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IntroductoryPhysics PHYS101 Dr RichardH.CyburtOfficeHours TRF9:30-11:00am AssistantProfessorofPhysics F12:30-2:00pm Myoffice:402cintheScienceBuilding Myphone:(304)384-6006 Meetingsmayalsobearrangedatothertimes, byappointment Myemail:[email protected] Inpersonoremailisthebestwaytogetahold Checkmyscheduleonmyofficedoor. ofme. PHYS101 PHYS101:IntroductoryPhysics 400 Lecture:8:00-9:15am,TRScienceBuilding Lab1:3:00-4:50pm,FScienceBuilding304 Lab2:1:30-3:20pm,MScienceBuilding304 Lab3:3:30-5:20pm,MScienceBuilding304 Lab20:6:00-7:50pm,MScienceBuilding304 PHYS101 MasteringPhysicsOnline GotoHYPERLINK"http://www.masteringphysics.com."www.masteringphysics.com. ◦ UnderRegisterNow,selectStudent. ◦ Confirmyouhavetheinformationneeded,thenselectOK!Registernow. RCYBURTPHYS101),andchooseContinue. ◦ Enteryourinstructor’sCourseID( ◦ EnteryourexistingPearsonaccountusername andpassword andselectSignin. ◦ YouhaveanaccountifyouhaveeverusedaPearsonMyLab &Masteringproduct,suchasMyMathLab,MyITLab,MySpanishLab,or MasteringChemistry. ◦ Ifyoudon’thaveanaccount,select Create andcompletetherequiredfields. ◦ Selectanaccessoption. ◦ Entertheaccesscodethatcamewithyourtextbookorwaspurchasedseparatelyfromthebookstore. PHYS101 Midterm2 Therewillbeabonusassignment,basedonyourexam ◦ ◦ ◦ ◦ Willearnyouextrapointsonyourexam Itwillbeonlineasahomework Youmustdobetteronthisassignment,thanyourtesttogetbonuspoints Bonus=30%x(Homework– Midterm) BonusHomeworkisOnline,dueOct17,12:59pm (justbeforelabsstartfortheday) AfterBonusHWisdue,therewillbeasignoutsheetinmyoffice ◦ Youmustsigntogetyourexam PHYS101 IntroductoryPhysics PHYS101 DouglasAdams Hitchhiker’sGuidetotheGalaxy PHYS101 You’realreadyknowphysics! Youjustdon’tnecessarilyknowtheterminologyand languageweuse!!! PhysicsofNASCAR PhysicsofAngerBirds PHYS101 Inclass!! PHYS101 Thislecturewillhelpyouunderstand: ConservationofMomentum InelasticCollisions Momentum&Collisionsin2D AngularMomentum PHYS101 Section9.4 Conservationof Momentum ©2015PearsonEducation,Inc. ConservationofMomentum Theforcesactingontwoballs duringacollisionforman action/reactionpair.They haveequalmagnitudebut oppositedirections(Newton’s thirdlaw). Ifthemomentumofball1 increases,themomentumof ball2willdecreasebythe sameamount. ©2015PearsonEducation,Inc. LawofConservationofMomentum Thereisnochangeinthetotal momentumofthesystem no matterhowcomplicatedthe forcesarebetweentheparticles. Thetotalmomentumofthe systemisconserved. ©2015PearsonEducation,Inc. LawofConservationofMomentum Internalforces actonly betweenparticleswithina system. Thetotalmomentumofa systemsubjectedtoonly internalforcesisconserved. ©2015PearsonEducation,Inc. QuickCheck9.7 Youawakeinthenighttofindthatyourlivingroomisonfire.Yourone chancetosaveyourselfistothrowsomethingthatwillhitthebackof yourbedroomdoorandcloseit,givingyouafewsecondstoescapeout thewindow.YouhappentohavebothastickyballofclayandasuperbouncySuperballnexttoyourbed,boththesamesizeandsamemass. You’veonlytimetothrowone.Whichwillitbe?Yourlifedependson makingtherightchoice! ◦ ThrowtheSuperball. ◦ Throwtheballofclay. ◦ Itdoesn’tmatter.Throweither. ©2015PearsonEducation,Inc. QuickCheck9.7 Youawakeinthenighttofindthatyourlivingroomisonfire. Youronechancetosaveyourselfistothrowsomethingthatwill hitthebackofyourbedroomdoorandcloseit,givingyouafew secondstoescapeoutthewindow.Youhappentohavebotha stickyballofclayandasuper-bouncySuperball nexttoyourbed, boththesamesizeandsamemass.You’veonlytimetothrow one.Whichwillitbe?Yourlifedependsonmakingtheright choice! ◦ ThrowtheSuperball. Larger Dp Þ more impulse to door ◦ Throwtheballofclay. ◦ Itdoesn’tmatter.Throweither. ©2015PearsonEducation,Inc. QuickCheck9.8 Amosquitoandatruckhaveahead-oncollision.Splat!Whichhasalarger changeofmomentum? ◦ ◦ ◦ ◦ Themosquito Thetruck Theyhavethesamechangeofmomentum. Can’tsaywithoutknowingtheirinitialvelocities. ©2015PearsonEducation,Inc. QuickCheck9.8 Amosquitoandatruckhaveahead-oncollision.Splat!Whichhasalarger changeofmomentum? ◦ ◦ ◦ ◦ Themosquito Thetruck Theyhavethesamechangeofmomentum. Can’tsaywithoutknowingtheirinitialvelocities. Momentum is conserved, so Dpmosquito + Dptruck = 0. Equal magnitude (but opposite sign) changes in momentum. ©2015PearsonEducation,Inc. LawofConservationofMomentum Externalforcesareforcesfromagents outsidethesystem. Externalforcescan changethemomentum ofthesystem. ©2015PearsonEducation,Inc. LawofConservationofMomentum Thechangeinthetotalmomentumis isthenetforceduetoexternalforces. Ifthetotal momentumofthesystemdoesnotchange. Anisolatedsystem isasystemwithnonetexternalforceactingonit,leaving themomentumunchanged. ©2015PearsonEducation,Inc. LawofConservationofMomentum Thelawofconservationofmomentumforanisolatedsystemiswritten Thetotalmomentumafteraninteractionisequaltothetotal momentumbeforetheinteraction. ©2015PearsonEducation,Inc. LawofConservationofMomentum Sincemomentumisavector,wecanrewritethelawofconservationof momentumforanisolatedsystem: ©2015PearsonEducation,Inc. Example9.5Speedoficeskaterspushing off Twoiceskaters,SandraandDavid, standfacingeachotheronfrictionlessice. Sandrahasamassof45kg,Davidamass of80kg. Theythenpushofffromeachother. Afterthepush,Sandramovesoff ataspeedof2.2m/s. WhatisDavid’sspeed? ©2015PearsonEducation,Inc. Example9.5Speedoficeskaterspushing off(cont.) PREPARE Thetwoskatersinteract witheachother,buttheyforman isolatedsystembecause,foreach skater,theupwardnormalforceof theicebalancestheirdownward weightforcetomake Thusthetotalmomentumofthesystemofthetwoskatersisconserved. FIGURE9.17showsabefore-and-aftervisualoverviewforthetwoskaters. Thetotalmomentumbeforetheypushoffis becausebothskatersareatrest.Consequently,thetotalmomen-tumwill stillbe0aftertheypushoff. ©2015PearsonEducation,Inc. Example9.5Speedoficeskaterspushing off(cont.) SOLVE Sincethemotionisonly inthex-direction,we’llneedto consideronlyx-componentsof momentum. WewriteSandra’sinitialmomentumas (pSx)i =mS(vSx)i, wheremS ishermassand(vSx)i herinitialvelocity. Similarly,wewriteDavid’sinitialmomentumas(pDx)i =mD(vDx)i. Boththesemomentaarezerobecausebothskatersareinitiallyatrest. ©2015PearsonEducation,Inc. Example9.5Speedoficeskaterspushing off(cont.) Wecannowapplythe mathematicalstatementof momentumconservation, Equation9.15.Writingthe finalmomentumofSandraas mS(vSx)f andthatofDavid asmD(vDx)f ,wehave ©2015PearsonEducation,Inc. Example9.5Speedoficeskaterspushing off(cont.) Solvingfor(vDx)f ,wefind Davidmovesbackwardwithaspeed of1.2m/s. ©2015PearsonEducation,Inc. Example9.5Speedoficeskaterspushing off(cont.) Noticethatwedidn’tneed toknowanydetailsaboutthe forcebetweenDavidand SandrainordertofindDavid’s finalspeed.Conservationof momentummandates this result. ASSESS ItseemsreasonablethatSandra,whosemassislessthanDavid’s,would havethegreaterfinalspeed. ©2015PearsonEducation,Inc. LawofConservationofMomentum Text:p.265 ©2015PearsonEducation,Inc. LawofConservationofMomentum Text:p.265 ©2015PearsonEducation,Inc. ItDependsontheSystem Thegoalistochoose asystemwhere momentumwillbe conserved. Foraskateboarder,if wechoosejustthe person,thereisa nonzeronetforceon thesystem. Ifwechoosethesystemtobethepersonand thecart,thenetforceiszeroand themomentumisconserved. ©2015PearsonEducation,Inc. ExampleProblem Jackstandsatrestonaskateboard. ThemassofJackandtheskateboardtogetheris75kg. Ryanthrowsa3.0kgballhorizontallytotherightat4.0m/stoJack,whocatches it. WhatisthefinalspeedofJackandtheskateboard? ©2015PearsonEducation,Inc. Explosions Anexplosion iswhenthe particlesofthesystem moveapartafterabrief, intenseinteraction. Anexplosionistheopposite ofacollision. Theforcesareinternal forcesandifthesystemis isolated,thetotalmomentum isconserved. ©2015PearsonEducation,Inc. QuickCheck9.10 Thetwoboxesareonafrictionlesssurface.Theyhadbeensittingtogetherat rest,butanexplosionbetweenthemhas justpushedthemapart.Howfastisthe2-kgboxgoing? ◦ ◦ ◦ ◦ ◦ 1m/s 2m/s 4m/s 8m/s There’snotenoughinformationtotell. ©2015PearsonEducation,Inc. QuickCheck9.10 Thetwoboxesareonafrictionlesssurface.Theyhadbeensittingtogetherat rest,butanexplosionbetweenthemhas justpushedthemapart.Howfastisthe2-kgboxgoing? ◦ ◦ ◦ ◦ ◦ 1m/s 2m/s 4m/s 8m/s There’snotenoughinformationtotell. ©2015PearsonEducation,Inc. QuickCheck9.11 The1-kgboxisslidingalongafrictionlesssurface.Itcollideswithandsticksto the2-kgbox.Afterward,thespeedofthetwoboxesis ◦ ◦ ◦ ◦ ◦ 0m/s 1m/s 2m/s 3m/s There’snotenoughinformationtotell. ©2015PearsonEducation,Inc. QuickCheck9.11 The1-kgboxisslidingalongafrictionlesssurface.Itcollideswithandsticksto the2-kgbox.Afterward,thespeedofthetwoboxesis ◦ ◦ ◦ ◦ ◦ 0m/s 1m/s 2m/s 3m/s There’snotenoughinformationtotell. ©2015PearsonEducation,Inc. Example9.7Recoilspeedofarifle A30gballisfiredfroma 1.2kgspring-loadedtoyrifle withaspeedof15m/s.What istherecoilspeedoftherifle? PREPARE Astheballmoves downthebarrel,thereare complicatedforcesexerted ontheballandontherifle.However,ifwetakethesystemtobetheball+ rifle, theseareinternal forcesthatdonotchangethetotalmomentum. ©2015PearsonEducation,Inc. Example9.7Recoilspeedofarifle(cont.) Theexternal forcesofthe rifle’sandball’sweightsare balancedbytheexternalforce exertedbythepersonholding therifle,so Thisis anisolatedsystemandthe lawofconservationof momentumapplies. FIGURE9.20showsavisualoverviewbeforeand aftertheballisfired.We’llassumetheballisfiredinthe+x-direction. ©2015PearsonEducation,Inc. Example9.7Recoilspeedofarifle(cont.) SOLVE Thex-componentofthe totalmomentumisPx = pBx + pRx. Everythingisatrestbeforethetriggerispulled, sotheinitialmomentumiszero. Afterthetriggerispulled,theinternalforceof thespringpushestheballdownthebarrelandpushestheriflebackward. Conservationofmomentumgives ©2015PearsonEducation,Inc. Example9.7Recoilspeedofarifle(cont.) Solvingfortherifle’svelocity,wefind Theminussignindicatesthat therifle’srecoilistotheleft. Therecoilspeed is0.38m/s. ©2015PearsonEducation,Inc. Example9.7Recoilspeedofarifle(cont.) ASSESS Realriflesfiretheir bulletsatmuchhigher velocities,andtheirrecoil iscorrespondinglyhigher. Shootersneedtobrace themselvesagainstthe “kick”oftherifleback againsttheirshoulder. ©2015PearsonEducation,Inc. Section9.5Inelastic Collisions ©2015PearsonEducation,Inc. InelasticCollisions Aperfectlyinelastic collision isacollisionin whichthetwoobjectsstick togetherandmovewitha commonfinalvelocity. Examplesofperfectly inelasticcollisionsinclude clayhittingthefloorand abulletembeddingitself inwood. ©2015PearsonEducation,Inc. QuickCheck9.9 Thetwoboxesareslidingalongafrictionlesssurface.Theycollideandstick together.Afterward,thevelocityofthe twoboxesis ◦ ◦ ◦ ◦ ◦ 2m/stotheleft 1m/stotheleft 0m/s,atrest 1m/stotheright 2m/stotheright ©2015PearsonEducation,Inc. QuickCheck9.9 Thetwoboxesareslidingalongafrictionlesssurface.Theycollideandstick together.Afterward,thevelocityofthe twoboxesis ◦ ◦ ◦ ◦ ◦ 2m/stotheleft 1m/stotheleft 0m/s,atrest 1m/stotheright 2m/stotheright ©2015PearsonEducation,Inc. Example9.8Aperfectlyinelasticcollision ofrailroadcars [InsertFigure9.23] Inassemblingatrainfrom severalrailroadcars,two ofthecars,withmasses 2.0´ 104 kgand4.0´ 104 kg, arerolledtowardeachother. Whentheymeet,theycoupleandsticktogether. Thelightercarhasaninitialspeedof1.5m/s;thecollisioncausesittoreverse directionat0.25m/s. Whatwastheinitialspeedoftheheaviercar? ©2015PearsonEducation,Inc. Example9.8Aperfectlyinelasticcollision ofrailroadcars(cont.) PREPARE Wemodelthecars asparticlesanddefinethe twocarsasthesystem.This isanisolatedsystem,soits totalmomentumisconserved inthecollision.Thecarsstick together,sothisisaperfectly inelasticcollision. FIGURE9.23showsavisualoverview.We’vechosentoletthe 2.0´ 104 kgcar(car1)startoutmovingtotheright,so(v1x)i isapositive1.5m/s. Thecarsmovetotheleftafterthecollision,sotheircommonfinalvelocityis(vx)f = −0.25m/s.Youcanseethatvelocity(v2x)i mustbenegativeinorderto“turn around”bothcars. ©2015PearsonEducation,Inc. Example9.8Aperfectlyinelasticcollision ofrailroadcars(cont.) SOLVE Thelawofconservationofmomentum,(Px)f = (Px)i,is wherewemadeuseofthefactthatthecombinedmass m1 + m2 movestogetherafterthecollision. ©2015PearsonEducation,Inc. Example9.8Aperfectlyinelasticcollision ofrailroadcars(cont.) Wecaneasilysolveforthe initialvelocityofthe 4.0´ 104 kgcar: ©2015PearsonEducation,Inc. Example9.8Aperfectlyinelasticcollision ofrailroadcars(cont.) Thenegativesign,whichwe anticipated,indicatesthat theheaviercarstartedout movingtotheleft.Theinitial speedofthecar,whichwe wereaskedtofind,is 1.1m/s. ASSESS Thekeystepinsolvinginelasticcollisionproblemsisthatbothobjects moveafterthecollisionwiththesamevelocity.Youshouldthuschooseasingle symbol(here,(vx)f)forthiscommonvelocity. ©2015PearsonEducation,Inc. ExampleProblem A10gbulletisfiredintoa1.0kgwoodblock,whereitlodges. Subsequentlytheblockslides4.0macrossafloor(μk =0.20forwoodonwood). Whatwasthebullet’sspeed? ©2015PearsonEducation,Inc. Section9.6Momentum andCollisions inTwoDimensions ©2015PearsonEducation,Inc. MomentumandCollisioninTwo Dimensions Whenthemotionofthecollisionsoccurintwo dimensions,wemustsolveforeachcomponent ofthemomentum: Inthesecollisions,the individualmomentacan changebutthetotal momentumdoesnot. ©2015PearsonEducation,Inc. ExampleProblem Twopucksofequalmass100gcollideonanairhockeytable. Neglectfriction. Priortothecollision,puck1travelsinadirectionthatcanbeconsideredthe+xaxisat1m/s,andpuck2travelsinthe–y-directionat2m/spriortothecollision. Afterthecollision,puck2travels30degreesabovethe+x-direction(between+x and+y)at0.8m/s. Whatisthevelocity(directionandspeed)ofpuck1afterthecollision? Howdoesthefinalkineticenergycomparetotheinitialkineticenergy? ©2015PearsonEducation,Inc. Section9.7Angular Momentum ©2015PearsonEducation,Inc. AngularMomentum Momentumisnotconserved foraspinningobjectbecause thedirectionofmotionkeeps changing. Still,ifitweren’tforfriction,a spinningbicyclewheelwould keepturning. Thequantitythatexpressesthis ideaforcircularmotioniscalled angularmomentum. ©2015PearsonEducation,Inc. AngularMomentum WecancalculatetheangularmomentumL. Newton’ssecondlawgivestheangularacceleration: Wealsoknowthattheangularaccelerationisdefinedas Ifwesetthoseequationsequalandrearrange,wefind ©2015PearsonEducation,Inc. AngularMomentum Forlinearmotion,theimpulse-momentumtheoremiswritten Thequantity Iωistherotationalequivalentoflinearmomentum,soitis reasonabletodefineangularmomentumL as TheSIunitsofangularmomentumarekg× m2/s. ©2015PearsonEducation,Inc. AngularMomentum ©2015PearsonEducation,Inc. ConservationofAngularMomentum Angularmomentumcanbewritten Ifthenetexternaltorqueonanobjectiszero,thenthechangeinangular momentumiszeroaswell: ©2015PearsonEducation,Inc. ConservationofAngularMomentum Thetotalangularmomentum isthesumoftheangularmomenta ofallthe objectsinthesystem. Ifnonetexternaltorqueactsonthesystem,thenthelawofconservationof angularmomentumiswritten ©2015PearsonEducation,Inc. Example9.11Analyzingaspinningice skater Aniceskaterspinsaroundonthetipsofhisbladeswhileholdinga5.0kg weightineachhand.Hebeginswithhisarmsstraightoutfromhisbody andhishands140cmapart.Whilespinningat2.0rev/s,hepullsthe weightsinandholdsthem50cmapartagainsthisshoulders.Ifweneglect themassoftheskater,howfastishespinningafterpullingtheweightsin? ©2015PearsonEducation,Inc. Example9.11Analyzingaspinningice skater(cont.) PREPARE Thereisnoexternaltorqueactingonthesystem consistingoftheskaterandtheweights,sotheirangular momentumisconserved.FIGURE9.29showsabefore-and-aftervisualoverview, asseenfromabove. ©2015PearsonEducation,Inc. Example9.11Analyzingaspinningice skater(cont.) SOLVE Thetwoweightshave thesamemass,moveincircles withthesameradius,andhave thesameangularvelocity.Thus thetotalangularmomentumis twicethatofoneweight.Themathematicalstatementofangularmomentum conservation,If wf =Iiwi,is ©2015PearsonEducation,Inc. Example9.11Analyzingaspinningice skater(cont.) Becausetheangularvelocity isrelatedtotherotation frequencyf byw =2pf,this equationsimplifiesto Whenhepullstheweightsin,hisrotationfrequencyincreasesto ©2015PearsonEducation,Inc. Example9.11Analyzingaspinningice skater(cont.) ASSESS Pullingintheweights increasestheskater’sspinfrom 2rev/sto16rev/s.Thisis somewhathighbecausewe neglectedthemassoftheskater, butitillustrateshowskatersdo“spinup”bypullingtheirmassintowardthe rotationaxis. ©2015PearsonEducation,Inc. ExampleProblem Bicycleriderscanstayuprightbecauseatorqueisrequiredtochangethe directionoftheangularmomentumofthespinningwheels. Abikewithwheelswitharadiusof33cmandamassof1.5kg(each)travelsata speedof10mph. Whatistheangularmomentumofthebike?Treatthewheelsofthebikeas thoughallthemassisattherim. ©2015PearsonEducation,Inc.
