P2Tutorial1 - Tutorial1(Sep29,2010 1 , distanceofR=5.=3.0856108m/sinanalmostcircular

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Unformatted text preview: Tutorial1(Sep29,2010) 1) Inanewlydiscoveredplanetarysystem,aplanetliketheearthisrotatingata distanceofR=5.15lightminutesusingc=3.0856108m/sinanalmostcircular orbit.ThisnewplanettakesT=121.4daystoorbititsstar.Whatisthemassof thestar(M)tothecorrectnumberofsignificantfigures?Usethefactthat 42R3=GMT2andNewton'sconstantG=6.674281011m3/kg/s2.[Ifyouwantto compare,themassofthesunis21030kg.] M=4*2(5.15*60s*3.0856108m/s)3/ (6.674281011m3/kg/s2)/(121.4*24*3600s)2 =4.661030kg[keep3sigfigssinceRisknownto3sigfigs] Massofstarisabouttwicethemassofthesun. 2) Applytherulesforsignificantfiguresinorderoftheoperationsbelowusing a=2.1andb=0.1.First(a+b)2andthena2+b2+2ab.Arethetwoanswersthe same?Nowtrythesamewitha=2.1andb=0.11. Firstsetofnumbers:a+b=2.2,andthen(a+b)2=4.8[4.84roundedto2sigfigs] a2+b2+2ab=4.4+0.01+0.4=4.8[4.81roundedto1decimalplace] 2ndsetofnumbers:a+b=2.2,andthen(a+b)2=4.8[4.84roundedto2sigfigs] a2+b2+2ab=4.4+0.012+0.46=4.9[4.872roundedto1decimalplace] Whatyouhavelearnthereisthatroundingintheintermediatestepscanchange youranswer.Whenyoudoproblems,don'tapplythesesigfig(rounding)rules untilthelaststep. 3) McanmopafloorthriceasfastasJand1.5timesfasterthanK.Working togethertheymopthisfloorin10minutes.HowfastcanKmopthefloorby himself? Job=MopthefloorRateofKmoppingfloor=RK(Unknown) RM=3*RJandRM=(3/2)*RK RJ=RM/3=RK/2 Job=(RM+RJ+RK)*10mins Job=(3*RK/2+RK/2+RK)*10mins=3*RK*10mins SoRK=Job/30mins Jalonecanmopthefloorin30minutes. 4) Youpourtwofullbottlesof1%milkandonefullbottleof2%milkintoa container.Youhaveonefullbottleof2%milkleftinthefridge.Howmuchofthat bottlemustyouusetomakeyourveryown1.4%milk?(Assumeeachbottleof milkweighsthesame.) X=fractionofthebottleused Writeanequationforamountoffat 2*1%+(1+X)*2%=(3+X)*1.4% 4+2X=4.2+1.4X X=1/3 5) JoelovesCheerioscereal.However,hehasaproblemheneedsexactly25 cheeriospiecesin100mLofmilktostarteating.Hepourshimselfabowland findsoutthatthereare35cheeriosand110mLofmilkinthebowl.Howmuch milkorhowmanycheerios(eithermilkorcheeriosbutnotboth)mustheaddto eat? LetaddedmilkvolumebeM. Then,(25cheerios)/(100mL) =(35cheerios)/(110mL+M) 2750mL+25M=3500mL M=750mL/25=30mL 6) Youhavesmallsculpturesmadeofcopperandgold.Thefirstsculpturehas5% goldwhilethesecondonehas10%gold.Thefirstsculpturehastwicethemass ofthesecondone.Youmeltboth,extractthegoldandyoumakearingofpure goldthatis10g.Whatisthemassofthelightersculpture? LetthemassofthelightersculpturebeM Then10g=5%of2M+10%ofM Or10g=0.1M+0.1M=0.2M SoM=50g(massoflightersculpture) 7) Acontractorrequiresacementmixthatis70%sandand30%cement.Hehas 700kgofacementmixthatis80%sandand20%cement.Howmuchcement shouldheaddsothathegetstherequiredmix? X=amountofcementaddedinkilogram Amountofsanddoesn'tchange. So700kg*80%=(700+X)*70% 560=490+0.7X X=70/0.7 Needstoadd100kgofcement. 8) Joestartsfromhishomeat5PM.Heruns2milesataconstantpaceandthen restsfor10minutes.Hethenwalks3milesathalfthepacethatheruns.When hefinishesthewalk,thetimeis6:30PM.Whatishisrunningspeedinmph? LetthepaceatwhichJoerunsbev,thetimeforwhichJoerunsbet1,andthe timeforwhichJoewalksbet2 Writeanequationfordistancecoveredwhenrunning2mi=v*t1 Writeanequationfordistancecoveredwhenwalking 3mi=(v/2)*t2 Or6mi=v*t2 Usetheabovetwoequationstofind t2=3*t1 Writeanequationforthetotaltimetaken90mins=t1+t2+10mins Solvethelasttwoequationstoget t1=20minsandt2=60mins. SoJoe'srunningpacev=2mi/20mins=6mph. ...
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This note was uploaded on 11/21/2010 for the course PHYSICS Physics 2 taught by Professor Manojkaplinghat during the Fall '10 term at UC Irvine.

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