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This 14 page Class Notes was uploaded by Mrs. Linda Wiegand on Friday September 18, 2015. The Class Notes belongs to PHY 2053 at University of Florida taught by Staff in Fall. Since its upload, it has received 15 views. For similar materials see /class/206771/phy-2053-university-of-florida in Physics 2 at University of Florida.
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Date Created: 09/18/15
Announcements 1 va11 due Aprii 22 2 Makeup exam Aprii 22 Wednesday 7 2n 7 9 1 pm meet at w Reiues amre NPB 2255 raves at materiai m the raurse TD take the makeup exam vnu must Dbtain permissiun tram Pmr Owen Dr W Reme Announcements 3 Finai exam Aprii 25 Samrdav 1 am tn mm mm assignments st AGAR ramputa SEimEE Engineering AID GEE39J Fine Arts a ma K MAZ Finrida Gym 23m M 00 iurida c u P R Finrida va2EEI srz ruughiv V2 quuestinns an mpics Dverad n mnterms the rest an Chapters 9 13 14 Simple pendulum from last lecture Clan catmn betwem pa39md andtensmn T27r 8 Period not tension 13 Vibrations and Waves Found everywhere in the universe and in daily life hearing and vision Ultrasound diagnostics image Absmpiianmansmissmm and R etiectiun ut uttvasuund Waves Chapter 134137 Transverse mve 1 Wm WWW Eachpartufspnngmuves WI quot 39 9 WM w We Mewmi i I 1 x arreaan spacenut ame Longitudinal or compression wave Wm vduma autumnzrvmmimiimmm wn gt A wavelength Simple harmonic motion Waves Wave motionWave velocity c Chapter 14 F et i e Tuning Forks produce single frequency sound frat ii i 1 Always true Lightetransverse 1 Saundrlungitudinal 39 A 39 Wave As the tuning fork vibrates a succession of 39 s and rarefactions spread o fro t r 39 al curve can be used to represent the longitudinal wave Waves need a medium CreS S C quotquot xcept light espond to compressions and troughs to rarefactions Categories of Sound Waves Audible Waves Wavefronts Planar wave 39unt spherical wave 39unt 7 human hearing Nurmallybetvveen 2n Hztu zu uuu Hz lnfrasunicvva e Fre yes eneies are beluvvthe audible ranger Earthquakes ur car stereus Ultrasonic Waves 7 Frequencies are abuve the audible range Dug Whistles Distance between wave 39unts A speed of sound Doppler EffectSource in Motion L39qU39d As the source moves i B is the Bulk Modulus ofthe liquid toward the observer A V E p is the density ofthe liquid the wavelength appears p shorter and the frequency increases Solid Rod R 7 Y gtY is the Young39s Modulus ofthe V 3 material 7 7 quot quot gtp is the density ofthe material As the source moves I G I away from the observer 93919 B the avelength a e rs longer and the frequency appears to be lower Doppler Effect Observer movingSource stationary frunts per secundecluser tugether The frequency heard is increased Goes away from source The observer detects fewer wave fronts per secondfarther apart The frequency sounds lower Doppler EffectGeneral Case V V V f0fj 0 f0fj V V 7 VS Use positive values of VB and vS ifthe motion is toward each otherFrequency appears higher Use negative values of VB and v5 ifthe motion is away from each otherFrequency appears lower Both the source and the observer could be moving vv 1912 Product ofthe two equations Speed ofSound in Air V 33 1 E L S 273 K Tis abso ute temperature in Kelvin C 273 Announcements 1 vas due March 4 2 Prof Relue of ce hour this Week Friday 3 r 5 pm 3 Mldterml grades posted in shaming solutions and grade distribution pasted on Waste lfynu Want to look at your srantmn 522 me chan hsturs Marrh 3 4 Makeup exam April 21 7 30 pm was all material in the Bur need to let Prof chan and Prcf Rsitzs knuw manna lfyuu need to miss the midtermsar nal laratian TBA In a collision the momentum of each The total momen 0 he system remains onstant c Recap conservation of Momentum UHHIC mllisiou h object will change 0 Mm rolliunu l 391 H airplanes need Air Rocket Propulsion The operation ofarocket depends on the law ofconservation ofmomen m as applied to a system where the system is the rocket plus its ejected fuel 7 This is different than propulsion on the e where two objects exert forces on each other Ruad an Ear Train un track Rocket Propulsion 2 The rocket is accelerated as a result ofthe thrust ofthe exh This represents the inverse ofan inelastic collision e Momentum is conse d e Kineti Energyis increased at the eXpense of the stored energy ofthe rocket fuel Milkjug rocket Milk jug rocket Rocket Propulsion u Am MZrunket Am fuel ejected m W i 7quot 39 quot the total momentum afthe System In each dneetxan 3 w m mme m m conserved 4quot 4 Vwe rszz x mew rszzvx 5quot Pa xgt 9 and Fly Pry m1vwmzvzw m1V1wm2V2w Mumentumxs cunservedm the x aueeuun and m they dxrecnun For me gure above Apply cunservanun ufmumenmm separately m eaeh mm mm CO e mm cos it xrcomponent dxrecnun 0 an er mzvzfsm 4 yecomponent Kinetic energy is conserved for glancing elastic collisions too Remember kinetic energy is a scalar so the KE conservation equation is the same for glancing and headon collisions 1 2 1 2 1 2 1 2 Emlvli sz2i Emlvlf m2V2f 2 2 W Chapter 7 Rotational Motion and The Law of Gravity The Radian More About Radians 39 The radian is a unit 0f Comparing degrees and radians angular measure 360 The radian can be 1 rad 573O de ned as the are 211 length 5 along a circle Converting from degrees to radians divided by the radius r I 7139 l 9 rad 9 de rees 9de rees 9 E 180 g 573 g r Average Angular Speed Angular Displacement The average angular t Axis ofrotation is the speed a ofa rotating e center of the disk WWW rigid object is the ratio I Need a xed reference quotquot W ofthe angular Iix line H displacement to the x 391 During time t the P tune Interval L reference line moves l quot through angle 9 quotAW 1 w 9f 9 bl quot752quotquot av ff 7 1 At 1 i mm m Unit rads Average Angular Acceleration The average angu1ar acceleration a ofan object is de ned as the ratio ofthe change in the angu1ar speed to the time it takes for the object to undergo the change iwfiw Am 0 W t e t At Unit rads2 Relationship Between Angular and Linear Quantities Displacements Every point on the g rotating objecthas the speeds sameangul rn 39on V2 w meverygorntonthe Accdmdons rotating objecthas the 7 same linear motion at 7 ar Rotational kinematic equations EEE l l l gt 03 mi oct Similarly m2 033 20c A9 A9 nit 12 0th Analogies Between Linear and Rotational Motion Ymhhlcv and t m w v lil l77l in r W mu mquot m39 i L39nJll l39l9l A coin with a diameter of 240 cm is dropped on ed e onto a horizontal surface The coin starts out with an initial angular speed of 180 rads and rolls in a straight line without slipping If the rotation slows with an angular acceleration of magnitude 190 rad52 how far does the coin roll before coming to rest Centripetal Acceleration Centripetal refers to gs t The directed towar the center ofthe circle of tion Centripetal Acceleration final The magnitude ofthe centripetal acceleration is given y r This directionis toward the center ofthe circle Centripetal Acceleration and Angular Velocity The angular velocity and the linear velocity are related v1 or The centripetal acceleration can also be related to the angular velocity Announcements 1 HWIO due April 15 2 MldtermZ exam and solution posted m course Website lfyDu Wanttu look at your stawtron aee Prof REitzE before md armeeday Ifyou forgot to bring to during exam you must see Prof Reitze With your to or our exam Will not be graded 3 Final exam April 25 m am to noon roughly v of questions on topics covered m midtams the rest on Chapters 9 13 14 Buoyant Force The magnitude ofthe buoyant force always equals the weight 0 the displaced uid 3 P udv udg W ud The buoyant force equation is the same for a totally submerged object ofany size shape or e 39 Totally Submerged Object B pfmeg Wm quot79 pooeclvobjeatg For completely submerged object Voneel V uid displaced If pooled ltpr mg lt B If pubest gt Prim my gt B Floating Object If power lt MW mg lt B when object is fully submerged Fm B Fg gt 0 Object rises Floating Object Vobjecl VYLld displaced The forces balance pubi Vlluid e and Vubj 739 quotquot Vi Will it float Concrete block Concrete bowl lron cylinder Wood cylinder Water bottle w e 4 A looekg beaker containing 200 kg ofoil density 916 kgm ests on a scale Azooelcg block of iron densit c 786 x 103 kgm3 is suspended from a spring scale and is completely submerged in lie oil Find the equilibrium readings of both scales E o Equation of Continuity Am szz The plclddcl cll the c 7 Speed ls pldp lelpe I i plpe ls llallclw and speed quot quot ls lch wpele lpe plpe pas a large dlalnelel Av ls called the flow lale volume pel llme 7 7 Bernoulli s Equation PEpv2 pgy constant States that the sum ofthe pressure kinetic energy quot quot unit volume and the 1 potential energy per unit Wm has the same A 3 value at all points along a ll lac1 streamline 313 39l Just due to energy conservation Snuvvsfluld uvvlng in p llzclnlal Speed changes as Call be usedm ln Applications of Bernoulli s Principle Venturi Tube lcldgpa cl cclllslllcle plpe dlalnelel changes e dcl SlDle m vl g lldlds Ppv2 pgy constant 5 The inside diameters ofthe larger pcnions of the horizontal pipe depicted in Figure P955 aie 250 constriction f L ill l7 7 Application Airplane Wing Ul d c all eed abEIVE the Wlllg ls greatertha the speed pelch The all plessdle abEIVE the Wlng ls less than the all plessdle pelch There ls a net upward lcllce s Called MI othelractuls ale alscl lllvulved 13 Vibrations and Waves Found everywhere in the universe and in daily life hearing and vision Ultrasound diagnostics image AbsurptiunTransrnissiun and R ei iecliun ulultrasuund Vibrations and Waves Hooke s law kx 1Force is proportional to displacement from equilibrium position 2 Force always opposes x 1Force always points towards 2lt is called the restoring fo Simple harmonic motion Simple harmonic motion Amplitude A The am litude is the maximum position of the object relative to the equilibrium position In the absence offriction an object in simple harmonic motion will oscillate between the positionsx tA Time period T and frequencyf The period T is the time that it takes for the object to complete one complete cycle of motion FrurnxAtugtltrA and backtuxA The frequency f is the number of complete cycles or vibrations per unit time 1 Frequencyisthe reciprocal ufthe period Units are cycles per second s 1 ur hertz Hz Energy keeps going back and forth between kinetic and potential Hi i V39 m l mm Ljiiwm E u Conservation of Energy allows a calculation of the velocity of the object at any position in its motion k vr A27gtlt2 The 1 indicates the object can be traveling in either direction u o Q A I a smaller height SB does not bounce and How high will the balls bounce Both BB and SB bounce to the original height Both BB and SB bounce to BB bounces to original ounces higher than original height and BB NOT FOR POINTS slightly less than original height With their centers vertically aligned both balls are released from rest at the same time to fall through a distance of 120 m What are the velocities ofthe tennis ball and basketball immediately before they strike the oor up positive A VT 485 ms VB 485 ms VT 485 ms VB 485 ms C VT 485 ms VB 485 ms D VT 485 ms VB 485 ms m w mgh gt W 2m independent ntm both mnWlQ downwards gt negative velnc v
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