You can easily adjust the position of the lamp and it will always remain in the position you left it in Its working principle is very simple but very clever at the same time And you can now calculate how it works The original Anglepoise lamp was inv ID: 56215
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(a)Original1932AnglepoisedesignbyGeorgeCarwardine. (b)ModernversionoftheAnglepoiselamp,theType75.Figure1:TheAnglepoisedesklampisadesignclassicandamechanicalengineeringmarvel.2 1c)Showthatthetotalenergystoredinthesystemisindependentoftheangle .RememberthatthepotentialenergyofamassisUp=mghwherehistheverticaldisplacement,andthatthespringenergystoredinthesespringsisUs=1 2kL2.Hint:Usethecosineruletoexpressthelengthofthespringintermsofa,rand .Also,usethehorizontalpositionofthebaras`zero'congurationforthepotentialenergyofthemass.1d)Wenowchangetoaslightlymorecomplexbalancer,whichisstartingtoresembletheclassicAnglepoiselamp.Itconsistsofaparallelogramxedtotheworld,andsupportedbyazero-free-lengthspringattachedtothetoparmoftheparallelogram.Itsupportsapayloadmatadistancedfromtheendoftheparallelogram.Drawafreebodydiagramforeachofthecomponents,andshowthatdistancedisirrelevantforthecorrectworkingofthebalancer.NB:youdonotneedtondexactexpressionsfortheforcestoanswerthisquestion,butacorrectforceanalysisinthefreebodydiagramsisessential! Figure4:TheparallelogrambalanceristhebasecomponentoftheclassicAnglepoisedesign.4 CreatingtheAnglepoiseLampYoucannowquiteeasilyunderstandhowwecancreateanAnglepoiselamp:wesimplyconnectanumberofparallelogramsinseries|seeFigure5.Ifbyanychanceyou'rekeentolearnmoreaboutthemodernAnglepoiselamp,anin-depthmechanicalanalysisisgivenbyFrenchandWidden(2000). Figure5:SchematicofclassicAnglepoisedesign;itworksbyconnectingtwobalancedparallelograms.TheprincipleofcounterbalancingwithspringscanbeappliedtoavarietyofotherproductsbesidestheAnglepoiselamp.Thebalancingarrangemente ectivelymakesapayloadweightless,sotheonlyforcerequiredtomovethemass,istoaccelerateanddecelerateit.Applicationsincludearmsupportsforpeoplewithamusculardiseasewhocannotlifttheirarmwiththeirownmusclestrength,butalsoroboticarmswheretheactuatorscanbelessstrongastheyneednotliftthedeadweightoftheroboticarm.BeforestartinghisPhD,yoursupervisorworkedforacompanythatisdevelopinganadvancedapplicationofthistechnology,thatcaneasilycounterbalancethingslikeTVsandkitchencabinets:http://www.balancebox.eu5 Question2:PuntingthroughJesusLockThisquestionisbasedonaseriesofrealevents...Onceuponatime,onadarkandavery,verycoldNovemberevening,veClaregraduatestudentsdecidedtomovetheMCRpuntsfromtheirberth,tothewinterstorageattheboathouses.AmajorobstacleinthisepicvoyagewastheweiratJesusgreen.Theyallagreedthattakingapuntdowntheonemetredropoftheweirwasprobablynotagoodidea,sotheydecidedtouseJesuslock.Problemwas,noneofthemhadactuallyeverusedalockbefore...buttheythoughttheyoughttobesmartenoughtodealwithsuchasimplecontraption! Figure6:JesusweirandlockinCambridge.Photofromhttp://www.panoramio.com/photo/10225736Theupstreamv-doorswereclosed,sothersttaskwastoclosethedown-streamdoors,openthesluicegatesontheupstreamsideandletthelockllup.Duetoastupidmistakebytheoneofthestudents(nevertrustazoologistwithalock),whohadaccidentallypartiallyopenedthelowersluicegatesaswell,ittookforevertollupthelock.Weallknowtimeisrelative,butwhenit'sverycoldandyou'vebeenpromisedapintaftermov-ingthepunt,timereallyticksveryslowly!Afterabout30minutesoneofthegraduateshadgottenverycoldandalsoratherboredandwhilststaringdownatthelockslowlyllingup,concoctedanexamplepaperquestiontoannoyhissuperviseeswith...6