Physics221:FinalExam,Spring-09Name:Section.No:______________________NOTE:EachproblemisworthZOpts1.(10pts)Alightspringofconstantk=90.0N/rnisattachedverticallytoatable(seeFig.below).A2.00gballoonisfilledwithhelium(density=0.180kg/rn3,densityofair=1.29kg/rn3))toavolumeof5.00m3andisthenconnectedtothespring,causingittostretch.DeterminetheamountofstretchYwhentheballoonisinequilibrium.4c4’JCfYg4(V’4’fr’\I&vcF‘SLI’‘I—-,fsiejt-si.,3<?.c29.j”=S57MF;y.Iv&.i72.(10pts)Avillagemaintainsalargetankwithan opentop,containingwaterforemergencies.Thewatercandrainfromthetankthroughahoseofdiameter6.00cm.Thehoseendswithanozzleofdiameter2.20cm.Arubberstopperisinsertedintothenozzle.Thewaterlevelinthetankiskept7.50mabovethenozzle.a)Calculatethefrictionforceexertedbythenozzleonthestopperb)Thestopperisremoved.Whatmassofwaterflowsfromthenozzlein2.0h?c)Calculatethegaugepressureoftheflowingwaterin thehosejustbehindthenozzlePL’)1It‘?/,/b,)(Cf0X1-3/d”&i’-f4h“-‘-PV-2./p6j)cy,-;:7Sv_/VrOt*4Stoppc.t.-“A1.L)I_22.tCtV)pe5L1Af/A‘&‘1c7...AJif7.3sxiO”P.Kb)),$l,s‘)/O)7.2..,x,035..t’A2)j/Tt0j‘IZ.——7__Cl3.(10pts)Insomediatomicmoleculeswitheachatomhavingamassofm,theforceeachatomexertsontheothercanbeapproximatedbyCDF=——i-+rrwhereristheatomicseparationandCandDarepositiveconstants.Assumeoneatomiskeptatresta)Findtheequilibriumpositionr0intermsofCandDb)LetzSrr-robeasmalldisplacementfromequilibriumwhere&<<ro.Showthatforthesesmalldisplacementsthemotionisapproximatelysimpleharmonicc)Determinetheforceconstantintermsofm,C,andDd)Findtheperiodofsuchmotion2)k’112e1.iif?/7.-,oI--t-4-ph)Vh.t——.—.3,c.)—3—II[-I..-L—2.0-c-3A3vjIAVbrr•_•)It-J---U—4)f1’—&Cb--3t0=_3t\sk—I___——t)iA\.•14.(12pts)Ascubadiverreleasesa3.00cm-diameter(spherical)bubbleofairfromadepthof14.0m.Assumethetemperatureisconstantat298K,andthattheairbehavesasaperfectgas.SketchaP-Vdiagramoftheprocess.Whatisthediameterofthebubblewhenitreachesthesurface?c)Findtheworkdonebytheairinrisingtothesurface.d)Findthechangeininternalenergyoftheair.e)Findtheheataddedorremovedfromtheairasitrises.-DATA:Densityofwater=1,000kg/rn3;AtmosphericpressureisPa=1.013xiOPa.V,ftVLI.lL3xIO’2.b)rco,St,:a)C-L/V(V1Jim.fm)‘JvaPL--.kLi!Vtp.-._1C’t-C‘(3t)::Z3If-L.5.(12pts)Abatfliestowardamothataspeedof6.5m/swhilethemothisflyingtowardthebataspeedof5.0m/s.Thebatemitssoundwavesoffrequency51.35kHz.(‘2)3P3.i/4)a)Whatisthefrequencydetectedbythemoth?b)Whatisthefrequencyofthewavesdetectedbythebataftertheyreflectoffthemoth?5i-V&mfiipzc.l.&-JL/f5e,daVL.j%./17/4i-_/*3q3x‘1k-___3’3AS311O/4343)IcI-4)riT1WfrsI.-ii0;l+L-e-otL16.(12pts)Anobjectisplacedinfrontoftwothincoaxiallenses1and2withfocallengthsf1=+24cmandf2=+9.0cm.,respectively,andwithlensseparationL=10cm.Theobjectis6.0cmfromlens1.a)Locatethepositionoffinalimageb)Determinethemagnificationofthefmalimagec)Isthefinalimagerealorvirtual?d)Isthefinalimageerectorinverted?SI’+L4CSe14’P”LCBS1Lcns2ac)S’1-...L-..—LD•ILS(‘21t‘1-4--—I__I_It),çv‘I_L-j_5L’—__z—_L.—IObject4Cft/OIL).5’--JC-./LC3I)1ve,’+7.(12pts)AmassmisconnectedtotwospringswithequalspringconstantkandunstretchedlengthL.Inthehorizontalpositionshown,eachspringisstretchedanamountasothata=L+za.Themassisraisedverticallyandbeginstooscillateupanddown.a)Assumingthatthedisplacementissmall,and ignoring gravity,showthat themotionissimpleharmomcb)Findtheperiodintermsofk,a,za,andm6/-/;4fFc.yc=Lof-&Pvk’hS?LSL)ILrtransverseoscillationdirectionk