Problems & Solutions. Theoretical Competition Experimental Competition Best Solutions

Transcript

1 Problems & Solutions Theoretical Competition Experimental Competition Best Solutions

2 The 9th Asian Physics Olympiad TheoreticalCompetition TheoreticalProblem1.TeaCeremonyandPhysicsofBubbles Pab ABs R ab r R ab ab VBs T T MAB NAE, ii

3 1 Problems & Solutions 3 Hints: F R P R iii

4 The 9th Asian Physics Olympiad R t 1 t Usefuldata: P w T T P T g R Figure 1. Bubbles in teakettle T P Figure 2. Air bubble detaching from the bottom Figure 3. Vapor bubble collapsing iv

5 Questions(total10points): Consider water boiling in a flat-bottomed cylinder glass teakettle at normal atmospheric pressure. The bottom of the kettle heats up uniformly and a vertical temperature gradient exists, bubbles appear and evolute (Fig. 2). Q1h<H H r P r P ab 0 P R ab g hh w v (1.0point) Q2 r R r R (1.5points) Q3 R m m T T T T P P R H (1.5points) Q4 R (1.0points) Q5 R. (1.5points) Q6 (1.2points) Q7 (0.5points) Q8 R.H (0.6points) Q9 R H (1.2points) Problems & Solutions

6 Solutions: The 9th Asian Physics Olympiad S1. h H S2. r R P P P P g H h R R F g g R F F A r F R g down r S3. P P P g H R m m m P V RT V P P g H P m RT RT R T R vi

7 T R S4. R M a F V gv g M V t R a g t R R S5. AB gv r r gr r Problems & Solutions S6. t a vii

8 The 9th Asian Physics Olympiad F collap R a R a R t F R P R R P P R Figure. 4. A vapor bubble collapsing evolution. [M. P. Brenner, S. Hilgenfeldt, D. Lohse, Rev. Mod. Phys. 74, 425 (2002)] viii

9 S7. R R R S8. Figure 5. Laminar type of flow for rising air bubbles alaminarflow F R gr Problems & Solutions Figure 6. The rectilinear air bubble trajectory (R=0.69mm) rising from the bottom. On the left the XZ view and on the right the YZ view. The black areas are part of the reference system outside the water tank. [Benjamin(1987), A.de Vries (2001)] ix

10 The 9th Asian Physics Olympiad S9. theturbulentflow Figure 7. Turbulent type of flow for rising air bubbles in water. F R g M h R F W W M M h F F h Figure 8. The trajectory of a spiralling bubble in two perpendicular views, XZ and YZ (R=1.1mm) [Benjamin(1987), Antoine de Vries (2001)]. gr x

11 Problems & Solutions H t H [MarkingScheme] Q Item Answer Points P P P P g H h R R g r P g Hr P P P g H R P V m RT m V 0.1 m T T 4 V M P g H P P m RT RT R a F gv g M V g t R R xi

12 The 9th Asian Physics Olympiad 5 gr r 6 r gr r F R a R a R t F R P R R P P R R R 0.3 R F gr R M h R W F M W M h h gr 0.1 H t turb TOTAL xii

13 Theoreticalproblem2.IonicCrystal,YukawatypePotential andpauliprinciple q q V r k r k ±e V r V r E.Madelung, Phys. Zs, 19 Problems & Solutions Figure 1. The face-centered cubic lattice of the sodium chloride (NaCl). The lattice spacing between the atomar centres is constant and is given by parameter r 0 (1918)p542 xiii

14 The 9th Asian Physics Olympiad r V r e V r b r n bn E xiv Table1.PropertiesofSaltCrystalswiththeNaClStructure r E Questions(total10points): Q1.attractive V ( r) C0 r 0 r r (1.5points) Q2. ( r r 1 0 V1 ( r0 )., r, r,, (1.5points) 0

15 Q3. 22 N [1/mol] (2.0points) A Q4. V ( r) r r V r 2. rr bn (2.0points) Q5. (1.5points) Q6. E (1.5points) Solutions: S1. r e V r k r Problems & Solutions e V r k r r r r e V r k r r r r r e V r V r V r V r k r xv

16 The 9th Asian Physics Olympiad S2. e V r V V k e r r = r 0 r 0 dv e r Fr r k e dr r r k e e r e V r k r r S3. E E N e E V r k r r r E pair r ke r xvi

17 Table2.PropertiesofSaltCrystalswiththeNaCl E S4. e b att rep n V r V V k r r = r 0 r 0 dv r e nb Fr k n dr r r r n bn k e V r k r n e S5.S3S4 n r Table3.TheexperimentalfitfortheBornexponent. Na F K Cu Cl Au I Problems & Solutions xvii

18 The 9th Asian Physics Olympiad S6. E E bind E pair E E [MarkingScheme] Q Item Answer Points e V r V r V r V r k r dv r e r Fr k e dr r e V r k r r E E N e E V r k r r r E r ke r 0.1 dv r e nb Fr k n dr r r 0.5 xviii

19 5. 6. total r 0 r n bn k e V r k r n n E E r e E E Problems & Solutions xix

20 The 9th Asian Physics Olympiad Theoreticalproblem3.Howdoesasuperluminalobjectlook like? u u c 1.Radiatingsuperluminalparticle M O,x xt Figure 1. 1) (1.0point) xx

21 Problems & Solutions 2) (2.0points) 3) t. (2.0points) 4) t.. (1.0point) 5) (0.2points) 6) O (0.2points) 7) t (1.0point) 8) (0.2points) 2.Radiatinglinearobject x A.Parallelmovement x Figure 2. 9). (0.3points) xxi

22 The 9th Asian Physics Olympiad 10) (0.4points) Perpendicularmovement x x Figure 3. 11) (0.7points) 12) (0.5points) 13) (0.5points) xxii

23 Problems & Solutions Answer 1.Radiatingsuperluminaldot (1) (2) t. (3) xxiii

24 The 9th Asian Physics Olympiad (4) (5) (6) = u/(+) =u/() (7) t xxiv

25 (8) 2.Radiatinglinearobject A.Parallelmovement (9) Problems & Solutions (10) B.Perpendicularmovement (11) xxv

26 The 9th Asian Physics Olympiad (12) xxvi

27 Problems & Solutions Solution3.Howdoesasuperluminalobjectlooklike? Figure 1. xt= is, Figure 2. xxvii

28 The 9th Asian Physics Olympiad two u u u Figure 3. t xxviii

29 Parallelmovementoflinearobject Figure 4. L d f L x t x L Perpendicularmovementoflinearobject x xc y a Problems & Solutions b xxix

30 The 9th Asian Physics Olympiad at t Figure 5. x L L t t xxx

31 ExperimentalCompetition ThePhysicsofSoundWave(20points) ListofApparatusandmaterials A K B L C M D N E O F G P R H T I J Problems & Solutions xxxi

32 The 9th Asian Physics Olympiad Figure1.Apparatusandmaterials Figure 1. Apparatus and materials 1.InstructionsforSynthesizedFunctionGenerator(ItemA) V/F xxxii

33 Problems & Solutions 2.AmplifierAdaptor(itemB) xxxiii

34 The 9th Asian Physics Olympiad xxxiv 3.ACMillivoltmeter(ItemC)

35 Problems & Solutions 4.Frequencycounter(ItemD) Caution:Besureswitchoffthepowerofequipmentsbeforeplugin/outallconnections, otherwisedamageofequipmentsorsensorswillbeoccurred. Ifmorethantwosignalscometothefrequencycounter,ittendstomeasurethesignal withhigheramplitude. xxxv

36 The 9th Asian Physics Olympiad Part1.Characteristicsofthemicrophonesystem(3points) Introduction Listofcomponents Experimentsandprocedures Hints:Thevoltageofthesignalgiventothesource(S)shouldbeadjustedaround1V.Ifit ismorethanthistheultrasonicwavewillbesaturatedanditwillaffectyourresult. Themicrophonesareplacedintherotatingholderandconnectedtoanelectricalcycle with ultrasonic amplifier scheme. The distance between the source and the detector should not be changed during the experiment. And please, make sure that the microphonesareplacedparalleltoholderbaseandtheaxesofthemicrophonesarelaid onthesameline. 1a.(1.5points) Otherwise,themicrophonewillbedamagedoroutoforder. xxxvi

37 rms f f rms 1 / 2 f f f f 1b.(1.5points) AAAA Part2.InterferenceofWaves(6points) Introduction nodes antinodes Listofcomponents Problems & Solutions DescriptionoftheExperiments 2a.StudyoftheWaveInterference (1.6points) xxxvii

38 The 9th Asian Physics Olympiad Figure2.1Studyofthewaveinterference. 2a.1. A SMD 2a.2. B MDS 2a.3.MeasurementofWavelength. S D M 2b.Findexperimentallythecorrectanswerstothefollowingstatements.(2.8points) X xxxviii

39 S M SM SMnn A B SM SM DB SMSM=n n SM SM S M 2c.StudyoftheStandingWave (1.6points) BM Condition OnthesurfaceofMirror OnthesurfaceofSource D D Part3.TheDopplereffect(8points) c f f c c f f c xxxix Problems & Solutions

40 Listofcomponents The 9th Asian Physics Olympiad DescriptionoftheExperiment S If the apparatusisnotadjustedproperlytheremayoccuranerrorinthemeasurementsof thesoundintensitylevelandfrequency 3a.FormulasfortheDopplershiftofsoundfromtherotatingdisk. (1.5points) f f c f f f c f xl

41 Figure1.Thesawtoothoftherotatingdisk 3b.CalculationsfortheDopplereffectfromtherotatingdisk (1.4points) ll, 3c.TheDopplereffectindependenceonthemotorvoltage (2.8points) f f U U f Hints:MaketherotatingdisktorotateinClockwise(CW)directionanddon tchangeit further. Choose the detector position that it measures more stable and more effective. TosaveyourtimeyoucanmeasureelectriccurrentforTask3d,simultaneouslywiththe measurementofmotorvoltage. MakesureequipmentsthatyouuseinExperimentalpart,arecalibratedandmeasured verywellbeforeusingthem.eachsystemhasownspecificationwhichisgivenonspecial sheet.forexample,at10vvoltage,thefrequencyshiftofthedopplereffectisgiveninthe specificationsheet.usingtheseexperimentalresults,youshouldcalibrateyoursystem. Otherwise,themeasurementwillbeincorrect. 3d.LineardependenceofU (0.8points) UI U xli Problems & Solutions

42 The 9th Asian Physics Olympiad 3e.SpeedofsoundinairfromtheDopplereffect (1.5points) f f f f c c c c Part4:ThresholdandResolvingPowerofHearing(3points) I I I I ListofApparatusesandAccessories A C N T P Preparation xlii

43 Problems & Solutions Figure4.1(A).Connectionsoftheapparatuses.(B)Connectionsoftheleadstotherheostat: plugintheredleadfromthefunctiongeneratortotheredsocketandblackleadtotheblack socket;connecttheredleadofacmillivoltmetertoyellowsocketandtheblackleadtotheblack socket;andpluginheadphoneleadtotheheadphonesocket. Figure4.2.Theconnectionscheme. xliii

44 The 9th Asian Physics Olympiad Measurements 4a.Thefrequencyregionofone sownhearing (0.5points) A.f B.f f f 4b.Thefrequencyregiontobeheardthebest(1point) f f f f f f f 4c.Resolvingpower(R)ofearfordifferentfrequenciesofsound. (1.0point) f f th f th f th f th f R f / f f 4d.FindtheminimumspeedofthemirrorwhichgivesDopplereffectdetectedbyone s ownearsintheabovefrequencyregion. (0.5points) f 2v f c c xliv

45 Samplesolutions Part1.(3points) 1a.Characteristicofthesupersonicmicrophones (1.5point) f U U/U Problems & Solutions xlv

46 The 9th Asian Physics Olympiad 1b.Dependenceamplitudeemittedsignalofangle (1.5points) S D D U U/U U U/U xlvi

47 Part2.InterferenceofWave.(6points) 2a.DeterminationtheWavelength. (1.6points) yy 1 y 2 Problems & Solutions xlvii

48 The 9th Asian Physics Olympiad 2b.StudyofthewaveInterference.Observeanddescribethephenomenaofintensity fluctuationofthedetectedsignal. (2.8points) 2a12a2 A SM xlviii

49 B AB B Problems & Solutions xlix

50 The 9th Asian Physics Olympiad Part3.TheDopplereffect(8points) 3a.FormulasfortheDopplershiftofsoundfromtherotatingdisk (1.5points) Solution: l

51 Problems & Solutions 3b.ToconnecttheequationofDopplereffectwiththeparameter ofarotatingdisk. (1.4points) 3c.ExperimentalstudyofTheDopplereffect. (2.8points) li

52 U The 9th Asian Physics Olympiad Table1.Dopplershiftdependenceonvoltagedropsonmotor. (Indirectionofincreasingfrequency) I f P=IU Z=U/I lii

53 Table2.Dopplershiftdependenceonvoltagedropsonmotor. (Indirectionofdecreasingfrequency) U I f Problems & Solutions P=IU Z=U/I liii

54 The 9th Asian Physics Olympiad Dynamicsofmotor liv

55 Problems & Solutions 3d.Lineardependenceoftheangularvelocityasfunction ofthemotorvoltage (0.8points) 3e.SpeedofsoundinthefromtheDopplereffect (1.5points) lv

56 The 9th Asian Physics Olympiad A.Directionofrotationofthedisk:decreasingfrequency lvi B).Directionofrotationofthedisk:increasingfrequency

57 Problems & Solutions Part4.ThresholdLevelandResolvingPowerofHumanEar(3points) 4a. (0.5point) f f 4b. (1point) f f, f f f f 4c. (1Point) f R f / f 4d. (0.5points) f v lvii

58 The 9th Asian Physics Olympiad Best solutions Best solution in Theoretical Problem - 1 lviii

59 lix Problems & Solutions

60 The 9th Asian Physics Olympiad lx

61 Problems & Solutions Best solution in Theoretical Problem - 2 lxi

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66 The 9th Asian Physics Olympiad Best solution in Theoretical Problem - 3 lxvi

67 lxvii Problems & Solutions

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76 The 9th Asian Physics Olympiad Best solution in Experimental Problem lxxvi

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90 The 9th Asian Physics Olympiad xc

91 xci Problems & Solutions

92 The 9th Asian Physics Olympiad Questions & Solutions xcii