Quiz (Oscillation)

Quiz (Oscillation) - Physics7A:Quiz6...

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Unformatted text preview: Physics7A:Quiz6 UCBerkeley,Fall2010,GSI:AaronAlpert INSTRUCTIONS:Thisisatake ­homequiz.Itisduebythebeginningofclass(2pm)onWednesday,Dec. 1.Ifyoucannotbeinclassthatday,youareexpectedtoemailmeyouranswer.Youmayconsultany booksoronlineresources,butyoumaynotconsultotherpeople.Atthetopofyourquiz,writethe followingsentence,andsignyourname:"Ididnotaskfororreceive helpfromanyotherpersononthisquiz." r  AU ­shapedtubewithcross ­sectionalradiusrisfilledwithan incompressibleliquidofdensity .Thefluidcomestoarestingpoint d suchthatthetopofthefluidisHabovethebottomofthetube.One d columnoffluidisdisplacedsuchthatitisdbelowHandtheother columnisdaboveH.  H Assumingthatthecurveinthebottomofthetubeisnegligible,find theperiodofoscillationofthefluid.  EXTRACREDIT OPTIONAL Supposethatweplaceaventuritubeontopoftheu ­tube,asshowntotheleft.Theventuri tube'scrosssectionalareadecreasesfrom to .Ifair(density )isblownthrough theventuritubeatamassflowrateof kg/s,howwillthisaffectthemotionofthefluid?Will theperiodincrease,decrease,orstaythesame?Why?    Physics7A:Quiz6 UCBerkeley,Fall2010,GSI:AaronAlpert INSTRUCTIONS:Thisisatake ­homequiz.Itisduebythebeginningofclass(2pm)onWednesday,Dec. 1.Ifyoucannotbeinclassthatday,youareexpectedtoemailmeyouranswer.Youmayconsultany booksoronlineresources,butyoumaynotconsultotherpeople.Atthetopofyourquiz,writethe followingsentence,andsignyourname:"Ididnotaskfororreceive helpfromanyotherpersononthisquiz." r  AU ­shapedtubewithcross ­sectionalradiusrisfilledwithan incompressibleliquidofdensity .Thefluidcomestoarestingpoint d suchthatthetopofthefluidisHabovethebottomofthetube.One d columnoffluidisdisplacedsuchthatitisdbelowHandtheother columnisdaboveH.  H Assumingthatthecurveinthebottomofthetubeisnegligible,find theperiodofoscillationofthefluid.  EXTRACREDIT OPTIONAL Supposethatweplaceaventuritubeontopoftheu ­tube,asshowntotheleft.Theventuri tube'scrosssectionalareadecreasesfrom to .Ifair(density )isblownthrough theventuritubeatamassflowrateof kg/s,howwillthisaffectthemotionofthefluid?Will theperiodincrease,decrease,orstaythesame?Why? SolutionforPhysics7A:Quiz6 UCBerkeley,Fall2010,GSI:AaronAlpert  Thereisaforceimbalanceinthefluidduetotheadditionalfluidon r therighthandsideoftheu ­tube.(Showninblueinthefiguretothe right.)Thisfluidhasacrosssectionalareaof andaheightof . Multiplyingthevolumebythedensitygivesusthemass.Multiplying x by9.8m/s2givesustheweightofthisadditionalfluid. x   Alloftheotherforcescancel,sowesetthesumoftheforcesequal H tomasstimesacceleration.    Whatis ,themassofthefluid?Thecrosssectionalareais andtheheightoftheentirefluidis , meaningthatthevolumeoffluidis ,anditsmassis .  Werearrangetermsandsubstituteintheexpressionformass.   Thisiseffectivelythesameastheequation thiscase,thenaturalfrequencyis where ,thenaturalfrequency.In .Periodisrelatedtonaturalfrequencyinthefollowingmanner.   EXTRACREDIT Introducingtheventuritubewill,effectively,addpressuretotheleftside.Why?Airflowsthroughata constantmassflowrate .Sincetheareadecreases,andthedensityofairisconstant,that meansthevelocitymustincrease.FromBernoulli'sequation, ,isconstantalonga streamline.Sincetheheight doesn'tchangebutthevelocityincreases,thatmeansthepressuredrops fromthelefttotheright.Thisextrapressurewilldisplacethefluidslightly.Now,insteadofhavingthe equilibriumpointbewherebothfluidsareat ,nowtheleftwillbeat andtherightwillbeat .(Wecandetermine exactlyfromtheinformationgiven,butthatisnotnecessaryforthis problem).  However,noneofthiswillchangethegoverningequation, ,ifweassumethat ismeasured relativetothenewequilibrium, .Thus,theperiodisunchangedbytheventuritube.  ...
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  • Spring '08
  • Lanzara
  • Physics, EXTRA0200CREDIT0200 0200OPTIONAL0200 Suppose0200that0200we0200place0200a0200venturi0200tube0200on0200top0200of0200the0200u02, d0200 column0200of0200fluid0200is0200displaced0200such0200that0200it0200is0200d0200below0200H0200and0200the0200other0200 column0200is0200d0200above0200H.020002000200, r0200 0200 A0200U02

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