dimensional analysis (conversion factors)：量纲分析（转换因子）

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1、DimensionalAnalysis(ConversionFactors)Reading:Ch.2sections6Homework:2.6,questions58,60*,62*,66*=‘important’homeworkquestionBackgroundWedosimpleconversionsbetweendifferentunitsonadailybasis.Forexample:Question:Howmanyeggsaretherein1dozeneggs?________Astatementsuchasthiscanbewrittenasan

2、identity1dozeneggs=12eggsRecall:Istheaboveidentityameasuredorexactrelationship?Howwoulditsuseaffectthenumberofsignificantfiguresusedinanyanswer?UsingIdentitiesandConversionFactorsOverviewExample:Howmanyeggsaretherein42dozeneggs?Usetheappropriateidentitytocreateaconversionfactor.Thecon

3、versionfactorwilltransformthequantityintothedesiredform.Math:42dozeneggsx=_______________Conversionfactorsaresimplyidentitieswrittenasfractions.Eachconversionfactorhastwo‘versions’Task:Completethefollowingtablebytransformingthestatedidentityintoitstwocorrespondingconversionfactors.Als

4、oincludeatleastthreeadditionalconversionfactorsthatyouhaveencountered.IdentityConversionfactorsExact?(Y/N)1in=2.54*cm1kg=2.205lb1m=100cm1ft=12inchesDiscussion:Howdoyouknowwhichversionoftheconversionfactortouse?Why?Fornoneexactidentitiesandconversionfactors,howmanysig.figsareimplied?Ex

5、ample:Usetheinformationfromabovetodeterminehowmanycmtherearein12.00inches.12.00inchesx=_______________TheunitbelongingtothequantityandthedenominatoroftheconversionfactorcanceltoleaveafinalanswerwiththedesiredunitGenericForm:ExtraCredit(3pts.,typedfornexttime):Dr.Millsgetsverycrankywit

6、hthetextasitsays“1in=2.54cmexactly”.WhatisthesourceofDr.Mills’confusion?Hint:IstheinchreallyanS.I.unit?Trysearchingfor‘Internationalinch’togetstarted.Task:Completethefollowingconversions.Seeyourtextforappropriateconversionidentities.5.51cmtometers23.0ouncestopounds50.0nmtometers6.56mi

7、lestokm45.7inchestocm220poundstokg(youchooseexamples)ConversionFactor‘Chains’Question:Howdoyouapproachaproblemlike“Convert55cmintofeet”–wherethereisnoavailablesingleconversionfactor?Answer:55cmxx=_______________Linkasmanyconversionfactorsasnecessarytogetherinordertocratea‘chain’.Each‘

8、link’