeasurementhasuncertaintyduetotheaccuracyorprecisionoflaboratory equipmentandtherandomdistributionofourdata.Sincewedonotnormallyknowtheactualerror (discrepancyfromthetruevalue)inexperimentalresults,weseektodevelopamethodof determiningtheestimatederror.Analysisofthedistributionofrepeatedmeasurementscanleadto anunderstandingoftheexperimentalerror,reportedasthespreadofthedistribution.Determine thebestvalue anduncertaintyestimate ,andreporttheresultas . Uncertaintyinexperimentalmeasurementscanbeestimatedinanumberofways,including standardreadingofanalogordigitalinstruments,orstatisticalanalysisofthedistributionof repeatedmeasurements. xxii (B1) Physics110HJournal‐2013‐2014 AppendixB:SignificantFigures,UncertaintyandErrorPropagation UncertaintyinAnalogMeasurements Uncertaintyinreadinganalogdevices(rulers,balances,graduated cylinders,etc.)isestimatedasonehalfthesmallestdivision markedonthedevice. Example:Alengthmeasurementistakenusingarulermarkedin incrementsof1mmasshowninFigureB2.Uncertaintyisonehalfthe smallestincrement,or0.5mm.Thelengthisreportedas26 0.5mm accordingtoEqn.B1. FIG.B2.Analogmeasurement usingaruler. UncertaintyinDigitalMeasurements Manymodernlaboratorydevicesaredigital(scales,timers, multimeters,etc.).Systematicerrorisreducedifthedeviceis properlycalibrated.Estimateduncertaintyistheleastsignificant digitthatcanbedisplayedifthereadingisconstant(i.e.not fluctuating).Ifthereadingisfluctuating,repeatedmeasurements mustbetakenandothermethodsofestimatinguncertaintymustbe used. FIG.B3.Digitalmeasurement Example:Atimemeasurementistakenusingaphotogatetimerreadingto usingphotogatetimer. one‐thousandthofasecondasshowninFigureB3.Uncertaintyistheleast significantdigit,or0.001s.Thetimemeasurementisrecordedas1.673 0.001saccordingtoEqn.B1. UncertaintyinRepeatedMeasurements Repeatedmeasurementshelpusextractthebestvalueofourexperimentalresultsanddetermine theestimatederrorwithconfidence.Aswetakemoremeasurements,weexpectapatternto emergewithdatapointsdistributedaroundthecorrectvalue(assumingwecorrectforsystematic errors). Supposeduringanexperiment,wetakeasampleof measurementsofaquantity . Thearithmeticmean ̅ oftheexperimentaldistributionisgivenas ̅ ∑ . (B2) Theexpressionforthestandarddeviation ofthesamplepopulationisgivenby ∑ ̅ (B3) whichrepresentsthebestestimateforthedeviationsquaredoftheparentdistribution(asifwe tookandinfinitenumberofmeasurements)basedonthesmallersampledistribution.Thestandard deviation representsaquantitativemeasureoftheuncertaintyinanysinglemeasurement.Ifwe xxiii 13.6% 13.6% weretotakeanothersamplemeasurementthereisa68.2% chanceitwillbewithin ̅ ,a95.4%chanceitwillbewithin ̅ 2 ,anda99.7%chanceitwillbewithin ̅ 3 ,asshown inFigureB4. 34.1% Physics110HJournal‐2013‐2014 34.1% AppendixB:SignificantFigures,UncertaintyandErrorPropagation Givenrepeatedtrialsandcalculationsofthemean,itis 2 ̅ 2 possibletodeterminevariationinthevalueofthemean. FIG.B4.Normal(Gaussian)distribution Whendeterminingexperimentalresultswithalargesample withstandarddeviation . size,weseekaquantitativemeasureofthestandarddeviation ofthemean,orthestandarddeviationinthesamplemeanrelativetothetrue(mean)value. ∑ √ ̅ (B4) Experimentalresultsbasedonthissampledistributionarereportedas ̅ . (B5) Forsmallsamplesets(threeorfewertrials),wemayestimateuncertaintyusingtheexpression . (B6) ErrorPropagation Experimentalquantitiesderivedfrommeasuredvalueswithuncertaintywillinturnhave uncertainty.Estimateduncertaintyiscalculatedbasedonthemathematicaloperationsusedinthe derivation.Supposewemeasurevalues( , , , , , )withuncertainty( , , , , , ).We seektheuncertaintyinacalculatedvalue . AdditionorSubtractionwithUncertainty If then . MultiplicationorDivisionwithUncertainty If xxiv (B7) Physics110HJournal‐2013‐2014 AppendixB:SignificantFigures,UncertaintyandErrorPropagation then | | . (B8) MultiplicationbyaKnownValuewithUncertainty IfQiscalculatedbymultiplyingbyaknownvalue (e.g. 2 or )byaquantity with uncertainty, then | | (B9) orequivalently | | . (B10) | | UncertaintywithExponents If isanexactnumberand then | | | | . | | (B11) ReportingExperimentalValues Itshouldbeemphasizedthatuncertaintyestimatesareonlyestimatesandvaluesshouldbe presentedwithappropriateprecision. Rulesforreportingexperimentalvalues: 1. Theleastsignificantfigureinanyreportedvalueshouldbethesameorderofmagnitude (samedecimalposition)astheuncertainty. 2. Estimateduncertaintyisnormallyroundedtoonesignificantfigure. xxv AppendixC:MathematicsReference Physics110HJournal‐2013‐2014 AppendixC:MathematicsReference QuadraticFormula Solutionsofthequadraticequation 0aregivenbythequadraticformula. √ 2 QuadraticFormula 4 CoordinateSystems Conventiondictatesright‐handedcoordinatesystems.Alternatecoordinatesystemsmaybeused– besuretoclearlyindicatechosencoordinateaxes.Twocommoncoordinatesystemsusedin physicsareshownbelow. CartesianCoordinateSystem , , ̂ ̂ ̂ ̂ SphericalCoordinateSystem , , 0 0 0 sin cos ̂ sin sin 2 xxvi ̂ sin sin sin ̂ ̂ cos Physics110HJournal‐2013‐2014 AppendixC:MathematicsReference Trigonometry Opposite sin Opp Hyp csc 1 sin Hyp Opp cos Adj Hyp sec 1 cos Hyp Adj Adjacent sin cos tan Opp Adj 1 tan cot cos sin Adj Opp sin LawofSines sin LawofCosines sin 2 cos TrigonometricIdentities sin sin sin 2 sin sin cos cos 1 1 2 sin cos sin cos cos tan cos 2 sec cos cos sin sin cos 1 1 cot 2 sin cos cos sin sin 2 sin cos cos cos 2 cos cos cos cos 2 sin sin xxvii ∓ csc 2 cos 1 ∓ sin sin AppendixC:MathematicsReference Physics110HJournal‐2013‐2014 Vectors Givenvectors ̂ ̂ and ̂ ̂ , cos ∙ ∙ ̂ sin ̂ ExponentialsandLogarithms ln ≅ 2.71828 … ln ln ln ln ln ln ln ln ln ln 10 log ln 1 ≡ 0 1 DerivativesandIntegrals 1 , sin where isaconstant. cos cos sin 1 1 cos cos ln / / xxviii 1. sin 1 1 sin ln , 1 √ √ Physics110HJournal‐2013‐2014 AppendixC:MathematicsReference TaylorSeriesExpansionsandApproximations ATaylorseriesexpansionofarealfunction aboutapoint isgivenby ⋯ 2! . ! SeriesExpansionsofCommonFunctions(for| | 1) For| | ≪ 1 1 sin cos 1 2! 3! 5! 7! 2! 4! 6! ln 1 1 2 3 2! ⋯ cos ⋯ ⋯ sin ⋯ 4 1 1 1 ⋯ 3! xxix 1 2 ln 1 1 1 AppendixD:EquationDictionary Physics110HJournal‐2013‐2014 AppendixD:EquationDictionary Oncertainlessons,youwillhavetheoptiontocompleteaworksheetonaparticularequationfor pre‐flightpoints.Theequationdictionaryisdesigned:(1)toallowyoutobecomemorefamiliar withanequation,and(2)toenableyoutocreateahighlyorganizedandeasilyaccessiblestudy guideforexampreparation.Themoretimeyouspendcreatingmeaningfulentriestoyourequation dictionary,themorepreparedyouwillbeforexamsinthecourse. Inthewhiteboxontheupperleftcorner,youwillfindtheequationreferencenumber.Intheblack boxintheupperrightcorner,youwillfindthelessonnumberwheretheequationisfirst introduced.Anexampleofahigh‐qualityequationdictionaryentryisshownbelow. xxx Physics110HJournal‐2013‐2014 AppendixD:EquationDictionary #1 PhysicsConcept Variables(includeallunits) DescriptionandNotes Diagram xxxi AppendixD:EquationDictionary Physics110HJournal‐2013‐2014 1 2 #2 PhysicsConcept Variables(includeallunits) DescriptionandNotes Diagram xxxii Physics110HJournal‐2013‐2014 AppendixD:EquationDictionary #3 PhysicsConcept Variables(includeallunits) DescriptionandNotes Diagram xxxiii AppendixD:EquationDictionary Physics110HJournal‐2013‐2014 #4 ∙ PhysicsConcept Variables(includeallunits) DescriptionandNotes Diagram xxxiv Physics110HJournal‐2013‐2014 AppendixD:EquationDictionary #5 ∆ / PhysicsConcept Variables(includeallunits) DescriptionandNotes Diagram xxxv AppendixD:EquationDictionary Physics110HJournal‐2013‐2014 #6 PhysicsConcept Variables(includeallunits) DescriptionandNotes Diagram xxxvi Physics110HJournal‐2013‐2014 AppendixD:EquationDictionary 1 2 #7 PhysicsConcept Variables(includeallunits) DescriptionandNotes Diagram xxxvii AppendixD:EquationDictionary Physics110HJournal‐2013‐2014 #8 PhysicsConcept Variables(includeallunits) DescriptionandNotes Diagram xxxviii Physics110HJournal‐2013‐2014 AppendixD:EquationDictionary cos #9 PhysicsConcept Variables(includeallunits) DescriptionandNotes Diagram xxxix AppendixE:RotationalInertiasandAstrophysicalData Physics110HJournal‐2013‐2014 AppendixE:RotationalInertiasandAstrophysicalData Table10.2RotationalInertias AstrophysicalData Earth Mass Meanradius OrbitalPeriod SurfaceGravity 5.97 10 kg 6.37 10 m 3.16 10 9.81 m s Moon Mass Meanradius OrbitalPeriod SurfaceGravity 7.35 10 kg 1.74 10 m 2.36 10 1.62 m s Sun Mass Meanradius OrbitalPeriod SurfaceGravity 1.99 10 kg 6.96 10 m 6 10 274 m s xl Physics110HJournal‐2013‐2014 AppendixF:UnitsandConversions AppendixF:UnitsandConversions Ref:http://wwwppd.nrl.navy.mil/nrlformulary/NRL_FORMULARY_07.pdf PhysicalQuantity Dimension Length Mass Time ElectricCurrent Temperature AmountOfSubstance SIUnits BASEUNIT BASEUNIT ElectricPotential ∙ 3 10 3 ∙ / 1 3 1 3 ∙ / / / ∙ ∙ , Inductance 1 , MagneticField MagneticFlux Φ Momentum,Impulse Permeability Pressure,Stress Tension SpecificHeatCapacity ∙ ∙ ∙ ∙ ∙ / ‐‐‐‐‐ 36 10 ‐‐‐‐‐ 10 10 Work Energy ∙ 10 ∙ / 10 10 ∙ ∙ ∙ xli ∙ ∙ ∙ 10 ∙ 10 ∙ ∙ 1 4 ∙ 10 10 ∙ 10 1 ∙ ∙ ∙ VectorPotential ∙ 10 10 ∙ / 1 ∙ / / ∙ ∙ ∙ ThermalConductivity ∙ ∙ / 10 1 1 9 1 9 ∙ ∙ ∙ ∙ 10 10 10 1 Permittivity 10 10 ∙ 1 Impedance,Resistance Viscosity 10 Frequency Velocity 3 12 ,ϕ 10 10 / 9 / BASEUNIT / ElectricCharge Torque / / GaussianUnits 1 ∙ ∙ / Displacement Power Conversion Factor CurrentDensity Force SISymbol 1 ElectricField SIUnits 10 1 Entropy InTermsof OtherSIUnits AngularVelocity 10 GaussianUnits 1 3 PhysicalQuantity Density 10 BASEUNIT Dimensions SI Gaussian Current 10 Capacitance BASEUNIT Acceleration Conversion Factor SISymbol 10 10 ∙ Physics110HJournal‐2013‐2014 Ref:http://physics.nist.gov/cuu/Constants/index.html PhysicalConstant Symbol Value Uncertainty AtomicMassUnit 1.660 538 782(83) 10-27 kg AtomicUnitOfCharge 1.602 176 487(40) AvogadroConstant BohrMagneton C 927.400 915(23) 10-26 J T-1 5.788 381 7555(79) 10-5 eV T-1 0.529 177 208 59(36) 10-10 m 0.529 177 208 59(36) Å 1.380 6504(24) 10-23 J K-1 8.617 343(15) 10-5 eV K-1 0.695 035 6(12) cm-1 K-1 2.083 664 4(36) 1010 Hz K-1 0.510 998 910(13) MeV 5.485 799 0943(23) 10-4 amu 8.187 104 38(41) 10-14 J 1.073 544 188 8.065 544 65(20) ComptonWavelength 2.426 310 2175(33) 10-12 m ElectronMass 9.109 382 15(45) 10-31 kg 1.602 176 487(40) ElectronVolt FaradayConstant Fine‐StructureConstant Impedance Vacuum J 7.297 352 537 6(50) 10-3 1.112 650 056 10-17 kg 1.380 6504(24) InverseCentimeter MolarGasConstant 10-23 J 6.241 509 65(16) 1018 eV 5.034 117 47(25) 1022 cm-1 8.617 343(15) 0.695 035 6(12) cm-1 10-5 eV 2.417 989 454 1014 Hz 6.022 141 79(30) 1026 amu 5.609 589 12(14) 1035 eV 8.987 551 787 1016 J 1.986 445 501(99) 10-23 J 1.239 841 875(31) 10-4 eV 1.331 025 0394(19) 10-13 amu 2.997 924 58 1010 Hz 1.008 664 915 97(43) amu 1.505 349 505(75) 10-10 J 8.314 472(15) J mol-1 K-1 (@ 273.15 K, 101.325 kPa) 1.674 927 211(84) 10-27 kg 939.565 346(23) MeV ⁄2 5.050 783 24(13) 3.152 451 2326(45) 12.566 370 614 10-7 N A-2 Permeability MagneticConstant 10-27 J T-1 Permittivity ElectricConstant 8.854 187 817 10-12 F m-1 PlanckConstant 6.626 068 96(33) 10-34 J s ProtonMass RydbergConstant Stefan‐BoltzmannConstant NUMBERSandAPPROXIMATIONS 10-8 eV 1.054 571 628(53) Js 6.582 118 99(16) 10-16 eV s 1.672 621 637(83) 10-27 kg 938.272 013(23) MeV 10 973 731.568 527(73) 101 325 Pa (@ 273.15 K) 2.542 623 616(64) 10-4 cm-1 T-1 4.135 667 33(10) 10-15 eV s 10-34 m-1 T-1 4 π 10-7 H m-1 109 737.315 8 299 792 458 m s-1 StdAtmosphere StdAccelerationOfGravity cm-1 1 / 137.035 999 679(94) 22.413 996(39) 10-3 m3 mol-1 NeutronMass SpeedOfLight Vacuum amu 103 376.730 313 461 Ω Kilogram PlanckConstant/2π 10-9 ∙ 13.996 246 04(35) 109 Hz T-1 6.674 28(67) 10-11 m3 s-2 kg-1 Kelvin NuclearMagneton Joule MolarVolumeOfIdealGas 10-19 ∙ 0.466 864 515(12) cm-1 T-1 96 485.339 9(24) C mol-1 ⁄ GravitationalConstant 1.492 417 830(74) 10-10 J ⁄2 ⁄ 7.513 006 671(11) 1012 cm-1 6.022 141 79(30) 1023 mol-1 BoltzmannConstant 931.494 028(23) MeV BohrRadius 10-19 cm-1 1.007 276 466 77(10) amu 1.503 277 359(75) 10-10 J ( ( ) 13.605 691 93(34) eV ) 2.179 871 97(11) 10-18 J / 29.92 inHg 14.696 psi 760 Torr 9.806 65 m s-2 5.670 400(40) 10-8 W m-2 K-4 π 3.141592653589793… e 2.718281828459045… xlii ≅1973.27 eVÅ ≅0.511MeV Physics110HJournal‐2013‐2014 Physics215ConstantsandEquationsSheet ElectricForce(Coulomb)Const ElectricConst(Permittivity) MagneticConst(permeability) ElementaryCharge 8.99 10 N m C 8.85 10 4 10 1.60 10 4 C N m Conversions: NA 1G C 1eV ElectronMass 9.11 10 kg ProtonMass 1.67 10 kg PlanckConst 6.63 10 J s 10 T 1.60 10 MaxwellEquations Gaussfor ∙ Faraday ∙ Φ Gaussfor ∙ Ampère ∙ 0 Φ ⋅ ∆ ∆ sin sin 1.22 Φ Ɛ ⋅ ̂ ∆ ∙ Φ ̂ Φ ∙ xliii ∆ ∆ 2 J Physics110HJournal‐2013‐2014 Physics110HCourseSyllabus KEY: –Doubleperiod; CE–ConceptualExample; EPQUIZ–Exam‐PrepQuiz; CTE‐CriticalThinkingExercise Lab– LabExercise; Learning Objectives LessonTitle 1 Introduction PHYSICSTESTING 2 Displacement,Velocity,andAcceleration 3 Lab1–AccelerationDuetoGravity 4 Two–Dimensional&ProjectileMotion 5 ProjectileMotion EPQUIZ 6 Lab2–ProjectileMotion 7 AccelerationinCircularMotion Reading Examples Homework Problems 2.1,2.2 1.16,1.24,2.51 4–9 Chapter1. 2.1,2.2 2.3,2.4 2.1–2.3 2.20,2.35,2.79 10 2.5,Lab1 2.6 2.38,2.42,2.78 11–14 3.1–3.5 3.3 3.34,3.53,3.54 14,15 3.5 3.4 3.55,3.70,MP 15 Lab2 3.4 MP,3.58,MP 16,17 3.6 3.7,3.8 MP,MP,3.80 4.15,4.26,4.60 1–6 8 GRADEDREVIEW1 18–20 4.1–4.4 4.1,4.2 10 UsingNewton’sLaws 9 ForcesandNewton’sLawsofMotion 19–23 4.5,4.6 4.3,4.4,4.5 4.34,4.47,4.49 11 Newton’sLawsinTwoDimensions 22 5.1 5.1,5.2 5.16,MP,5.38 12 Newton’sLawswithMultipleObjects 13 Lab3–Newton’sLaws 14 Newton’sLawsinCircularMotion EPQUIZ 23 5.2 5.4 5.19,5.21,5.71 23 5.2,Lab3 5.4 MP,MP,MP 16,17,22 5.3 5.5,5.6,5.7 5.65,5.73,MP 15 Newton’sLawswithFriction 24,25 5.4,5.5 5.9,5.10,5.11 5.43,MP.5.57 16 CTE:Newton’sLawswithNon‐constantMass 18 9.3,Handout None 5.30,5.62,6.54 18 WorkwithConstantandVaryingForces 26,27 6.1,6.2 6.1–6.5 6.18,6.20,6.52 19 KineticEnergyandPower 28–29,34 6.3,6.4 6.6,6.7,6.9 6.29,6.64,6.71 20 PotentialEnergy 30–33 7.1,7.2 7.1,7.2 7.14,7.31,7.42 21 ConservationofMechanicalEnergy 34–35 7.3,7.4 7.4,7.5,7.6 7.24,7.25,7.55 34 7.3,Lab4 7.5 7.56,7.59,7.63 23 OrbitalMotion 36–38 8.1–8.3 8.1,8.2,8.3 8.17,8.39,MP 24 GravitationalEnergy 39–41 8.4 8.4 8.27,8.52,13.41 17 GRADEDREVIEW2 22 Lab4–ConservationofEnergy 25 CTE:OrbitalEnergies 39,40 8.4 8.5 MP,8.61,8.67 26 CenterofMass EPQUIZ 42 9.1 9.16,9.37,9.89 27 ConservationofLinearMomentum&Collisions 43–48 9.1–9.5 46–48 9.5,9.6,Lab5 9.1,9.2,9.3 CE9.1,9.4,9.5, 9.7 None 9.28,9.44,9.61 47,48 9.3,9.4 9.10 MP,9.68,9.78 49–51 10.1,10.2 10.1,10.2,10.3 10.19,10.32,10.45 52–55 10.2,10.3 10.4,10.5 10.30,10.28,10.52 55–56 10.3 10.56,10.57,MP 34 RotationalEnergyandRollingMotion 57–59 10.4,10.5 35 RotationalVectorsandAngularMomentum 60,61 11.1–11.3 10.8,10.9 10.10,10.11, 10.12,CE10.1 11.1 28 Lab5–Collisions 29 CollisionsandConservationofEnergy 9.38,MP,MP 30 GRADEDREVIEW3 31 RotationalMotion 32 Torque&RotationalInertia PHYSICSTESTING 33 RotationalAnalogofNewton’sSecondLaw 36 ConservationofAngularMomentum 10.60,10.62,10.68 11.16,11.17,11.21 62 11.4 CE11.1 11.26,11.27,11.43 62 Chpt10&11 None 11.46,11.49,MP 62 11.4,Lab6 11.2 11.45,12.69,12.87 39 SimpleHarmonicMotion 63–65 13.1–13.3 13.1,13.3 13.22,13.67,13.43 40 ApplicationsofSimpleHarmonicMotion 66 13.5 13.5 13.29,13.63,13.73 37 CTE:EnergyandAngularMomentum EPQUIZ 38 Lab6–ConservationofAngularMomentum FINALEXAM
