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1、SCALINGBUILDINGS-4-SCALINGBUILDINGSInthisactivitywewillseehowscalingaffectsvariouspropertiesofabuilding.1.Let’sbeginwithaverysimplebuilding:abuildingthathasa2x3rectangleasabaseoutline,andauniformheightof1cube.Let’scallthisBuilding1.2.Wemightbeinterestedinplantinganarrowflowerbedaroundtheba
2、seofthebuilding.WhatistheperimeterP1ofthebaseoutline?3.Wemightbeinterestedinpaintingthesidesandtheroofofthebuilding.HowmanysquareunitsofsurfaceareaA1doweneedtopaint?4.Wemightbeinterestedintheamountoflivingspaceinthebuilding.HowmanycubicunitsofvolumeV1doesthebuildingcontain?SCALINGBUILDINGS
3、-4-Nowlet’smakeanewbuilding,Building2,byscalingBuilding1byascalefactorof2.ThismeansthatwewilldoublethelengthofeverysegmentinBuilding1.Howdothemeasurementsinproblems2-4change(let’scallthemP2,A2,andV2)?Canyouexplainwhythismakessense?SCALINGBUILDINGS-4-Nowlet’smakeanewbuilding,Building3,bysca
4、lingBuilding1byascalefactorof3.Howdothemeasurementsinproblems2-4changethistime(let’scallthemP3,A3,andV3)?Canyouexplainwhythismakessense?1.ComparetheratiosP3/P1,A3/A1,andV3/V1.Canyouexplainyourresults?2.ComparetheratiosP3/P2,A3/A2,andV3/V2.Canyouexplainyourresults?Whatscalingfactormustyouus
5、etoscaleBuilding2uptothesizeofBuilding3?3.Repeatproblems1-8withthebuildinggiveninProblem1.3ofRuinsofMontarek.Summarizeyourresults.4.Roughlyspeaking,theabilityofawarm-bloodedorganismtogenerateheatisproportionaltoitsvolume,andtheabilitytoradiateheatisproportionaltoitssurfacearea.Awell-design
6、edorganismmustkeepthesetwoprocessesinbalancesothatitdoesnotgeneratemoreorlessheatthanitradiates.Ifsuchanorganismisscaledupbyascalingfactorof10,bywhatfactorisitsabilitytogenerateheatmultiplied?Bywhatfactorisitsabilitytoradiateheatmultiplied?Whydoesthishelpexplainwhybirdseatmuchmoreinproport
7、iontotheirsizethanhumans?SCALINGBUILDINGS-4-1.Roughlyspeaking,theweightofanorganismisproportionaltoitsvolume,andthestrengthofitsbonesisproportionaltothecross-sectionalareaofthebones.Awell-designedorganismmusthavebonesstrongenoughtosupportitsweight.Ifsuchanorga
