AP Physics C: Summer Assignments
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PopeJohnAPPhysicsC SummerAssignment WelcometoAPPhysicsC!APPhysicsCisequivalenttoacollegelevelphysicscourseforengineeringmajors.Itcoversa varietyofphysicstopicsusingcalculus. ForthoseofyouwhotookAPPhysics1orhonorsphysics,thiscourseisdifferentinthatitusescalculusmethodsand conceptstoanalyzephysicalsituations.Italsostressesprecisemathematicalderivationsofallphysicalphenomena.You willfindfewornoproblemsthataskfornumericsolutions.Rather,mostproblemswillaskforsymbolicderivationsusing algebraandcalculus. AnotherdifferencewithAPPhysics1isthatAPPhysicsCissplitintotwoindependenttests:MechanicsandE&M.You willtakebothtestsonMondayMay9,2016intheafternoon.ThesetwotestsareeachabouthalfthelengthoftheAP Physics1test,sothetotaltestingtimeisthesame,butyougettwoscores. TherearefewertopicscoveredinCthaninAP1/Honors.InC,thereisnothermal,nuclear,fluid,sound,waves,oroptical physics.However,youwillgointomuchmoredepthonthemechanics,electricity,andmagnetismtopics.Thereisalsoa considerableamountofrotationalmotioninAPPhysicsC,whereastherewasrelativelylittleinAPPhysics1(orhonors physics). Thepurposeofthesummerworkistoensurestudentsarereadytotacklethematerialstartingwiththeveryfirstclass inSeptember. Sendmeyouremailaddress Pleaseemailmeyouremailaddressandtheemailaddressofatleastoneparent.Iwillmaintainamailinglist,andifany errorsorchangestothesummerassignmentarefound,Icaninformyouofthenewinformation.Sendto stephenpendergrast@popejohn.org Also,feelfreetosendemailwithanyquestionsyouhaveabouttheassignment,thecourse,etc.Ifyouarehaving troublelearningthematerialfromtheresourcesprovidedhere,Imaybeabletosuggestotherresources,orImaybe abletoclearupanymisconceptionsviaemail. MandatorySummerAssignment Toprepareforthecourse,allstudentsmustsuccessfullycompletethissummerassignment.Failuretohandinthe summerassignmentwillresultinremovalfromtheclass. Thesummerassignmentisequaltoamajortestgradeinmarkingperiod1,sopoorperformanceontheassignmentwill severelyimpactyourMP1grade.Thatmeansyoucan’tjusthandinahalf-heartedeffortonthesummerassignment. Inaddition,thesummerassignmentwillprepareyouforatestwhichwillbeadministeredwithinthefirst7daysofclass. Thatmeansyouneedtodotheworkyourselfsoyouknowthematerial.Lookingupanswersontheinternetorcopying someoneelse’sworkwillessentiallyguaranteeyouwilldopoorlyonthoseearlytestsbecauseyouwillnothave practicedthematerial.Whileit’sfinetoaskforhelponaproblemhereorthere,youneedtodothebulkofthework yourselftoreallyunderstandthematerial. DeliveryDatesandProcedures Therearethreepartstotheassignmentdueoverthecourseofthesummer.Youmaydelivertheassignmentinthe followingways: • • • EMAIL:stephenpendergrast@popejohn.org FAX:973-587-8154 POSTALMAIL: StevePendergrast 146HendersonRd Stockholm,NJ07460 Thedatesofeachsectionareshownbelow.Thematerialmustbepostmarkedbythedatelistedifsentbypostalmail. • • • PART1:July10 PART2:July31 PART3:Bringfirstdayofclass Latepenalties Latesummerassignmentsthataremailed,faxed,oremailedlose5percentagepointsperdaythattheyarelate.At10 dayslatetheassignmentismarked0andguidancewillbeinformedthatthestudenthasbeenremovedfromAPPhysics C.Thethirdpart,whichistobehandedinonthefirstdayofclass,ismarkedlateaccordingtotheclasshomework policy,10%perdayandmarked0at1weeklate. OnlineResources Thetextbookandotherresourcestobeusedbytheclassare: • • • • TWUPhysics:ManyfreeshortphysicstutorialsareavailableatTwuPhysics: https://sites.google.com/site/twuphysicslessons/ TherearemanyothervideosonyoutubethatarerelatedtoAPPhysicsC,feelfreetoexplore. CALCULUSVIDEOS:Therearesomegoodcalculusvideoshere: http://online.math.uh.edu/HoustonACT/videocalculus/ Forpurposesofthissummerwork,Isuggestyouusethesevideos:1,2,5,6,8,11,12,14,15,21,22, 23,24.Thisisabout4.5hoursofviewingtime.Youshouldtreattheseasanactualclassandtakenotes. STUDYGUIDE:Inaddition,anAPPhysicsCstudyguidewillberequiredstartingOctober1.Becausethe studyguidecompaniesdonotupdatetheirguidesuntilSeptemberyoucannotpurchasethisaheadof time.IwillevaluateallofthemajorstudyguidesinSeptemberandwillchooseonebeforeOctober1. SUMMERASSIGNMENTPART1:DifferentialCalculus:DueJuly10 Youshouldalreadyunderstandalittleaboutlimitsfromyourhonorsprecalcclass.Inthisassignment,youwillreview limitconcepts,thenextendthatintobasicdifferentialcalculus,thenyouwilldoapacketofproblems. Forthisassignment: 1. ViewUniversityofHoustonVideos:1,2,5,6,and8.Takenotes.Iwillasktoseeyournotesonthefirstdayof classforahomeworkgrade. 2. Doproblemsinpacket1(attached).Delivertomeusingoneofthemethodsoutlinedearlier. PART2:IntegralCalculus:DueJuly31 Integralcalculusallowsyoutofindareasundercurvesandisusefulinmanyphysicsderivations. Forthisassignment: 1. WatchUniversityofHoustonVideos:11,12,14,15,21,22,23,24,andtakenotes.Iwillasktoseeyournoteson thefirstdayofclassforahomeworkgrade. 2. Dotheproblemsinpacket2(attached).Delivertomeusingoneofthemethodsoutlinedearlier. PART3:FormulasandGreekLettersDrill:Handinonfirstdayofclass TheAPPhysicsCexamdoesnotallowyoutouseacalculatororhavealistofformulasforthemultiplechoicesection. Almosteveryquestionrequiresyoutoknowaformulaandapplyittoaphysicalsituation.Soyouwillmemorizesomeof theformulasinthisassignment.Inaddition,GreeklettersareextensivelyusedinPhysicsandmath.Greeklettersmake formulasseemmorecomplicatedbecauseyouarenotasfamiliarwiththatalphabet.Tocombatthiseffect,youwillalso memorizetheGreekalphabetinordertobecomemorefamiliarwithallthesymbols. Dothefollowing: 1. SeetheattachedpageswhichcompriseonesheetofequationsandonesheetlistingtheGreekalphabet.There arealsoblankversionsofthesesheetswhichincludethesubjectheadingsandthefirstpartoftheequation (like,“V=“)butdonotshowtheactualequation,orshowthenamesofGreeklettersbutnotthesymbols. 2. Makeseveralcopiesoftheblankversion.Foryourconvenience,aPDFfilecalledAP-PHYS-B-BLANKFORMULA GREEKTEST.pdfispostedintheresourceslinksoyoucansimplyuseyourcomputerprintertoreproducecopies. Ifyouaretravellingthissummeranddonothaveaccesstotheinternet,pleasemakecopiesbeforeyouleave. 3. Memorizebothsheets.Testyourselfbyfillingintheblanksheets.Youwillprobablyhavetodothisatleast10 timestogeteverythingright.Forthefinalversionthatyouhadin,limityourselfto15minutes. 4. Handinthefinal“test”yougiveyourselfathome.Noteonthesheettheamountoftimeittookyoutocomplete thetest. Donotbeconcernedthatyoudonotyetknowhowtoapplymanyorevenmostofthoseformulas.Iamnotaskingyou tounderstandhowtousetheformulas—Iamonlyaskingyoutomemorizethem.HINT:Lookforpatternsinthe formulas. NOTE:Ofcourseyoucouldcheatandsimplyhavethefullformulasheetinviewwhileyoutestyourselfathome.That’s notadvisablebecausetheveryfirstclasswillincludea15minutetestofthismaterialanditwillcountasaquizgradein markingperiod1. ANOTHERNOTE:Youshouldnotmemorizetheformulasbasedonthepageposition.Thetestyoutakeinclassmay changetheorderoftheequations.Youmaywanttoconsidermakingflashcards. APPhysicsCSummerAssignmentPacket1(DueJuly10) 1. Explaininyourownwordsthemeaningoftakingaderivativeofafunction. 2. Explaininyourownwordsthemeaningofthesecondderivativeofafunction. 3. Iff(x)isafunction,givetwodifferentbutequivalentnotationsforthederivativeofthat function. 4. Iff(x)isafunction,givetwodifferentbutequivalentnotationsforthesecondderivative ofthatfunction. 5. Iff(x)isacontinuousdifferentiablefunction,explaininwordsacalculusprocedureto findallthelocalminimaandmaximaofthatfunction. 6. Iff(x)isacontinuoustwice-differentiablefunctionandyouhaveobtainedalistof minimalandmaxima,explainhowyouwouldusecalculustodeterminewhichofthose valuesareminimaandwhicharemaxima. 7. π π₯ = π₯ ! + 3π₯ + 2 !! ! !" = 8. π π₯ = −3π₯ ! − 2π₯ + 4 π′(π₯) = 9. π π₯ = −π₯ ! + 4π₯ ! + 2π₯ !! ! a. = !" b. π′′(π₯) = 10. π π₯ = 2π₯ ! + 4π₯ ! + 2π₯ a. !! ! !" = !!! ! b. = !! ! 11. π π₯ = −2π₯ !" + π₯ ! − π₯ a. !! ! !" = b. π′′(π₯) = 12. π π₯ = π₯ ! + 4π₯ ! + 2π₯ − 4 a. π ! π₯ = b. π !! π₯ = 13. π π₯ = 2π₯ ! + 2π₯ ! + 2π₯ !! ! ! !! ! = 14. π π₯ = sin (π₯ ! ) a. π ! π₯ = b. π ! ′ π₯ = 15. π π₯ = sin! π₯ a. π ! π₯ = b. π ! ′ π₯ = Forthefollowingitems,usethechain,productandquotientrulesasappropriate.Donot multiplyoutthepolynomials! 16. π π₯ = 4π₯ ! + 2π₯ ! a. !! ! !" = 17. π π₯ = !!! ! ! ! !! a. π ! π₯ = Forthefollowing,findthelocalminimaandmaximaofthefunctionsanddeterminewhichare minimaandwhicharemaxima.Whereappropriate,usethechainrule,theproductrule,orthe quotientrule. 18. π π₯ = π₯ ! − 2π₯ ! + 3π₯ − 1 19. π π₯ = !!! ! !! ! 20. π π₯ = 2π₯ ! + 1 ! APPhysicsCSummerAssignmentPacket2(DueJuly31) 1. Explaininyourownwordsthemeaningofthedefiniteintegralofafunction. 2. Explaininyourownwordsthemeaningofananti-derivativeofafunction. 3. Explainhowderivativesandintegralsarerelatedtoeachotherbythefundamental theoremofcalculus.Yourexplanationdoesnothavetobeoverlyprecise,justtellme whatthebasicrelationshipis. 4. π π₯ = π₯ ! + 3π₯ + 2 a. ∫ π π₯ ππ₯ = ! b. ! π π₯ ππ₯ = 5. π π₯ = −3π₯ ! − 2π₯ + 4 ! !! π π₯ ππ₯ = 6. π π₯ = −π₯ ! + 4π₯ ! + 2π₯ ! π ! π₯ ππ₯ = 7. π π₯ = 6π₯ ! + 3π₯ ! + 2π₯ a. ∫ π π₯ ππ₯ = ! π ! b. π₯ ππ₯ = 8. π π₯ = −2π₯ !" + π₯ ! − π₯ ∫ π π₯ ππ₯ = 9. π π₯ = π₯ ! + 4π₯ ! + 2π₯ − 4 ! !! π π₯ ππ₯ = 10. π π₯ = −3 sin (π₯) !! ! π π₯ ππ₯ = 11. π π₯ = 3 cos π₯ + 2 sin π₯ + π₯ ! a. !! ! π π₯ ππ₯ = b. ! !! π π₯ ππ₯ = APPHYVICSMECHANICSFORMULASHEET UniformAcceleration AngularVelocity,Accel. Symbolmeanings π£ = π£! + ππ‘ ! π₯ = π₯! + π£! π‘ + ππ‘ ! π£ = ππ ! π= ! π = π! + πΌπ‘ πora=acceleration πΉ=force πΉ!"#$%& =normalforce f=frequency h=height g=accelofgravitynearearth’ssurface G=UniversalGravitationconstant I=rotationalinertia J=impulse K=kineticenergy k=springconstant l =length L=angularmomentum m=mass P=power π=momentum r=radius(ordistance) π=positionvector T=period t=time U=potentialenergy π£ ππ v=velocityorspeed W=workdoneonasystem x=position π =coefficientoffriction π=angle π=torque π ππ π=angularspeed πΌ =angularacceleration ! π£ ! = π£!! + 2π π₯ − π₯! GeneralForceEquations ∑πΉ = πΉ!"# = ππ = !! !" π½ = πΉ ππ‘ = π₯π πΉ!"#$%#&' ≤ ππΉ!"#$%& Work,Energy,Power,Momentum π = ∫ πΉ ⋅ ππ = ΔπΎ 1 πΎ = ππ£ ! 2 ππ π =πΉ⋅π£ = ππ‘ π π!"# = Δπ‘ π = ππ£ Gravitation π! = ππβ(nearEarth’ssurface) πΉ! = − !!! !! π! = − !!! !! !! ! (univ.lawofgrav.) SimpleHarmonicMotion π= !! ! ! = (periodisrecipoffreq) ! πΉ!"#$%& = −ππ₯ 1 π!"#$%& = ππ₯ ! 2 π!"#$%& = 2π ! ! π!"#$%&%' = 2π 1 π = π! + π! π‘ + πΌπ‘ ! 2 CentripetalAcceleration π!"#$ = π£! = π ! π π Torque(analogtoforce) ∑π = π!"# = πΌπΌ = !! !" π = π×πΉ MomentofInertia(analogtomass) πΌ = ∫ π ! ππ = ∑ππ ! CenterofMass π!" = ∑!! ∑! AngularMomentum πΏ = π×π = πΌπ RotationalWork,Energy,Power π= πΎ= !! π ππ !! ! πΌπ ! ! !! π =π⋅π = !" __________________________________ StaticEquilibrium ∑π = ∑πΉ = 0 ElasticCollision(bounceapart) ! ! π! π£! + π! π£! = π! π£!! + π! π£!! ! ! π! π£!! π! π£!! π! π£!! π! π£!! + = + 2 2 2 2 InelasticCollision(sticktogether) π! π£! + π! π£! = π! + π! π£ ! π! π£! + π! π£! π£! = π! + π! AP PHYVICS MECHANICSBLANKSHEET UniformAcceleration AngularVelocity,Accel. π£ = π₯ = π£ ! = π£ = π= π = π = GeneralForceEquations ∑πΉ = πΉ!"# = π½ = πΉ!"#$%#&' ≤ Work,Energy,Power, Momentum π = πΎ = π = π!"# = π = Gravitation π! =(nearearth surf.) πΉ! = grav.) π! = (univ.lawof SimpleHarmonicMotion π =(periodisrecipof freq) πΉ!"#$%& = π!"#$%& = π!"#$%& = π!"#$%&%' = Symbolmeanings πora= πΉ= πΉ!"#$%& = f= CentripetalAcceleration h= π!"#$ = g= G= Torque(analogtoforce) I= ∑π = π!"# = J= K= π = k= MomentofInertia(analogtomass) l = πΌ = L= CenterofMass m= π!" = P= AngularMomentum π= πΏ = r= π= RotationalWork,Energy,Power T= π = t= πΎ = U= π = ___________________________________________ π£ ππ v= W= StaticEquilibrium x= π = π= π= ElasticCollision(bounceapart) π ππ π= πΌ = InelasticCollision(sticktogether)
