物理学专业英语

BasicConceptofPhysics,Unitsanddimensions,Physicalquantity,Sayaplankis2meterslong.Thismeasurementiscalledaphysicalquantity.Inthiscase,itisalength.Itismadeupoftwoparts:,Note:2mreallymeans2meter,jusas,inalgebra,2ymeans2y,SIbaseunits,ScientificmeasurementsaremadeusingSIunits(standingforSystmeInternationaldunits).Thesystemstartswithaseriesofbaseunits,themainonesbeingshowninthetablebelow.Otherunitsarederivedfromthese.,*:Inscience,amountisameasurementbasedonthenumberofparticles(atoms,ionsormolecules)present.Onemoleis6.021023particles,anumberwhichgivesasimplelinkwiththetotalmass.Forexample,1mole(6.021023)ofcarbon-12hasamassof12grams.6.021023iscalledtheAvogadroconstant.,SIderivedunits,ThereisnoSIbaseunitfrospeed.However,speedisdefinedbyanequation.Ifanobjecttravels12min3s:,Theunitsmandshavebeenincludedintheworkingaboveandtreatedlikeanyothernumbersoralgebraicquantities.,Theunitms-1isanexampleofderivedSIunit.Itcomesfromadefiningequation.Thereareotherexamplesbelow.Somederivedunitsarebasedonotherderivedunits.Andsomederivedunitshavespecialnames.Forexample,1joulepersecond(Js-1)iscalled1watt(W).,Prefixes:,PrefixescanbeaddedtoSIbaseandderivedunitstomakelargerorsmallerunits.,Forexample:,1mm=10-3m1km=103m,Note:1gram(10-3kg)iswritten1gandnot1mkg.,Dimensions:,Herearethreemeasurement:,Length=10marea=6m2volume=4m3,Thesethreequantitieshavedimensionsoflength,lengthsquared,andlengthcubed.UsingthesymbolLforlength,thesedimensionscanbewritten:,LL2L3,StartingwiththreebasicdimensionslengthL,massM,andtimeTitispossibletoworkoutthedimensionsofmanyotherphysicalquantitiesformtheirdefiningequations.Thereareexamplesonthebelow.,Example1:,Example2:,Usingdimensionstocheckequations:,Thetwosidesofanequationmustalwayshavethesamedimensions.Forexample:,Work=forcedistancemoved,ML2T-2=MLT-2L=ML2T-2,Anequationcannotbeaccurateifthedimensionsonbothsidesdonotmatch.Itwouldbelikeclaimingthat6applesequals6oranges.,Dimensionsareausefulwayofcheckingthatanequationisreasonable.,Example:CheckwhethertheequationPE=mghisdimensionallycorrect.,Todothis,startbyworkingoutthedimensionsoftheright-handside:,mgh=MLT-2L=ML2T-2,Thesearethedimensionsofwork,andthereforeofenergy.Sotheequationisdimensionallycorrect.,Note:Thedimensionscheckcannottellyouwhetheranequationisaccurate.Forexample,bothofthefollowingaredimensionallycorrect,butonlyoneisright:PE=mghandPE=2mgh,Dimensionlessnumbers,Apurenumber,suchas6,hasnodimensions.Herearetwoconsequencesofthisfact.,Dimensionsandunitsoffrequency,Thefrequencyofavibratingsourceisdefinedasfollows:,Asnumberisdimensionless,thedimensionsoffrequencyareT-1.TheSIunitoffrequencyinthehertz(Hz):1Hz=1s-1,Dimensionsandunitofangle,Ontheright,theangleinradiansisdefinedlikethis:,s/rhasnodimensionsbecauseLL-1=1.However,whenmeasuringanangleinradians,aunitisoftenincludedforclarity:2rad,forexample.,Measurement,uncertaintiesandgraphs,Scientificnotation,TheaveragedistancefromtheEarthtothesunis150000000km.,Therearetwoproblemswithquotingameasurementintheaboveform:Theinconvenienceofwritingsomaynoughts,Uncertaintyaboutwhichfiguresareimportant,(i.e.Howapproximateisthevalue?Howmanyofthefiguresaresignificant?),Theseproblemsareovercomeifthedistanceiswrittenintheform1.50108km.,1.50108tellsyouthattherearethreesignificantfigures-1,5and0.Thelastsignificantandtherefore,themostuncertain.Theonlyfunctionoftheotherzerosin150000000istoshowhowbigthenumberis.Ifthedistancewereknownlessaccurately,totwosignificantfigures,thenitwouldbewrittenas1.5108km.,Numberswrittenusingpowersof10areinscientificnotationorstandardform.Thisisalsousedforsmallnumbers.Forexample,0.002canbewrittenas210-3.,Uncertainty,Whenmakinganymeasurement,thereisalwayssomeuncertaintyinthereading.Asaresult,themeasuredvaluemaydifferfromthetruevalue.Inscience,anuncertaintyissometimescalledanerror.However,itisimportanttorememberthatitisnotthesamethingasamistake.,Inexperiments,therearetwotypesofuncertainty:,Systematicuncertainties:theseoccurbecauseofsomeinaccuracyinthemeasuringsystemorinhowitisbeingused.Forexample,atimermightrunslow,orthezeroonanammetermightnotbesetcorrectly.Therearetechniquesforeliminatingsomesystematicuncertainties.However,thisslidewillconcentrateondealingwithuncertaintiesoftherandomkind.,Randomuncertainties:Theseoccursbecausethereisalimittothesensitivityofthemeasuringinstrumentortohowaccuratelyyoucanreadit.Forexample,thefollowingreadingsmightbeobtainedifthesamecurrentwasmeasuredrepeatedlyusingoneammeter:,2.62.5,Becauseoftheuncertainty,thereisvariationinthelastfigure.Toarriveatsinglevalueforthecurrent,youcouldfindthemeanoftheabovereadings,andthenincludeanestimationoftheuncertainty:,Current=2.50.1,Writing2.50.1indicatesthatthevaluecouldlieanywherebetween2.4and2.6.,Note:Onacalculator,themeanoftheabovereadingworksoutat2.5125.However,aseachreadingwasmadetoonlytwosignificantfiguresi.e.2.5.Eachoftheabovereadingsmayalsoincludeasystematicuncertainty.,Uncertaintyasapercentage,Sometimes,itisusefultogiveanuncertaintyaspercentage.Forexample,inthecurrentmeasurementabovetheuncertainty(0.1)is4%ofthemeanvalue(2.5),asthefollowingcalculationshows:,Sothecurrentreadingcouldbewrittenas2.54%.,Combininguncertainties:,Sumsanddifferences:Sayyouhavetoaddtwolengthreadings,AandB,tofindatotal,C.IfA=3.00.1andB=2.00.1,thentheminimumpossiblevalueofCis4.8andthemaximumis5.2.So,C=5.00.2.,NowsayyouhavetosubtractBfromA.Thistime,theminimumpossiblevalueofCis0.8andthemaximumis1.2.SoC=1.00.2,andtheuncertaintyisthesameasbefore.,IfC=A+BorC=A-B,then,Thesameprincipleapplieswhenseveralquantitiesareaddedorsubtracted:C=A+B-F-G,forexample.,Productsandquotients:IfC=ABorC=A/B,then:,Forexample,sayyoumeasureacurrentI,avoltageV,andcalculatearesistanceRusingtheequationR=V/I.Ifthereisa3%uncertaintyinVanda4%uncertaintyinI,thenthereisa7%uncertaintyinyourcalculatedvalueofR.,Note:Theaboveequationisonlyanapproximationandapooroneforuncertaintiesgreaterthanabout10%.Tocheckthattheequationworks,trycalculatingthemaximumandminimumvaluesofCif,sayAis1003andBis1004.YoushouldfindthatABis10000approximately700(i.e.7%).Theprincipleofadding%uncertaintiescanbeappliedtomorecomplexequations:C=A2B/FG,forexample.AsA2=AA,the%uncertaintyinA2istwicethatinA.,Calculatedresults,Sayyouhavetocalculatearesistancefromthefollowingreadings:,Voltage=3.3V(uncertainty0.1V,or3%)Current=2.5A(uncertainty0.1A,or4%),Dividingthevoltagebythecurrentonacalculatorgivesaresistanceof1.32.However,asthecombineduncertaintyis7%or0.1,thecalculatedvalueoftheresistanceshouldbewrittenas1.3.Asageneralguideline,acalculatedresultshouldhavenomoresignificantfiguresthananyofthemeasurementsusedinthecalculation.(However,iftheresultistobeusedinfurthercalculations,itisbesttoleaveanyroundingupordownuntiltheend.),Choosingagraph:,Thegeneralequationforastraight-linegraphis:y=mx+c,Inthisequation,mandcareconstants,asshownbelow.yandxarevariablesbecausetheycantakedifferentvalues.xistheindependentvariable.yisthedependentvariable.Itsvaluedependsonthevalueofx.,Inexperimentalwork,straight-linegraphsareespeciallyusefulbecausethevaluesofconstantscanbefoundfromthem.Hereisanexample.,Problem:TheoreticalanalysisshowsthattheperiodT(timeperswing)ofasimplependulumislinkedtoitslengthl,andtheEarthsgravitationalfieldstrengthgbytheequation.,If,byexperiment,youhavecorrespondingvaluesoflandT,whatgraphshouldyouplotinordertoworkoutavalueforgfromit?,Answer:First,rearrangetheequationsothatitisintheformy=mx+c.Hereisonewayofdoingthis:,So,ifyouplotagraphofT2againstl,theresultshouldbeastraightlinethroughtheorigin(asc=0).Thegradient(m)is,fromwhichthevalueofgcanbecalculated.,Showinguncertaintyongraph,Inanexperiment,awireiskeptataconstanttemperature.Youapplydifferentvoltagesacrossthewireandmeasurethecurrentthroughiteachtime.Thenyouusethereadingstoplotagraphofcurrentagainstvoltage.,Thegeneraldirectionofthepointssuggeststhatthegraphisastraightline.However,beforereachingthisconclusion,youmustbesurethatthepointsscatterisduetorandomuncertaintyinthecurrentreadings.Tocheckthis,youcouldestimatetheuncertaintyandshowthisonthegraphusingshort,verticallinescalleduncertaintybars.Theendsofeachbarrepresentthelikelymaximumandminimumvalueforthatreading.Intheexamplebelow,theuncertaintybarsshowthat,despitethepointsscatter,itisreasonabletodrawastraightlinethroughtheorigin.,Thatiswhythegraphaxesarelabeledvoltage/Vandcurrent/A.Thevaluesofthesearepurenumbers.,Labelinggraphaxes:Strictlyspeaking,thescaleonthegraphsaxesarepure,unitlessnumbersandnotvoltagesorcurrents.Takeatypicalreading:,voltage=10V.,Thiscanbetreatedasanequationandrearrangedtogive:,voltage/V=10.,Showinguncertaintyingraph,Motion,Massandforces,Unitofmeasurement,ScientistsmakemeasurementsusingSIunitssuchasthemeter,kilogram,second,andNewton.Theseandtheirabbreviationsarecoveredindetailinattachment.However,youmayfinditeasiertoappreciatethelinksbetweendifferentunitsafteryouhavestudiedthewholeofthebasicconcept.,Forsimplicity,unitswillbexcludedfromsomestagesofthecalculationsinthiscourse,asintheexample:,Strictlyspeaking,thisshouldbewritten:,Displacement(I),Displacementisdistancemovedinaparticulardirection.TheSIunitofdisplacementisthemeter(m).Quantities,suchasdisplacement,whichhavebothmagnitude(size)anddirection,arecalledvectors.,Thearrowaboverepresentsthedisplacementofaparticlewhichmoves12mfromAtoB.However,withhorizontalorverticalmotion,itisoftenmoreconvenienttousea+or-toshowthevectordirection.Forexample:,Movementof12mtotheright:displacement=+12mMovementof12mtotheleft:displacement=-12m,Displacement(II),Displacementisnotnecessarilythesameasdistancetravelled.Forexample,whentheballbelowhasreturnedtoitsstartingpoint,itsverticaldisplacementiszero.However,thedistancetravelledis10m.,5m,Ballthrownupfromhere,Ballreturnstostartingpoint,SpeedandVelocity,Averagespeediscalculatedlikethis:,TheSIunitofspeedisthemeter/second,abbreviatedasms-1.Forexample,ifanobjecttravels12min2s,itsaveragespeedis6ms-1.,Averagevelocityiscalculatedlikethis:,TheSIunitofvelocityisalsothems-1.Butunlikespeed,velocityisavector.,Thevelocityvectoraboveisforaparticlemovingtotherightat6ms-1.However,aswithdisplacement,itisoftenmoreconvenienttousa+or-forthevectordirection.,Averagevelocityisnotnecessarilythesameasaveragespeed.Forexample,ifaballisthrownupwardsandtravelsatotaldistanceof10mbeforereturningtoitsstartingpoint2slater,itsaveragespeedis5ms-1.Butitsaveragevelocityiszero,becauseitsdisplacementiszero.,6ms-1,Acceleration,Averageaccelerationiscalculatedlikethis:,TheSIunitofaccelerationisthems-2(sometimeswrittenasm/s2).Forexample,ifanobjectgains6ms-1ofvelocityin2s,itsaverageaccelerationis3ms-2.,Accelerationisavector.Theaccelerationvectoraboveisforaparticlewithanaccelerationof3ms-2totheright.Howeveraswithvelocity,itisoftenmoreconvenienttousea+or-forthevectordirection.,Ifvelocityincreasesby3ms-1everysecond,theaccelerationis+3ms-2.Ifitdecreasesby3ms-1everysecond,theaccelerationis-3ms-2.,Mathematically,anaccelerationof-3ms-2totherightisthesameasanaccelerationof+3ms-2totheleft.,Timeins,Velocityinms-1,Acceleration=gradient=6/2=3ms-2,Acceleration=gradient=0/2=0ms-2,Acceleration=gradient=-6/2=-3ms-2,Onthevelocity-timegraphabove,youcanworkouttheaccelerationovereachsectionbyfindingthegradientoftheline.Thegradientiscalculatedlikethis:,Force,Forceisavector.TheSIunitisthenewton(N).,Iftwoormoreforcesactonsomething,theircombinedeffectiscalledtheresultantforce.Towsimpleexamplesareshownbelow.Intheright-handexample,theresultantforceiszerobecausetheforcesarebalanced.,Aresultantforceactingonamasscausesanacceleration.TheforceF,massm,andaccelerationaarelinkedlikethis:,Themoremasssomethinghas,themoreforceisneededtoproduceanygivenacceleration.,Whenbalancedforcesactonsomething,itsaccelerationiszero.Thismeansthatitiseitherstationaryormovingatasteadyvelocity(steadyspeedinastraightline).,Vectors,Vectorarrows:,Vectorsarequantitieswhichhavebothmagnitude(size)anddirection.Examplesincludedisplacementandforce.Forproblemsinonedimension(e.g.verticalmotion),vectordirectioncanbeindicatedusing+or-.Butwheretwoorthreedimensionsareinvolved,itisoftenmoreconvenienttorepresentvectorsbyarrows,withthelengthanddirectionofthearrowrepresentingthemagnitudeanddirectionofthevector.Thearrowheadcaneitherbedrawnattheendofthelineorsomewhereelsealongit,asconvenient.Herearetwodisplacementvectors.,3m,6m,Addingvectors:,IfsomeonestartsatA,walks4mEastandthen3mNorth,theyendupatB,asshownabove.Inthiscase,theyare5mfromwheretheystartedaresultwhichfollowsfromPythagorastheorem.Thisisanexampleofvectoraddition.Twodisplacementvectors,of3mand4m,havebeenaddedtoproducearesultantdisplacementvectorof5m.,Thisprincipleworksforanytypeofvector.Below,forcesof3Nand4Nactatright-anglesthroughthesamepoint,O.Thetriangleofvectorsgivestheirresultant.Thevectorsbeingaddedmustbedrawnhead-to-tail.Theresultantrunsfromthetailofthefirstarrowtotheheadofthesecond.,Parallelogramofvectors:,Bydrawingaparallelogram,theabovemethodcanalsobeusedtoaddvectorswhicharenotatright-angle.Herearetwoexamplesofparallelogramofvectors.,force,force,force,force,resultant,resultant,Note:Themagnitudeoftheresultantdependsontherelativedirectionsofthevectors.Forexample,ifforcesof3Nand4Nareadded,theresultantcouldbeanythingfrom1N(ifthevectorsareinoppositedirections)to7N(iftheyareinthesamedirection.)Inthediagramsonthispage,theresultantisalwaysshownusingadashedarrow.Thisistoremindyouthattheresultantisareplacementfortheothertwovectors.Therearenotthreevectorsacting.,Multiplyingvectors,Whenvectorsaremultipliedtogether,theproductisnotnecessarilyanothervector.Forexample,workistheproductoftwovectors,forceanddisplacement.Butworkisascalar,notavector.Ithasmagnitudebutnodirection.Generally,theproductoftwovectorsreferstoeitherdotproductorcrossproduct.,InEuclideangeometry,thedotproductofvectorsexpressedinanorthonormalbasisisrelatedtotheirlengthandangle.ForsuchavectorAandB,thecrossproductofthemcanbecalculatedlikethis:,crossproduct:alsoknownasvectorproduct,isabinaryoperationontwovectorsinthree-dimensionalspace.Itresultsinavectorwhichisperpendiculartobothofthevectorsbeingmultipliedandthereforenormaltotheplanecontainingthem.,Thecrossproductabisdefinedasavectorcthatisperpendiculartobothaandb,withadirectiongivenbytheright-handruleandamagnitudeequaltotheareaoftheparallelogramthatthevectorsspan.,Matrixnotationofcrossproduct:,Thecrossproductoftwovectorsin3Dspace-aandb-alsocanbecalculatedinmatrixnotation.Say,vectoraandbcanbeexpressedlikethis:,Thedefinitionofthecrossproductcanberepresentedbythedeterminantofaformalmatrix:,Components,component,component,component,component,force,force,Twoforcesactingthroughapointcanbereplacedbyasingleforce(theresultant)whichhasthesameeffect.Conversely,asingleforcecanbereplacedbytwoforceswhichhavethesameeffect-asingleforcecanberesolvedintotowcomponents.Twoexamplesofthecomponentsofaforceareshownabove,thoughanynumberofothersetsofcomponentsispossible.,Note:Anyvectorcanberesolvedintocomponents.Thecomponentsaboveareshownasdashedlinestoremindyouthattheyareareplacementforasingleforce.Therearenotthreeforcesacting.,Inworkingouttheeffectsofaforce(orthevector),themostusefulcomponentstoconsiderarethoseateright-angles,asinthefollowingexample.,Verticalcomponent,horizontalcomponent,Below,youcanseewhythehorizontalandverticalcomponentshavemagnitudesofFcosandFsin.,Equilibrium,TheparticleOabovehasthreeforcesactingonitA,BandC.ForcesA,BandCcanbereplacedbyasingleforceS.AsforceCisequalandoppositetoS,theresultantofA,BandCiszero.Thismeansthatthethreeforcesareinbalancesystemisinequilibrium.,S,A,B,C,Ifthreeforcesareinequilibrium,theycanberepresentedbythethreesidesofatriangle,asshownright.Notethatthesidesandanglesmatchthoseinthepreviousforcediagram.Theforcescanbedrawninanyorder,providedthattheheadofeacharrowjoinswiththetailofanother.,A,B,C,Momentsandbalance,Theturningeffectofaforceiscalledamoment.,*:measuredfromthelineofactionoftheforce.,Thedumb-bellbelowbalancesatpointObecausethetwomomentsaboutOareequalbutopposite.,Principleofmoments,Thebeaminthediagramonthebelowhasweightsonit.(Thebeamitselfisofnegligibleweight.)ThetotalweightissupportedbyanupwardforceRfromthefulcrum.,Asthebeamisnottippingtotheleftorright,theturningeffectsonitmustbalance.So,whenmomentsaretakenaboutO,asshown,thetotalclockwisemomentmustequalthetotalanticlockwisemoment.(Note:RhaszeromomentaboutObecauseitsdistancefromOiszero.),Asthebeamisstatic,theupwardforceonitmustequalthetotaldownwardforce.SoR=10+8+4=22N.,Thebeamisinastateofbalance.Itisinequilibrium.,ThebeamisnotturningaboutO.Butitisnottruingaboutanyotheraxiseither.Soyouwouldexpectthemomentsaboutanyaxistobalance.Thisisexactlythecase,asyoucanseeinthenextdiagram.Thebeamandweightsarethesameasbefore,butthistime,momentshavebeentakenaboutpointPinsteadofO.(Note:RdoeshaveamomentaboutP,sothevalueofRmustbeknownbeforethecalculationcanbedone.),Theexamplesshownaboveillustratetheprincipleofmoments,whichcanbestatedasfollows:,Ifanobjectisinequilibrium,thesumoftheclockwisemomentaboutanyaxisisequaltothesumoftheanticlockwisemoments.,Hereisanotherwayofstatingtheprinciple.Init,momentsareregardedas+or-,andtheresultantmomentisthealgebraicsumofallthemoments:,Ifarigidobjectisinequilibrium,theresultantmomentaboutanyaxisiszero.,Centreofgravity,Alltheparticlesinanobjecthaveweight.Theweightofthewholeobjectsistheresultantofallthesetinny,downwardgravitationalforces.Itappearstoactthroughasinglepointcalledthecentreofgravity.,Inthecaseofarectangularbeamwithanevenweightdistribution,thecentreofgravityisinthemiddle.Unlessnegligible,theweightmustbeincludedwhenanalysingtheforcesandmomentsactingonthebeam.,Theforcesleftareequivalentto,Conditionsforequilibrium,Therearetwotypesofmotions:translational(fromoneplacetoanotherplace)androtational(turning).Ifastatic,rigidobjectisinequilibrium,then:Theforcesonitmustbalance,otherwisetheywouldcausetranslationalmotion.Themomentsmustbalance,otherwisetheywouldcauserotationalmotion.,Thebalancedbeamonthepreviouspageisasimplesysteminwhichtheforcesareallinthesameplane.Acoplanarsystemlikethisisinequilibriumif:theverticalcomponentofalltheforcesbalance,thehorizontalcompon