!!!!! General!Physics!I!&!II!Lab!!! Course!Description!! Lab!Report!Template!and!Sample!! Grading!Rubrics! Pre>Lab!Quizzes!!!!!!!!

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1 GeneralPhysicsIIILab CourseDescription LabReportTemplateandSample GradingRubrics Pre>LabQuizzes Source:ChristopherJohnson; 1

2 TableofContents GeneralPhysicsCourseInformation 3 GeneralPhysicsLabWritingGuide 6 SampleLabReport..12 Labs: AtomicEnergyLevels GradingRubric.23 PreHLabQuiz.24 CapacitorsandRCDecay GradingRubric.25 PreHLabQuiz.27 CircularMotionandCentripetalForce GradingRubric.28 PreHLabQuiz.30 ConvergingLenses GradingRubric.31 PreHLabQuiz.33 ElectricandPotentialFields GradingRubric.34 PreHLabQuiz.36 ImpulseandMomentuminCollisions GradingRubric.37 PreHLabQuiz.39 MotioninFreeHFall GradingRubric.40 Ohm slaw GradingRubric.42 PreHLabQuiz.44 ProjectileMotion GradingRubric.45 PreHLabQuiz.47 PropertiesofaVerticalSpringHMassSystem GradingRubric.48 PreHLabQuiz.50 TransverseMechanicalWavesandResonance GradingRubric.51 PreHLabQuiz.52 WavelengthofLight GradingRubric.53 PreHLabQuiz.55 2

3 96.104'[fill,in,section],General,Physics,II,Lab CourseInformation Lab,Meeting,Time:Thislabsectionmeetseveryother[fillinweekday](starting with[fillindate])at[fillintime]sharp.thelabsessionruns aslongasittakestofinishtheexperimentwithsatisfactory data. Location:Theroominwhichwemeetwillvaryfromweektoweekdependingon theavailabilityofroomsandlaboratorymaterials(wesharebothwith manyotherlabsections).theroominwhichwearemeetingwillbe postedonthedoorstothelabrooms.checkthepostingseachtime youcomeintolabtofindoutwherewearemetingthatday.theroom inwhichwemeetwillnotnecessarilybethesameroomlistedonisis. Instructor:[fillinname] Instructor,Contact,Information:[fillin ] Office/Office,Hours:,Ihaveacubicle[fillincubiclenumber]inOlney219whereI canmeetyoubyappointment.contactmewellinadvanceto ensurethatthereistimeforustomeetbeforeyourlabreport isdue,ihaveaverybusyscheduleasagraduatestudentsoitis difficulttomaketimeatthelastminute. Restrictions:Consumptionoffoodordrinksisstrictlyprohibitedinthelaboratory. Attendance/Make,Up,Work:,Thereareonlysixlaboratorysessionspersemester. Thescoreforeachlabreportcontributesequallytoeachstudent s grade.attendanceisrequiredforfivelabsessions,butattendanceat allsixisencouraged.anystudentthatmissesmorethanonelab session(excusedornot)willautomaticallyfailthecourseandwillbe encouragedtowithdraw.makeupworkisnotallowedinanycasefor anyexperiment.ifthestudentisawareofaconflictinadvance,itis theirresponsibilitytoarrangeattendanceatanotheroneofthe instructor slabsessions.studentsarerequiredtobepunctual;failure todosowillresultinmissedpreslabquizzesandotherimportant information.performingtheexperimentunderthesupervisionof anotherinstructorisnotpermittedbecauseeachinstructorteaches eachlabslightlydifferentlyandhasslightlydifferentlabswriting requirements., 3

4 Academic,Conduct:Eachstudentisrequiredtowritetheirownoriginallabreport. Studentsareencouragedtoworktogethertoperformthe experimentandanalyzedata,butthelanguageofeachreport mustbeunique.thestudentisresponsibleforappropriate academicconduct.cheatingofanyformwillresultinafailing gradeonthelabreportandpossiblyinthecourseaswell.the university sacademicintegritypolicyisavailableonline. Whetherornotastudentisguiltyofacademicmisconductis lefttothediscretionoftheinstructor,asaretheconsequences. Labreportsthatraisesuspicionwillbesubmittedtothe physicsdepartment.don tcheat. Scoring Pre'Lab,Quizzes:TherewillbeapreSlabquizatthebeginningofeachlabsessionto testthestudent spreparationfortheexperiment.thestudentis responsibleforreadingandunderstandingthelabmanualbefore comingtothelabsession.itisadvisedthatthestudentdothereading wellinadvancesothattheyhavetheopportunitytocontactthe instructorwithanyquestionsbeforemeetingtoperformthe experiment.thepreslabquizzeswillbescoredoutoftenpointsand willcontributetenoutoftheonehundredpointsavailableforeach report.missingapreslabquizduetotardinesswillresultinascoreof zeroonthequiz. Lab,Reports:Eachlabreportwillconsistoffoursections:thecoverpage/lab manualpages,theobjectivestatement,theresults/analysissection, andthediscussion/conclusionssection.labswritingrequirementsare discussedindetailinthelabswritingguidehandedoutalongwiththe courseinformation. Grading:Eachlabreportwillbescoredoutof100possiblepoints.Eachcomponent (preslabquiz,coverpage/labmanualpages,objectivestatement, results/analysis,anddiscussion/conclusions)willaccountfora certainamountofthe100possiblepoints.eachreportwillbegraded accordingtoarubricthatinstructorwilluseachecklisttodetermine whatnecessaryinformationisincludedineachsectionofthereport. Therubricforeachexperimentwillbehandedoutatthelabsession duringwhichthestudentsareperformingtheexperiment,sothereis noexcuseforomittinganycontentfromanysectionofthelabreport. Ateachlabmeeting,eachstudentwillreceivetheirgradedlabreport fromthepreviousexperimentwithcomments.thecommentsare intendedtohelpthestudentimproveonhowtheywritethenextlab report.studentswhodonottakethecommentsintoconsideration 4

5 willbeheavilypenalizedforrepeatingthesamemistakes.oftentimes, somecommentsaremadeveryfrequently.forthisreason,the instructorwilluseanabbreviatednotationforsomecomments.there willbeafrequentcommentskeythatgivesthedefinitionofeach abbreviationforeachexperiment.anystudentwhohasperformedan experimentandhandsinanywrittenreportwillreceiveaminimum scoreof40pointsonthereport.attheendofthesemester,the instructorwilldetermineeachstudent sfinalgradebyaveragingthe fivehighestlabreportscores.theinstructorwillscalethegrades appropriatelybasedonthemeritoftheclass soverallperformance. Standardlettergradeswillbeassociatedwithpercentscores. Deadlines:Labreportsaredueoneweekfromthedateonwhichtheexperiment wasperformedatthestartofthealternatelabsession.labsthatare turnedinafterthestartofthelabsession([inserttime]exactly)will beconsideredonedaylate.studentscanhandlatelabreportsintothe lateboxoutsideofolney113.labreportsthatareturnedinonthe nextdaywillbeconsideredtwodayslate,thenextdaywillbethree dayslate,etc.fivepointsperdaywillbetakenoffthescoreoflatelab reports.sincelatelabreportsdonotgodirectlyintothehandsofthe instructor,itisnotguaranteedthattheinstructorwillreceivethelab report.ifastudentneedstogoprintalabbeforeturningitin,thelab reportisnotexempttothedeadline.itisstronglyencouragedtoturn thelabreportinontimeandforthisreasonitisadvisedthatthe studentprintandstaplethelabreportwellinadvancebeforecoming tolab.latenessalsodecreasestheminimumlabreportscore.the minimumscoreforalabreportthatisontimeis40/100,the minimumscoreforalabthatisonedaylateis30/100,etc. 5

6 Lab$Writing+Guide+ + Firstandforemost,itisessentialforeachstudenttorealizethatlabwritingis awriting'exercise.alllabreportsmustbewritteninformalenglish.allguidelines thatapplytonormalformalwritingstillapplytolabwriting(indentnew paragraphs,useproperpunctuation,etc.).every+statement+that+appears+ anywhere++in+the+lab+report+(otherthanthecoverpageandtitlesandaxislabelson graphs)must+be+a+complete+sentence.+use+of+sentence+fragments+and+ incomplete+sentences+will+greatly+decrease+the+grade+on+the+lab+report.alllab reportsmustbeword@processed,double@spacedineithercambriaortimesnew Romansize12font.Donotattempttomakeyourlabreportlooklongerby increasingthemarginsize,thefontsize,ortheline@spacing.thegoaloflab@writing istoincludeallofthecontentnecessarytoexplainyourgoalstothereaderandto explainhowyouachievedthosegoals.itissomewhatofanarttobeascompleteas possiblewhilealsobeingas'concise'as'possible.forthisreason,westrictlyadhereto atechnicalwritingformat.therequirementsforwritingeachsectionofthelab reportareoutlinedbelow.itisessentialthatyouincludeeverysectionintheorder listed.everysectionotherthanthecoverpageandlabmanualpagesrequiresa bolded,left@justifiedheading.donotitalicize,underline,orenlargethesection headings.donotpunctuatesectionheadings(donotusecolonsoranythinglike that).donotleavesectionheadingsstandingontheirownatthebottomofapage, putthesectionheadingonanewpagesothatthebeginningofthenewsection appearsdirectlybelowit.usethesamplelabreportthattheinstructorhandedout alongwiththelab@writingguideandcourseinformationasaformattingreference. Treatthesamplelabreportonlyasaformattingreference,donotuseittoinfluence yourwritingstyleorcontent.thesearetherequirementsforeachsection: Cover+Page:Thecoverpagelistsyourname,thecourseandsectionnumber,the instructor sname,thetitleoftheexperiment,thedateonwhichyou performedtheexperiment,andyourlabpartner sname.thecover pageshouldbeitsownpieceofpaperwiththeaboveinformation typedonitsownlineintheorderlistedaboveandcentered(vertically andhorizontally)onthepage.usenormalsize12fontforeverypiece ofinformationonthecoverpage(noenlarged,bolded,italicized, underlined,orotherwisealteredtext).the+cover+page+counts+ FOR+FREE+EASY+POINTS.+DO+NOT+LOSE+POINTS+ON+THE+COVER+ PAGE + Lab+Manual+Pages:Youarerequiredtohandinthelabmanualpagesthatpertain totheexperiment.thelabmanualpagescanbephotocopiedortaken directlyoutofthelabmanualitself.thesepageswillsufficeasthe introductionandproceduresections;itisnotnecessarytowritean originalintroductionorproceduresection.includealllabmanual pagesfortheexperimentexceptforthosepertainingtotheresults andanalysissection(tables,figures,instructionsforanalysis,etc.). 6

7 Includethelabmanualpagesintheorderinwhichtheyappearinthe labmanual. Objective+Statement:Donotcopytheobjectivestatementfromthelabmanual.You willreceiveascoreofzeroontheobjectivestatementifyou copytheobjectivestatementfromthelabmanual.the objectivestatementisessentialtothelabreport.ittellsthe readerwhatyourgoalsare,andtherestofyourreport explainshowyouachievedyourgoals.theobjectivestatement, likeallstatementsinyourlabreport,mustbeacomplete sentence.itshouldbewritteninthepasttenseandactive'voice anditshouldusefirstpersonpronouns.hereisanexampleof agoodobjectivestatementforoneofthegeneralphysicsi labs, toexaminetherelationshipsbetweenposition,velocityand acceleration,aswellastodeterminethegravitationalconstant, Noticehowitisacomplete sentence,notasentencefragmentlike, Todeterminethe gravitationalconstant,g.also,itusesafirstpersonpronounin thepasttenseandactivevoice, Weconducted.DONOTUSE THEPASSIVEVOICE.DONOTWRITE theexperimentwas conducted.remember,youconductedtheexperiment. Theseguidelinesapplytoeverysentenceineverysectionof yourlabreport.forclarity:everysentenceinyourlab REPORTSHOULDALWAYSBEINTHEACTIVEVOICE,INTHE PASTTENSE,ANDYOUSHOULDUSEFIRSTPERSON PRONOUNSASOFTENASPOSSIBLE.NEVERUSETHEPASSIVE VOICE. Results+and+Analysis:Theresultsandanalysissectionisthemeatofthelabreport andcarriesthemostweightintermsofthegrade.theresultsand analysissectionisone+section+thatincludesyourresultsandyour analysis.likeallothersections,theresultssectionrequiresaleft justified,boldedheadingwithoutpunctuation.theresultsand analysissectionexplainshowyoumanipulatedyourdatainorderto achieveyourobjectives.youdonotneedtoexplainhowyouobtained yourrawdata;theproceduresectionfromthelabmanualpages coversthatinformation.thereareessentiallythreethingsthatyou willbeaskedtodointheresultssection.youwillbeaskedtoexplain calculations,todisplaytables,andtodisplayfigures.itisessential thatyoudoeachofthesethingscompletelyandproperly. Whenyouareaskedtoexplainacalculation,youwillneedtoproperly includeanequationandthenproperlydisplayasamplecalculation. Whenyouincludeanequation,itshouldbecenteredonitsownline, separatedfromthetext,withitsnumberinparenthesesontheright 7

8 sideofthepage.thenumbershouldbeinbetweenoneopenandone closedparenthesis,nootherpunctuation.itisextremelyimportant thatyounumberequationsproperlyintheorderinwhichtheyappear inthetext.afteryouhaveassignedanumbertoanequationyoucan refertothatequationbynumberifyoumentionitlaterinthereport. Itisessentialthatyoumasterthislabwritingtechnique.Youare requiredtonumberallequationsyouuseonyourown;youshould disregardtheequationnumbersgiveninthelabmanual.another essentiallabwritingtechniqueisthatyouincludetheequationfluidly asapartofacompletesentence.asusual,youshouldusefirstperson pronouns,pasttenseandactivevoice;ifitisnecessary,youshould includepunctuationwithyourequation.aspartofthesentencethat includestheequation,youmustalsodefine'the'symbolsthatappearin theequation.youmustdothiscompletelyandconcisely;definea symbolonceandsticktothatdefinitionfortherestofthereport.itis veryimportantthateachsymbolrepresentoneandonlyonephysical Whenyoushowtheequationonitsownline,youshouldusethe propersymbols;thisisveryeasytodowiththeequationeditorin Microsoftword.ThereshouldneverbeanyEnglishwordsaspartof anequation;onlyusesymbolsinequations.afteryoushowan equation,youneedtoshowasamplecalculation.asamplecalculation isanexampleofhowyouusedyourdatainthatequation.although youwillrepeatmanycalculations,youonlyneedtoformallyshowone' representativesamplecalculationinordertodemonstrateyour masteryofthatequation.liketheequationitself,thesample calculationshouldreadfluidlyasapartofthesentencethatitisin.in thissentence,youshouldstatethevaluesthatyouareusingforeach parameter;thisisanalogoustohowyoudefinethesymbolsinthe sentencethatincludestheequation.whenyoustatethevalues,you must'includetheunits,otherwisethevalueismeaningless.youshould alsoincludetheunitsinthesamplecalculationitself.thesample calculationshouldalsoappearonitsownline.unlikeequations,you donotneedtonumbersamplecalculations.hereisanexampleofhow toproperlyexplainacalculation,includingtheequationandthe samplecalculation: WedeterminedtheforceoneachobjectusingNewton ssecondlaw, F=ma, (1) wheremwasthemassoftheballandawasitsacceleration.forexample,whenthe 0.5kgballwasacceleratingat9.8m/s,wecalculatedaforceof 8

9 F=(0.5kg)(9.8m/s)=4.9N. Noticehowboththeequationandthesamplecalculationarepartof theirownsentence.bothsentencesusefirstpersonpronouns,active voice,andareinthepasttense.thesentencefortheequationclearly definesthesymbolsusedintheequationandthesentenceforthe samplecalculationclearlystatesthevaluesusedintheequation.idid symbolizesforcebasedonthefirstpartofthesentence, We determinedtheforces.theequationf=ma'ispunctuatedbecauseitis afluidpartofthesentenceandwillbereadassuch.ifineedtorefer tothisequationlaterinthelab,iwouldsimplyrefertoitas equation 1.Thesamplecalculationisalsopunctuatedbecause aforceof4.9 Newtons ispartofthesentence. Anotherthingyouwillbeaskedtodointheresultssectionisto displaytablesproperly.similarlytoequations,tablesshouldbe numberedintheorderinwhichtheyappearintext.ifthelabmanual givesatablenumberyoushouldignoreit;definetablesbyyourown numberingscheme(sometimesyourschemeandthelabmanual s schemecancoincide).donotnumbertableswithparenthesislikeyou doforequations.whenyouincludeatable,youmustwriteacomplete sentencethatreferstothetablebynumber.alwayscapitalizethe word Table whenyourefertoatablebynumber.youshouldalso usecompletesentencestocaptiontables.thecaptionshouldappear directlybelowthetable,centeredonthepageandsingle@spaced.you areallowedtousethetablesyoufilloutbyinthelabmanual,butitis requiredthattheyappearinaprofessionalmanner.ifyouplanto includethehandwrittentables,youareencouragedtotakeyourraw dataduringtheprocedureonyourownpapersoyoucanmakea finalized,neatversiononthelabmanualpage.youarealso encouragedtomakeyourowndigitaltables(inexcelorword). Regardlessoftheformatyouchoose,yourtablesmustbeincludedin thetextintheproperorderwhereyourefertothem.youshouldkeep tablesandtheircaptionscontinuous;ifacaptiondoesn tfitonthe pageunderthetable,movethetabletoanewpagesothatthecaption hasspacetofollowitdirectly.alwaysincludeunitsinparenthesisin thefirstrowtoindicatethattheyapplytoallvaluesinthecolumn. Continuingwithourexamplefromhowtoexplaincalculations properly,let ssupposewewantedtotabulatesomeforcecalculations. Youwouldwanttosaysomethinglikethis: Afterwecalculatedtheforcesactingonallthreeballs,weorganizedourdatainto Table1. 9

10 Ball# m(kg) a(m/s 2 ) F(N) Table1:Thistableincludesallofourforcecalculations. Noticehoweverystatementassociatedwiththetableisacomplete sentencewrittenintheactivevoice. Anotherthingyouwillbeaskedtodointheresultssectionisto includefiguresproperly.figuresincludeallgraphsand/ordiagrams. Figureshavetheirownnumberingscheme,separatefromequations andtables.allfigures,bothdiagramsandgraphs,areincludedinthe samenumberingscheme.ifyoushowadiagramfirst,thatdiagram willbefigure1,andifagraphweretofollowlater,thatgraphwould befigure2andviceversa.youshouldincludefiguresinessentially thesamemannerasyouincludetables.numberthemintheorderin whichtheyappearintextandrefertothembynumberinasentence beforeyoudisplaythem.alsoincludecaptionsincompletesentences directlyafterfigurescenteredonthepageandsingle@spaced.youcan includehand@drawnfigures,butagainmakesuretheylook professionalandappearfluidlyintextintheproperorderwhereyou refertothem.itisrecommendedthatyoumakeyourownfigures usingacomputerinordertoincludethemmostfluidlyinyourtext. Keepingwithourexample,thisishowyouwouldwanttoincludea figureproperly: ThenweplottedourforcecalculationsinFigure1. Force+vs+Mass Force+(N) Mass+(kg)+ Figure1:Ourresultsshowthatforceincreaseslinearlywithmass. 10

11 Again,everystatementisacompletesentence.Noticethatthefigure hasatitle,axeslabeledwithunits,andappropriatelyscaledaxes.all graphsrequireallofthesecomponents. Theimportantpartsoftheresultssectionareexplainingcalculations, displayingtables,anddisplayingfigures.usually,wewilldosome calculations,thenorganizethemintoatable,thenplotourresultsina figure.wealwayswanttoexplainourmanipulationsofdataina logicalorder,startingwithwhatweobtainedfromtheexperimental procedureandbuildingupfromthere.sometimes,youmaycreatea figureduringtheexperimentthenmanipulateyourdatafromthere;it dependsontheexperiment. Discussion+and+Conclusions:+Thissectiondiscussestheexperimentalfindingsof theexperimentandaddressesanyrelevantconclusions.here,the question Whatdotheresultsmean? shouldbeanswered. Essentially,whathasthestudentlearnedfromtheexperiment?These questionsshouldbeansweredscientifically,keepingtheobjectivesof theexperimentinmind.alwaysbesuretodirectlyaddressyour objectivesandhowwellyouachievedthem.thissectionshouldalso addressexperimentalerror(not'uncertainty).sourcesof experimentalerroraresystematicflawsinthedataacquisition processthatmaketheexperimentslightlynotideal.thestudent shouldstatethesourcesofexperimentalerrorandhow'theyaffected theresults. Humanerror isnotasourceofexperimentalerror.if therewas humanerror inanexperiment,thestudentwillbe requiredtoredotheexperimentbeforereceivingagradeonthelab report.thisisnotapaperforenglishorhistoryclasswherethe conclusionissimplyajumbleofrandomthoughtsthrownintothe paperjusttofinishitlateatnightthedaybeforeitisdue.conclusions writteninthismannerwillscoreverylow.donotshootforquantity here,trytobecompletewhilebeingasconciseaspossible.neatly writtenortypedanswerstothequestionsattheendofthelabmanual pagesshouldbeincludedaftertheconclusion. 11

12 Chris Johnson Physics Professor Michael Vineyard Bragg Reflection: Using X-Ray Diffraction Spectra to Determine the Lattice Constants of NaCl and KBr Monocrystals 4/15/2011 Partners: Arkadiy Norkin, Ana Mikler and Hillary Bauer 12

13 Abstract We used a Bragg x-ray reflection apparatus to detect the angles at which x-rays interfered constructively after they reflected off of NaCl and KBr crystals. From the interference peaks on the Bragg diffraction spectra, we were able to extract the lattice constant a 0 for each crystal. We calculated a 0 to be equal to 570 ± 30 pm and 660 ± 30 pm for NaCl and KBr respectively. The actual values of these lattice constants, a 0 = pm for NaCl and a 0 = pm for KBr, do fall within our range of uncertainty from our measured values (Atomic and nuclear physics 2). Introduction Bragg reflection is a way of measuring the interatomic spacing of a monocrystal by detecting and analyzing the interference pattern caused by the x-rays reflected off of the lattice planes of the crystal. This concept is very similar to slit diffraction of visible light, but in this case the uniform structure of the atoms in the crystals serves as the slit and we detect the angles at which constructive interference occurs. William Lawrence Bragg and William Henry Bragg first proposed Bragg reflection in 1913 when they found that crystal solids produced defined patterns of reflected x-rays. The Braggs explained this phenomenon by modeling the structures of these crystals as uniform parallel planes of atoms arranges in a lattice. Bragg diffraction is ideal for measuring interatomic spacing using x-rays because x-ray wavelengths are comparable to interatomic distances. The Braggs idea confirmed the existence of real particles at the atomic level and also provided a useful tool for measuring interatomic distances (Wikipedia). Figure 1 illustrates this concept. 13

14 Figure 1: Two x-rays reflecting off of successive lattice planes in a crystal will reflect and cause constructive interference when they reflect off of the planes at the correct angles. Here, λ is the wavelength of the x-rays, d is the lattice plane spacing and θ is the incident and reflected angle. The first and second planes correspond to n = 1 and n = 2 respectively. Image courtesy of Bragg Law. The x-rays will interfere constructively when the Bragg condition is satisfied, n λ = 2 d sin (θ ) (1) Changing the angle can cause displacement of the wavelengths; destructive interference occurs when the waves are out of phase by half of a wavelength. In a cubic crystal with NaCl structure, the d-spacing corresponds to half of the lattice constant, d = a 0 / 2 (2) This allows us to write Equation 1 in terms of a 0, n λ = a 0 sin (θ ) (3) In order to determine the lattice constant, a 0, we must therefore determine the sines of the angles that correspond to constructive interference caused by x-rays of a certain wavelength reflecting off of the n th lattice plane. The slope of a graph of sin (θ ) vs. n λ 14

15 will give a value for a 0. In our experiment, we used molybdenum x-rays of two wavelengths λα = pm and λβ = pm at the Kα and Kβ lines respectively. This causes the interference pattern to have two peaks (Kα and Kβ) for each diffraction order; one is caused by interference of x-rays of each wavelength (Solid-state physics 1). Procedure We used a Bragg diffraction apparatus called the Rontgenerat X-ray Apparatus to adjust the incident and reflected angles of x-rays incident on crystal samples as shown in Figure 2. Fig. 3 Experiment setup in Bragg configuration Figure 2: 2Our Bragg diffraction apparatus allowed us to sweep through a range of incident and reflected angles in order to find constructive interference. In our apparatus, we had an x-ray machine to the left of the collimator (part a in Figure 2). The x-ray source produced both Kα and Kβ x-rays that passed through the 15

16 collimator to get a direct, uniform beam of x-rays heading toward the crystal sample. The x-rays then reflected off of the sample held on the target stage (part f in Figure 2). After reflecting off of the sample, the x-rays moved toward the Geiger-Müller counter tube (part e in Figure 2) that detected the intensity of the x-rays. When we swept through ranges of angles, the machine electronically pivoted the detector and the crystal with respect to the incident x-ray beam in 2θ coupling in order to maintain equal incident and reflected angles. The detector was connected to a computer program that plotted the spectra of detected x-rays. Our machine had knobs on the side of it that controlled the voltage, U, the current, I, the increments of θ by which the system rotated, Δθ, the time step spent on detecting each angle, Δt and the range of angles over which the machine would scan. For both of our runs we used U = 35.0 kv, I = 1.00 ma, Δθ = 0.1 and Δt = 5 s. For the NaCl crystal, we scanned over a range of For the KBr crystal, we scanned over a range of Before each data acquisition, we set the machine back to the zero point (where the lattice planes and the counter tube are parallel to the incident x-ray beam) by pressing the reset button to calibrate it. After zeroing the apparatus and programming our desired rotation parameters, we ran the experiment, started the data acquisition and recorded the spectra searching for interference peaks. We then used a peak-fitting program to analyze the peaks to find their centroids and σ values. We took various safety measures including using lead-impregnated glass in the machine to block radiation and using the appropriate voltage and current. 16

17 Results We produced spectra of the Kα and Kβ interference peaks caused by x-rays reflecting off of NaCl and KBr crystals. Figures 3 and 4 show these plots of θ vs. the log of the counting rate, R. 700" 600" NaCl$Bragg$Spectrum$ 500" 400" Log$R$ 300" 200" 100" 0" 0" 5" 10" 15" 20" 25" 30" 35" 40" 45" θ( )$$ Figure 3: This shows the peaks produced by the interference of x-rays after reflecting off of the lattice planes of the NaCl crystal. 17

18 450" 400" KBr$Bragg$Spectrum$ Log$R$ 350" 300" 250" 200" 150" 100" 50" 0" 0" 5" 10" 15" 20" 25" 30" 35" 40" θ( )$$ Figure 4: This shows the peaks produced by the interference of x-rays after reflecting off of the lattice planes of the NaCl crystal. After analyzing our data with a peak-fitting program, we found values for the centroids of the peaks, θ and the σ value for each peak from which we extracted an uncertainty in θ, Δθ. The uncertainty in Δθ is equal to 3σ because 99.8% of data points lie within three standard deviations from the mean of a normal distribution. We then calculated the sine of each angle and propagated the uncertainty in θ by taking the sign of each Δθ. We then determined the diffraction order, n, for each set of peaks and the line (Kα or Kβ) to which each peak corresponded. Each of these combinations was associated with a certain wavelength (λα = pm and λβ = pm) that we multiplied by the diffraction order to get values for n λ. 18

19 Crystal n Line θ ( ) σ ( ) Δθ (± ) sin (θ) Δ sin(θ) (±) λ (pm) nλ (pm) NaCl 1 Kβ Kα Kβ Kα Kα KBr 1 Kβ Kα Kβ Kα Kα Table 1: This shows the angles at which we found constructive interference along with the diffraction order, line, and n λ to which each corresponds for each crystal. All uncertainties are shown. After we accumulated this data, we made a plot of sin (θ ) vs. n λ for each crystal s data set. From there, we fit a linear regression line to each set of data points and used the slope of each line to determine the lattice constant, a 0 for each crystal. Figure 5 shows this plot. 19

20 Linear$Plot$of$Sin(θ$)$vs.$nλ$$ 250" 200" 150" nλ"" (pm)" 100" 50" 0" 0" 0.05" 0.1" 0.15" 0.2" 0.25" 0.3" 0.35" 0.4" 0.45" Sin(θ$)$ Figure 5: This is the linear plot of sin (θ ) vs. n λ for each crystal s data set. The data points for NaCl are circular and the data points for KBr are diamond-shaped. Each data point is shown with error bars. The KBr error bars are difficult to see because they are so small. The equations of the regression lines for NaCl and KBr were n λ = (sin (θ )) pm and n λ = (sin (θ )) pm respectively. Propagating our uncertainties into the slopes by finding the maximum and minimum slopes within our uncertsainties, we get a 0 = 570 ± 30 pm for NaCl and a 0 = 660 ± 30 pm for KBr. This means we found the sum of ion radii to be d = 285 ± 15 pm for NaCl and d = 330 ± 15 pm for KBr. Discussions and Conclusion We were able to observe x-ray interference with our Bragg diffraction machine to determine the interatomic spacing in NaCl and KBr crystals. We calculated a 0 to be equal to ± pm and 660 ± 30 pm for NaCl and KBr respectively. The actual values of 20

21 these lattice constants, a 0 = pm for NaCl and a 0 = pm for KBr, do fall within our range of uncertainty from our measured values. This means we found the sum of ion radii to be d = 285 ± 15 for NaCl and d = 330 ± 15 for KBr. The NaCl lattice shows a significantly smaller lattice constant than the KBr lattice, as the radii of the ions involved are smaller. Although or data does appear to be accurate, there must be some error associated with our measurements that makes it imperfect. For instance, the linear regression lines of the plots of sin (θ ) vs. n λ for each crystal s data set are supposed to pass through the origin. Our equations, however, have n λ - intercepts just above and below the origin. Because the slopes appear to be correct, this must means that each set of data has been shifted by the sin (θ ) values (slightly high sin (θ ) values for NaCl and slightly low sin(θ) values for KBr). These discrepancies in the θ values were caused by imperfections in the crystal and imperfect calibration of the Bragg diffraction machine. Also, our spectra only show five peaks even though they cover the n = 1 to n = 3 diffraction orders. The β peak is invisible at the n = 3 diffraction order for both crystals because we did not acquire perfect spectra. This could also be attributed to imperfections in our samples. We could improve our data by setting a higher time step, Δt so that the detector could spend more time at each angle. This technique for measuring interatomic distances can be very useful for determine the composition of materials; it is often use to test the validity of diamonds (Wikipedia). It is incredible that we can learn so much about the composition of crystals by observing the behavior of x-rays reflected off of them. 21

22 Works Cited Atomic and nuclear physics. Leybold Physics Leaflets. Germany. Copyright Leybold Didactic GmbH. < "Bragg law." Encyclopædia Britannica. Encyclopædia Britannica Online. Encyclopædia Britannica, Web. 09 May < Bragg s Law. Wikipedia, the Free Encyclopedia. < Solid-state physics. Leybold Physics Leaflets. Germany. Copyright Leybold Didactic GmbH. 22

23 Atomic'Energy'Levels'Lab'Grading'Rubric' Name: Grade: /100 Pre9Lab: /10 ' Cover'Page/Lab'Manual'Pages: /5 Name CourseSection# Instructor sname TitleofExperiment DateExperimentwasPerformed Partner sname Labmanualpagespresentandinorder ' Objective'Statement: /10 Completelyandconciselyaddressallofyourobjectives Writeacompletesentence(s)inthepasttenseandactivevoicethatusesfirstperson pronouns. ' Results: /50 Usetheappropriateobjects(figures,tables,andexplanationsofcalculations)to explainhowyouaccomplishedyourobjectivestothereader.includethemina logicalorderandwithproperformaccordingtothelabrwritingguide. Answerthequestionsattheendofthelabmanualpagesforthisexperiment.Donot numberyouranswersormentionthelabmanual.simplyexplainyouranswersas thoughyouaregenuinelyinterestedincommunicatingyoufindingstothe reader. Conclusion: /25 Addressyourobjectives Explainhowsourcesofexperimentalerroraffectedyourresults 23

24 Atomic'Energy'Levels'Pre3Lab'Quiz Name: Score: /10 Section#: 1. Explainthesignificanceoftheequation = ".".Besuretoaddressthe sign,theunits,andthesymboln. 2. Whataretheobjectivesoftoday sexperiment? 24

25 Capacitors*and*RC*Delay*Lab*Grading*Rubric Name: Grade: /100 Pre8Lab: /10 * Cover*Page/Lab*Manual*Pages: /5 Name CourseSection# Instructor sname TitleofExperiment DateExperimentwasPerformed Partner sname Labmanualpagespresentandinorder * Objective*Statement: /10 Completelyandconciselyaddressallofyourobjectives Writeacompletesentenceinthepasttenseandactivevoicethatusesfirstperson pronouns. * * Results*and*Analysis: /50 Explainhowyoucalculatedtheinternalresistanceofthevoltmeter Explainhowyoucalculatedthecapacitanceofthelargercapacitor Explainhowyoucalculatedthecapacitanceofthesmallercapacitor Explainhowyoucalculatedthecapacitanceofthecapacitorsinseries Explainhowyoucalculatedthecapacitanceofthecapacitorsinparallel(youcould coverthisstepandafewofthepreviousstepsinonesentencetoavoidrepetition) Explainhowyoupredictedthecapacitanceofthecapacitorsinseries Explainhowyoudeterminedthepercentdifferencebetweenyourexperimental valueandthevalueyoupredictedforthecapacitorsinseries Explainhowyoupredictedthecapacitanceofthecapacitorsinparallel Explainhowyoudeterminedthepercentdifferencebetweenyourexperimental valueandthevalueyoupredictedforthecapacitorsinparallel 25

26 Includeatableincludingtheresultsofallthecalculationsyoujustexplained Includeagraphofthevoltageacrossthecapacitoragainsttime Explainhowyoudeterminedthecapacitanceofthelargerresistorfromyourgraph Includeanaturallogplotinordertolinearizetherelationshipbetweenthevoltage acrossthecapacitorandtime Explainhowyoudeterminedthecapacitancefromyourplot Discussion/Conclusions: /25 Commentonhowwellyouachievedyourobjective(s). Doyourresultsverifytheoreticalpredictions?Howdoyourvaluesforthe capacitancecompare? Explaintheconceptattheendofsectionxiiintheprocedure Identifysourcesofexperimentalerrorandexplainhowtheyaffectedyour results. Answerthequestionsattheendofthelabmanualpages.Makesuretoshowyour work Additional*Comments:* 26

27 Capacitance)and)RC)Decay)Pre0Lab)Quiz Name: Score: /10 Section#: Circleallappropriateanswers,theremaybemorethanone. 1.Youcandeterminetheequivalentcapacitanceforcapacitorsinseriesusing: a. thesamemethodyouusetodeterminetheequivalentresistancefor resistorsinseries. b. thesamemethodyouusetodeterminetheequivalentresistancefor resistorsinparallel. c. thesamemethodyouusetodeterminetheequivalentspringconstantfor springsinseries. d. thesamemethodyouusetodeterminetheequivalentspringconstantfor springsinparallel. e. thesamemethodyouusetodeterminethepowerdissipatedthrougha groundedresistor. 2.Youcandeterminetheequivalentcapacitanceforcapacitorsinparallelusing: a. thesamemethodyouusetodeterminetheequivalentresistancefor resistorsinseries. b. thesamemethodyouusetodeterminetheequivalentresistancefor resistorsinparallel. c. thesamemethodyouusetodeterminetheequivalentspringconstantfor springsinseries. d. thesamemethodyouusetodeterminetheequivalentspringconstantfor springsinparallel. e. thesamemethodyouusetodeterminethepowerdissipatedthrougha groundedresistor. 3.Whencapacitorsaredisconnectedfromtheirvoltagesupply,theydischarge: a. linearly b. periodically c. sinusoidally d. exponentially 4.TrueorFalse.Toagoodapproximation,thevoltmeterintoday sexperiment behavesasanidealvoltmetersowecanignoreitsresistancecompletely. 27

28 Circular(Motion(and(Centripetal(Force(Lab(Grading(Rubric Name: Grade: /100 Pre7Lab: /10 ( Cover(Page: /5 Name CourseSection# Instructor sname TitleofExperiment DateExperimentwasPerformed Partner sname Lab(Manual(Pages: /5 Present InOrder Objective(writeyourownobjectivenotcopiedfromthelabmanual) Results(and(Analysis: /60 Explainhowyoucalculatedthelinearforces. Explainhowyoufoundtheperiods.Eventhoughthisisatrivialcalculation,show theequationandasamplecalculationproperlytopracticegoodlabwriting techniques. Explainhowyoufoundtheangularvelocities. Explainhowyoucalculatedthecentripetalforces. Explainhowyoucalculatedthepercentdifferences. Statethatyourepeatedallofthesecalculationswhilevaryingdifferentparameters (statewhichparametersyouvaried). Showatable(s)ofyourdata.Includethetableproperly. Discussion/Conclusions: /20 Howwelldidyouachieveyourobjective?Thisshouldoneormaybetwoconcise statements. Whatsourcesofexperimentalerroraffectedyourresults? 28

29 Clearlyexplainhowtheexperimentalerroraffectedyourrawdataandpropagate thatflawtoyourendresult(conceptually,notmathematically). Answerthequestionsattheendofthelabmanual.Showallworkclearlyandwrite answersincompletesentences.thereadershouldbeabletotellwhatthequestion isaskingbyreadingyouranswer. Additional(Comments:( 29

30 Centripetal*Force*Pre/Lab*Quiz Name: Section#: 1.ShowthatFr=mrω 2 isnewton ssecondlawinradialform.hint:startwiththe usualformofnewton ssecondlawandmakesubstitutionsforathensimplifythe expression. 2.Clearlyexplainthefunctionoftheorangediskintoday sexperiment. 30

31 Converging)Lenses)Lab)Grading)Rubric) Name: Grade: /100 Pre4Lab: /10 ) Cover)Page/Lab)Manual)Pages: /5 Name CourseSection# Instructor sname TitleofExperiment DateExperimentwasPerformed Partner sname Labmanualpagespresentandinorder ) Objective)Statement: /10 Completelyandconciselyaddressallofyourobjectives Writeacompletesentenceinthepasttenseandactivevoicethatusesfirstperson pronouns. ) Results: /35 CylindricalLens Includeafigureforeachlensorientation Statethefocallengthyouobtainedforeachlensorientation Includeafigure(s)thatindicateaberration SphericalLens Explainhowyoucalculatedthefocallength Explainhowyoucalculatedthemagnificationfromtheobjectandimage distances Explainhowyoucalculatedthemagnificationfromtheobjectandimage heights Explainhowyoucalculatedthepercentdifferencebetweenthemagnifications Includeatableofthevariousobjectdistancesandtheircorrespondingimage distances 31

32 Stateyouraveragefocallengthyouobtainedfromyourtable Plot1/dovs1/di Determinethefocallengthfromtheaverageoftheinterceptvaluesonthetwo axes Compareyourfocallengths Answerquestion#4attheendofthelabmanualpages Conclusion: /30 Addressyourobjectives Explainhowsourcesofexperimentalerroraffectedyourresults(whydowehave percentdifferences?) Answerquestions1,2,3,and5attheendofthelabmanualpages 32

33 Converging)Lenses)Pre-Lab)Quiz Name: Score: /10 Section#: Drawaraydiagramforanobjectlocateddo=10cminfrontofaconverginglens whosefocallengthisf=30cm Determinetheimagedistance,di,usingthethinlensequation. Determinethemagnification(remembertoconsiderthe+/Gsign). 33

34 Electric(and(Potential(Fields(Lab(Grading(Rubric Name: Grade: /100 Pre6Lab: /10 ( Cover(Page/Lab(Manual(Pages: /5 Name CourseSection# Instructor sname TitleofExperiment DateExperimentwasPerformed Partner sname Labmanualpagespresentandinorder ( Objective(Statement: /10 Completelyandconciselyaddressallofyourobjectives Writeacompletesentenceinthepasttenseandactivevoicethatusesfirstperson pronouns(we). ( ( Results(and(Analysis: /40 Properlyincludeafigurethatrepresentsyourmapofthepotentialfield. Properlyincludeafigurethatrepresentsyourmapoftheelectricfield. Discussion/Conclusions: /35 Commentonhowwellyouachievedyourobjective(s). AnswerthequestionsattheendoftheMappingPotentialFieldsproceduresection (partiv)inthelabmanual. AnswerthequestionsattheendoftheMappingElectricFieldsproceduresections (partsv,vi,andvii)inthelabmanual. Identifysourcesofexperimentalerror 34

35 Explainhowsourcesofexperimentalerroraffectedyourresults. Answerthequestionsattheendofthelabmanualpages.Showworkclearlyand neatly. Additional(Comments:( 35

36 Electric(and(Potential(Fields(Pre0Lab(Quiz Score: /10 Name: Section#: Fillinyournameandsectionnumberoryouwillloseapointforeach. Question1 a).drawtheelectricfieldlinescomingoutoftheconductingsphereinthepicture. Useanappropriatenumberoffieldlinesanddonotattempttomakeathree7 dimensionaldrawing.(2pts.) b).afteryoudrawthefieldlines,drawtheequipotentiallines.twoorthree equipotentiallineswillsuffice.(2pts.) Question2 Whatisthenameoftheidealized,non7physicalentitythatweusetodeterminethe forceassociatedwithanelectricfieldatacertainpointinspace?(2pts.) Question3 Thediagramonthechalkboardrepresentsauniformelectricfieldpointedinthe positivexdirection.whichpath(a,b,orc)wouldrequirethemostworktomovea positivetestchargealong?whichpathwouldrequiretheleastamountofwork? Most: (2pts.) Least: (2pts.) 36

37 Impulse(and(Momentum(in(Collisions(Lab(Grading(Rubric Name: Grade: /100 Pre9Lab: /10 ( Cover(Page/Lab(Manual(Pages: /5 Name CourseSection# Instructor sname TitleofExperiment DateExperimentwasPerformed Partner sname Labmanualpagespresentandinorder ( Objective(Statement: /10 Completelyandconciselyaddressallofyourobjectives Writeacompletesentence(s)inthepasttenseandactivevoicethatusesfirstperson pronouns. Results(and(Analysis: /60 Properlydisplayafigure(s)thatpertainstooneofyourtypescollisions. Explainhowyoucalculatedtheimpulse. Explainhowyouobtainedtheimpulsewithoutdoinganycalculations.Youshould explainthisconceptuallyanddisplayanequation.youdonotneedtoshowasample calculation,butyoumuststatewhattheimpulseisbasedonthefigureyouhave shown. Properlyexplainhowyoufoundthepercentdifferencebetweenthevaluesyou obtainedfortheimpulse. Statethatyourepeatedthesecalculationsforvarioussituationsandstatewhat thesesituationswere. Includeallofyourcalculationsinatable(s)andbesuretoshowafigureforeach typeofcollision. 37

38 ( Discussion/Conclusions: /20 Directlyaddressyourobjective. Compareimpulseinelasticcollisionstoimpulseininelasticcollisionsbasedonyour results Whatsourcesofexperimentalerroraffectedyourresults? Howdidthesesourcesaffectyourresults? Answerthequestionsattheendofthelabmanual. Additional(Comments:( 38

39 Impulse(and(Momentum(in(Collisions(Pre3Lab(Quiz Name: Section#: 1.Indicatewhetherthecollisionbetweenthefollowingobjectsiselactic(E)or inelastic(i).considercollisionsthatareapproximatelyelastictobeelastic: Twobilliardballstravelingtowardeachother Ajavelincollideswiththegroundandsticksintoit Aballofclaythrownataconcretewallhitsthewallandfallsstraightdownto theground Alabcartonatrackcollideswithasprig Alabcartonatrackcollideswithaplasticairbag 2.Aforceisappliedtoanobjectforatotaltimeof10seconds.Duringthefirst3 seconds,themagnitudeoftheforceis6n.duringthelast7seconds,theforceis5n. Whatisthetotalimpulsefeltbytheobjectduringthetenseconds? 39

40 MotioninFree*FallLabGradingRubric Name: Grade: /100 CoverPage/LabManualPages: /5 Name CourseSection# Instructor sname TitleofExperiment DateExperimentwasPerformed Partner sname Labmanualpagespresentandinorder ObjectiveStatement: /10 Completelyandconciselyaddressallofyourobjectives Writeacompletesentence(s)inthepasttenseandactivevoicethatusesfirstperson pronouns. ResultsandAnalysis: /55 Displaytables12 Explainhowyoufoundthevelocities Explainwhythetimeassociatedwitheachvelocityisatthemidpointofthe correspondingtimeintervalforposition Displayvelocityvs.timeplot Explainhowyoufoundvoanda#intheequationv=vo+at# Displaypositionvs.timeplot 40

41 Explainhowyoufoundv*,theinstantaneousvelocites,byfindingtheslopeofthe tangentlinesandcomparethemtothevelocitiesinthetable Discussion/Conclusions: /30 Addresstherelationshipsbetweenposition,velocityandacceleration Addressexperimentalerror(whywasyourvalueforanotexactlyequaltothe acceptedvalueforg?).statesource(s)oferrorandexplainhowtheyaffectedyour results Howcouldweminimizeexperimentalerror? Answerdiscussionquestionsclearlyandneatly AdditionalComments: 41

42 Ohm slawlabgradingrubric Name: Grade: /100 Pre6Lab: /10 CoverPage/LabManualPages: /5 Name CourseSection# Instructor sname TitleofExperiment DateExperimentwasPerformed Partner sname Labmanualpagespresentandinorder ObjectiveStatement: /10 Completelyandconciselyaddressallofyourobjectives Writeacompletesentenceinthepasttenseandactivevoicethatusesfirstperson pronouns. ResultsandAnalysis: /50 Properlyincludeafigurethatgraphsthecurrentvs.thevoltageforthe10Ω resistor. Statetheresistanceyoufindfromthefigureandcalculatethepercentdifference betweenyourresistanceand10ω. Calculatethemaximumpowerfromyourgraph. Includeafigurethatgraphsthecurrentvs.voltageforthe100Ωresistorsin series Explainhowyoucalculatedthetheoreticalresistanceduetothetworesistorsin series. Explainhowyoucalculatedthepercentdifferencebetweenyourresistanceandthe theoreticalvalue. Includeafigureforthecurrentvs.voltageforthetwo100Ωresistorsin parallel. Explainhowyoucalculatedthetheoreticalresistanceduetothetwo100Ωresistors inparallel. 42

43 Explainhowyoucalculatedthepercentdifferencebetweenyourvalueandthe theoretical. Includethegraphofthecurrentvs.voltageforthelightbulb.Stateyourvaluefor theresistancefromthe straightline region. Explainhowyoucalculatedthemaximumresistancevalue. Explainhowyoucomparedthisvaluetothelightbulb sresistancerating. Includeafigureforthevoltageandcurrentvs.timeforthediode. Explainhowyoucalculatedtheratioofvoltage/current. Explainhowyoucalculatedthepowerandcomparedittothediode srating. Includeatableofyourcurrentcalculationsforvariousresistances. Includeafigure,plottingoftheinformationinthetable. Discussion/Conclusions: /25 Commentonhowwellyouachievedyourobjective(s). Doyourresultsverifytheoreticalpredictions?. Explainhowsourcesofexperimentalerroraffectedyourresults. Skipthequestionsattheendofthelabmanualpagesforbothexperiments. AdditionalComments: 43

44 Ohm slawprelabquiz Name: Score: /10 Section#: Eachcircuitshownbelowcontainstwo5Ωresistorsconnectedtoa2voltpower supply.incircuita,theresistorsareconfiguredinaseries,whileincircuitb,they areconfiguredinparallel. a)determinetheeffectiveresistance(req)foreachcircuit. b)usingohm slaw,determinethemagnitudeofthecurrentineachcircuit. TrueorFalse:Theslopeofthegraphofivs.Visequalto1/R,or1/Reqforasystem ofmultipleresistors. 44

45 Projectile*Motion*Lab*Grading*Rubric Name: Grade: /100 Pre5Lab: /10 * Cover*Page/Lab*Manual*Pages: /5 Name CourseSection# Instructor sname TitleofExperiment DateExperimentwasPerformed Partner sname Labmanualpagespresentandinorder * Objective*Statement: /10 Completelyandconciselyaddressallofyourobjectives Writeacompletesentence(s)inthepasttenseandactivevoicethatusesfirstperson pronouns. Results*and*Analysis: /55 Explainhowyoucalculatedtheinitialvelocityforeachofthethreepossibleinitial velocities. Explainhowyoucalculatedtheoreticalvaluesfort,Randymax. ExplainhowyoucalculatedtheΔt%,Δx%,andΔymax%values. Displayatableshowingallofthesevalues. Explainhowyouusedequation3fromthelabmanualtocalculatetheoreticaly positionvaluesforeachcorrespondingxpositionvalue. Explainhowyoucalculatedthepercentdifferencebetweenthetheoreticaland actualypositions. Displayatableofthedatafrompart2. Explainthefirst iftimepermits part. 45

46 Explainthemathbehindwhetherornotyoucanusethe2Wclickvelocitytoreachthe rangeyoufoundforthe70 launchwith3wclickvelocityusing.isitpossibletotake thesineofanumberthatisnotbetweenzeroandone?showmanipulationsof equationswithnumbershere. Discussion/Conclusions: /20 Commentonhowwellyouachievedyourobjective(s). Identifysourcesofexperimentalerror(whydowehavepercentdifferencesinthe firsttwopartsoftheexperiment?) Explainhowsourcesofexperimentalerroraffectedyourresults. Answerthequestionattheendofthelabmanualpages.Showworkclearlyand neatly. Additional*Comments:* 46

47 Projectile*Motion*Experiment*Pre1Lab*Quiz* Name: Section#: ThediagramshowsaballthathasbeenlaunchedfromlaunchpointLwithinitial velocityvoatanangleθ#relativetothehorizontalflatground.thetotaltimeofflight oftheballwast.duringthistime,theballcoveredahorizontaldistanced.theballis picturedatpositionsa,bandc.positionatookplaceattimet/4,positionbtook placeattimet/2andpositionctookplaceattime3t/4.theballisatitshighest pointatpositionb. B# # # # A C GGGGGGGGGL##)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))# GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGdGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG Onthediagram,drawvectorswithmagnitudeslabelednexttothemforthe following: a) Theball snetinitialvelocityatthelaunchpoint(vo).alsoshowtheangleθ b) ThexGcomponentoftheball sinitialvelocityatthelaunchpoint(vox) c) TheyGcomponentoftheball sinitialvelocityatthelaunchpoint(voy) d) ThexGcomponentoftheball svelocityatpositionsa,#bandc(vxa,b,c) e) TheaccelerationoftheballatpositionsA,#BandC(aA,B,C) f) TheyGcomponentoftheball svelocityatpositionb(vyb) Usingvox=dx/txwheredxisthedistancetraveledinthexGdirectionandtxisthe amountoftimeittooktogetthere,howfarhastheballtraveledhorizontallyat positionsa,#bandc? 47

48 Properties)of)a)Vertical)Spring2Mass)System)Lab)Grading)Rubric Name: Grade: /100 Pre2Lab: /10 ) Cover)Page/Lab)Manual)Pages: /5 Name CourseSection# Instructor sname TitleofExperiment DateExperimentwasPerformed Partner sname Labmanualpagespresentandinorder ) Objective)Statement: /10 Completelyandconciselyaddressallofyourobjectives Writeacompletesentence(s)inthepasttenseandactivevoicethatusesfirstperson pronouns. Results)and)Analysis: /60 Explainhowyoudeterminedthespringconstantkbyplottingthedisplacementdue tovariousmasses.thisinvolvesdisplayingafigureproperly. Explainhowyoudeterminedtheperiodsbasedonthespringconstantk. Explainhowyoufoundtheperiodsfromoneoftheplotsofthemass soscillation. Thisinvolvesshowingafigurethenexplainingacalculation. Explainhowyoufoundthepercentdifferencesbetweentheperiods. Displayatablethatshowsallcalculationsthatwentintodeterminingthepercent differences. Displayasetofmoredetailed(zoomedRin)plots(position,velocity,acceleration, forcevs.time)representingthemass soscillation. Explainhowyoudeterminedthekineticenergyatsomepointintime. Explainhowyoudeterminedthepotentialenergyatthesamepointintime. Explainhowyoudeterminedthetotalenergyatthesamepointintime. 48

49 Explainhowyoudeterminedtheforceusingtwodifferentmethods(Hooke slaw andnewton slaw)atthesamepointintime. Explainhowyoufoundthepercentdifferencebetweentheforcesyou calculated. Explainthatyoudidthesecalculationsforvariousmasseswhenthedisplacement wasatamaximum,aminimum,andsomewhereinbetween. Displayatableoftheenergyandforcecalculations. Discussion/Conclusions: /15 Directlyaddressyourobjectives. Whatdidyoudetermineabouttherelationshipsbetweenpotentialenergy,kinetic energy,totalenergyandforceinaverticalspringrmasssystem?makeafewconcise, wellthoughtroutstatements. Addresssourcesofexperimentalerrorthatlimitedyourabilitytoachieveyour objectives. Additional)Comments:) 49

50 Properties)of)Energy)in)a)Vertical)Spring4Mass)System)Pre4Lab)Quiz) ) Name: Section#: 1.WritedownHooke slawfortheforceexertedbyaspringonamassbasedonits displacementfromequilibrium. 2.Indicatewhetherthefollowingaretrue(T)orfalse(F) Whenamassattheendofaspringisoscillatingaboutequilibrium,thetotal energyofthesystematsomemomentintimeisalwaysequaltothetotalenergyof thesystematsomeothermomentintime. Whenamassattheendofaspringisoscillatingaboutequilibrium,the potentialenergyofthesystematsomemomentintimeisalwaysequaltothe potentialenergyofthesystematsomeothermomentintime. Whenamassattheendofaspringisoscillatingaboutequilibrium,thekinetic energyofthesystematsomemomentintimeisalwaysequaltothekineticenergy ofthesystematsomeothermomentintime. Thespringforceisatamaximumvaluewhenthedisplacementfrom equilibriumisataminimumvalue. 3.Intoday sexperiment,whatdoesthepositionsensormeasure?(circleanoption) a) Themass sdisplacementfromequilibrium b) Themass skineticenergy c) Themaximumdisplacementofthemass d) Thedistancefromthesensortothemass 50