**TI89**MAINAppVariable file 07/29/04, 22:56Rphyscseq‹„ZŠ¹óG槞°¾ĖDŽé¶• A Ū T+±VĀłN ā")'Õ),;/š0Ć3ī5b8 9–;³=”?Œ@iA­CŽEžEFīGßI!LÉMŌPdRµS,U«VŒZĢ[l]ā^ć`ņegČhkłmĘnhpÆrVv+yÕ|Ÿ~r€„c…„‡)‰Physics EquationsMr. Sean Bird29 July 2004Covenant ChristianyM Kinematic1 Z ĄŒ 4ųĄŒ Ģ @’€Ä „@€H @€Hž@’€P €P €` 4@ Ųą$DHpPv=velocity  vo=initial (original) vela=accelerationt=time%.Big 3 Kinematic equation 7for constant accelerationP”M Kinematic2 x$`0   @ @ <@  1€ą GĮž` €@ Ā€@ž€ƒž„€@ € ?„žĄ € „@    I€Į€ Ą Ž€(€HP`Pd-do=displacement  vo=initial (original) vela=accelerationt=time%.Big 3 Kinematic equation 7for constant accelerationPM Kinematic3 0 H8(D€ x€B@€@1€1€€ vv €ü€€  €€ų" ą €B  ü € F (( €BM HH €~vĢĢ@ 0@P€$‘( 0ĄPx-xo=displacement  v=velocityvo=initial (original) vela=acceleration%.Big 3 Kinematic equation 7for constant accelerationPjM 2nd Law %}?’ą `@ @ @ ĄĄÄaįą(b" ?š’ųdd`00Hh`  PP@ `ąĄĄ`0` ĄąĄ@0@ĄĄ€@`@’ųĄĮ€Ą`Ą€Į`€ ĀHĄ€|`š0@PNewton's second law of  motion (mass & acc) is constant.F=force%m=mass.a=accelerationPM Friction Fųpń@@€@ !(@ 0B(€ą0B$@ BD€@€„EĮ@„E@žƒī0Įēā:@"€D FĄ Pmu=coefficient of friction N=normal force, i.e. force perpendicular to the surface%.For kinetic friction 7(mu)(N) is equal to FP,M Centripetal -0€@@@€@Ą0 @€@Įž€’ü€ž@€  Pa=acceleration v=velocityr=radiusCentripetal Acceleration%points toward the centerPźM torque Qšd„ą@„uÄ@r,üGĄ–rü€‚"€b"ü"’" <ēwĄPtau=torque r=radius F=Force theta is angle between r&FPüM momentum Hp|š8Ē8  Į ’€Ć@Ć @‚1†€ ’€1† !„Œ! 0c€Pp=momentum (vector) m=massv=velocity (directional)PLM impulse-momentum Rü5 $ 5 Ą$Ą5 ’`5ą!B`5 p5 A„ƒp5 „’p5€ÄŽ`€IŽ`Ą’Ī’ŽĄPF=force delta t=change in time or durationdelta p=change in momentum%PŃM Kinetic Energy $`Ą € € ųš€@0@€@`€€€"€ `€ąh€ APĄ e¼`ąüaŒ Š AŽ˜üaŒĆ†üĆĀą††ĒĄ1‚ @šPK=Kinetic energy m=massv=speedP‹M Potential Energy `€|>€Ą @ g„ą@ ©e ` ų1F @ "L@0@ "ˆ@@ ų"@@@B@ €E ųxFĄa€ą@€€@€ą?ąPdelta U subg=  gravitational potential energy m=mass%g=acceleration of gravity.h=height from some 7arbitrary ground levelP M Work U÷€’€ Bp€ Āp€PÄrP Hrˆy HĄ~ˆ; Prˆ9r8 Ąp8Ąp8Ąp8€ü’|PW=work F=forcedelta r=displacementdot product so consider %the cosine of angle .between F & rP 3M Power 1R|š@0€1Q’” ( ( 0 ų5„‚?ąų5?’ü?ąŚ<JHJp€ Œ@€@ČpĄ@ˆAšš@@`€ €0€ łĄPP=average power W=workdelta t=timepower=energy used per time% or work done over timePõM Power2 Jųü5„„„„8üšš5 ü€€€Ą€Ąą€PP=power F dot v=dot product of force & veloctiy%consider cosine of angle .between F & vP@M Hooke's Law Jü5  {Ü !ˆą?ą@Š5 €ą Ē`?ą`°”8ĄĆ¼5€€€PF= restoring force for a  springk=spring constantx=position (how far pulled %away from equilibrium)PM Spring PE H0H`   ( ćų €p$8ü( €(@`E%€ĄFʀ@@ €PšPU= spring potential energy k=spring constantx=position, distance from equilibriumP3M Period /0š" €’ų€ą ąPT=period f=frequencyPFM Period spring 2V’Ą@@@@@€€ŒĢ…TŠdŒHˆˆˆˆ‘‘š€Ą" @Cü ų  @?’ų@,` Ų`b¢"€"€€x @€€€ P ` PT sub s= period of spring m=massk=spring constant%P¾M Period pendulum Bl’’€€€  ’ B? @CĀ€Ąž€ž€’€ € !’ž’€@ DH ?ˆp °?ˆ@ Š  <  L Ą   @€@€@ x@`@`@Ą@@@@@Ą€ @€`€`€€€€PT=period of pendulum l=length of pendulumg=acceleration of gravity%Note this does not depend .on the massP M law of gravity )`f ĢŖT2 dd ČEˆ‰€Š‘@ųyŒ‘@‡€@€€ €@ ĄĄą’@ōAą’’’ų ’ąų€@€€€€€€` PF=force G=gravitational constantm=massr=distance between center %of 2 objects.7Don't forget to square the @denominator!P<M grav PE *h3030PP))3&3&""")DRDQČDbDa 8 š x ’  x ’’’’š ˆš A@8Ą ą°Š€PU=gravitational potential  energyG=gravitational constantm=mass%r=distance between center .of 2 objects7PqEM Coulomb .e€€€€€Š€€0 €€ € !€c#€Į&$ųĄA:A Į €<ąą@@’’’’’’’Ąą   ’€4‘€ "€BŽ  0 1¢a¼(HP`PF=force q=charger=distnaceP,EM Elec Field --’aadd|dd``?ąų   € €€€ € €’Å € ?Ą&D„Œ˜č8PE=electric field F=forceq=chargePÆEM Electric PE )~@Ą@@@Š@ Ć0@‚ @“&@”i@ĮxąąA @B €… ‰9Ļ ‰@üü@!’’’?’’ąCįü#ü &@:Ą€€@€€€ƒćĄ…DĄ ‚D Ā‡‚ˆ„‰‰(HP`PU=potential energy q=chargeV=voltage, or potent. diffr=distance of separation %between q1 & q2PpEM Electric Field2 %Cœ  @€ą  €€ ü ?€@ü’Ą?€‚ h0`°PE sub average=elect field V=voltaged=distanceV=Ed%The electric field between .two parallel plates 7depends on the voltage & @distance of separationP'EM elect potential +_ ` 4 Ģ ˆ  € ’Į0 Įрąp@€@€@ €€Ąq € ü’’’€’šü €€ €@€’Ą‡ĆĄ’ĄlŠ„Ą(„„0Å …"‰ 0@“ F$ (00Pq=charge r=distance of separationV=electric potential diffPžEM Capacitance1 %*pˆ0ŠĄ05  šüAüž€58 @@€PC=capacitance Q=chargeV=voltage%Q=VCP*EM Capacitance2 &5€€€ą€`€€€€€€€Š€qÅ0  üAü’’ą€Ą@@@€€€€€PThe capacitance of a  capacitor depends on the area of two parallel plates & inversely on the %distnace of separation. .Epsilon naught is the 7permitivity of free spaceP³EM PE of capacitor ~Ą``  ‡ž /<  B ä0@ " D   " DAąp " p@@?Ą@$@?Ą@€ @D€@  ų@Eų@  h?Ą@…?Ą@Š@˜`c`! < 8Ą G ąPPššPU=potential energy Q=chargeV=voltageC=capacitance%.Capacitors store chargeP>EM resistivity )3„ ÄDH ˆ ˆ3ą\@€€ Ą€€@’’€@€ 00PPšxPR=reistance (ohms) rho=resistivityl=lengthA=area%The reistance of a reistor .depends on the type of 7material, lenght, and areaP‰EM Ohm's Law 0šsą@!€B B0 CĄ„€„@„@ Ü0PV=voltage, electr. pot.,  or potential differenceI=current (amps=C/s)R=resistance(ohms)P…EM Power 0ąīxD „@„€ „€Ąž  ž  ˆPP=power (watts), rate at  which energy is usedI=currentV=voltagePīEM capacitancePar .K’š0Ȁ8` p    €    € @C@˜Ą @@€€’š’šPAdd capacitors that in  parallel to find the equivalent capacitancePųEM capacitanceSer /L@8Ą@@@@@@@’š@0ą€@0€ ?’ų’’Å€ @䀐 p’š ’š      @!€ŒĮ€€  PCapacitors in series->  take the recipricalPEM resistanceParPPEM resistanceSerPP+EM magnetic force1 ^ųąĮ H @¬b äX Ą¦#Į,乀žB$!D €BD ÄD@€žĀ„ $D€@ ƒA$D€@‚Īī€€@@€€PF=force q=chargev=velocityB=magnetic field (tesla)%.A charge moving in the 7presence of a magnetic @field experiences a forcePAEM magnetic force2 b€ųü5""5HBB5@D…€‚ĄxŽ@ž€ž„„@‚€„ „A€ž„„A@„A˜@š<Īąą€@@€5PF=magnetic force B=magnetic field (tesla)I=currentl=length%A current carrying wire in .the presence of a magnetic 7field experiences a forcePrEM magnetic field *@p @@€@€@€€!€!€'€ąyŒĄ@€$€( 0Ą€  ’’Ēü €@€pˆ„?ĄŅ°Š"€ $@D„Ęż†PI=current r=distanceB=magnetic field tesla)A current carrying wire %produces a magnetic field .(right hand rule around 7the wire) that varies @inversely w/ the distancePłEM magnetic flux D@š€ € Ą   žš& @ @ž € …5šĆĄ*+PThe magnetic flux, phi,  depends on the strength of the magnetic field going through a certain amound %of area, and the angle .between the two.P3EM emf change flux ,Z  €šH‚HBHD $ $ óĘ ą @ą``ž€ų’’’ü Ąž €ÓĄ T€g5d5G5 """AA€€¤’ųPfunny e signifies emf delta phi=change in magnetic fluxdelta t means with respect %to time.The negative is Lenz's law 7indicating the direction @of the induced currentPÓEM emf=Blv < ~!AąB1…`|€’F€€‚  ‚ Ą’‚ €( ų0PThe emf (voltage) equals  the product of the magnetic field strength (in teslas), length of %wire, and its speed as it .moves through the magnetic 7fieldP=F/T pressure ]š?qÅ€ €€ € €A!3>Aą€>AÄ@ĄA„‚@‚ˆ‚€@‚p‚€Ģą`pó   @ų€PP=pressurePF/T buoyancy Oų<H @ņAńĄF!€š„ €%@š&€ f(Ś„€)J` *J  RŒ Ą{0 PBuoyancy F=upward forcepho=densityV=Volume%g=acceleration of gravityPF/T pascal N0PPc Œ1?Ą ÄšD!H`?Ą!0PĄ AHa z ēˆ@!   @ ( pxąPA=area v=speedThe product of the area and speed are constant %through a noncompressible .fluidP†F/T bernouli princ 3‚ Ąš@@@<@€fĆ@ ŲĄą‚ˆąL@ž’€‚€ĄD@5š „€  …ž˜ĄĄ3ą€ \! @ Š € @€ ą€8q˜ó€Éˆ©É Ā"2*$€įĀ3Ē PP=pressure rho=densityg=acceleration of gravityy=height%v=speedP*F/T LinearExpansn Q`ž " $Č@@H@@‚üP@€@„ €€€D@€@€Dü@€@€JŃ@A?ģqƒ?ćĄu Palpha=coeffiPQF/T Pressure ,3ų@@Ą€€<šą?Ąž?Ą0Pš`“Ą5J’ą‹ “ śĄ$8PThe temperature of an  object is the average kinetic energy of the molecules %.k sub B=Boltzmann's 7constant=1.38x10^-23J/KP1F/T Temp & speed 4 ’’’’Ą’’’’ü0<?ąćžF" #" D@D/@$ @HĄ@p€€P€€P@€Š AxŒ<<<3Ą$1€x€€’ž  ’’’’’’’š ’ž Q€ĄńD P€@¢€$8 ³ $0 PB$P„$„% „% & F@<õšĢ ```` PThe temperature of an  object is related to the speed of the molecules (that is the root mean %square speed).M=molar mass, R=gas const.7mu=mass of molecule@k sub B=Boltzmann's const.PõF/T Work R÷€ü<5BB Ă  H‚ H„@ Püų€į ‰  ‰5Ąü@JĄ@L€€’čPWork=pressure times change  in volumeP7F/T 1st law thermo Zšą<{Ž€@@Ā!€€€€#@€€€% @€€€% @€ž€)@!ųJ@!€R€ž€c5„€c5?ųxą€B5†xPdelta U=change in tnternal  energyQ=heat transferred to a system%W=work done ON a systemPŠF/T efficiency1 6<@@@@@{Ą@!@b@¤@¤@(@ H@ P@ `@ `@@@@@@€E€@ƒü@#E< ’’ž@ ü@1E@@@€@@@ @@ @@ @€ @€@@€@@€ƒø@C@| @ ą@@ @šÄ@@ą@@@Pe=efficiency of a heat  engineW=work done by a machineQ=heat that goes into %machinePxF/T efficiency2 2[ü’Dˆ"€ € € ?Ą@@ø@h€˜‚ įą @€ąą€€ų#<’’’’’’€ ų1  (ü0Dˆ€€€Ü€ˆš pPe=efficiency of a heat  engineT sub H=temp of hot resevoir%T sub C=temp of cold .resevoirP –W speed .8I€B@€€1€Ą€€€‡š€ € š€  AĄPv=speed f=frequencylambda=wavelengthP+W index of refract ,)xˆąĄ @Ažu€ž€ž!@!€ˆ Ą€Pn=index of refraction c=speed of light in a  vaccuumv=speed of light through% that mediumP¶W Snell's law Ą€@€ @ @Ąą@gą€ @7Ą)7?€@@ąQ €€ €b !€ €BA˜!0ąB0B0!H…H$H!ˆ?8†?88((8xxPn=index of refraction in a  specific mediumtheta=angle of light in a particular medium measured %from the normal linePW critical angle 0O ą @@F€©€Į@@ą€7?€ €š !ABš?’š$?88 @P`p  &RbPźtheta sub c=critical angle  is the angle such that anything larger than that angle will be total %internal reflection..It depends on the 7difference of the indecies @of refraction. It must go Pfrom a more optically  dense medium to a less optically dense medium. This equation is a special %case of Snell's law where .one angle equals 90 7degrees P0W lens maker eq 0V ąą8        pp@@@@’ü@’€@?’ą’’į@@Ą@ĄĄ@@„€€€   ĄPs sub i=distance of the  image from the lens (or mirror)s sub o=distnace of the %object from the lens (or .mirror)7f=focal lengthPÜW magnification 2i0 ')"S bBBD …D†`xĄĄ @ @†@€uŠ`ĄŠ’’ų¤ąu¤’’’žuÄ’ųuČ>¾u` @N<RD¦@Ä „„ˆ ˆ š8pHˆ ąĄPM=magnification depends on  the ratio of the height of the image & the height of the object%.or the negative of the 7ratio of the distances @from the lens (or mirror)PwW forcal length 16!€ €@€A~„„„‚ƀ2 @ą@@ü€€’ą€ü€p  üüPThe focal length of a  mirror is half of the radius of curvaturePW diffraction Y`0 $P B@‚@ń„f` Į8ü* 0ąS P€Įb@!€!‚D@ "€‚ąDA$%A ˆ¢(ć¹ĮĄˆÄPd=distance of separation  between the lines (1/#lines per mm)theta=angle between normal %and the light that is .diffracted7m=integer@lambda=waveleth of lightPŪW diffraction aprx ,O0P€f`* 0S Pb@D@ DA$@ˆ¢(€ˆÄ?€ą0€L€C’’’’š0€L€ @C1@Ą@ € ĄŠ0  `  P`Pįx=position (distance of  constructive interference from the origin)m=integer (order, e.g. 1st %order, 2nd order, etc.).lambda=wavelength7L=distance of diffraction @grating from "wall"Pd=distance of separation  of the diffraction grating (1/#lines per mm)Be careful of unit %agreement.This is an approximation 7method for small angles, @where sin(theta)=tan(thetaPA energy T`š @P@ @\š6ĄT €¤@Ą1€Č@!  ˆ@Ą" @€D"Ą€x€@€ĄPE=energy h=planck's constantf=frequencyp=momentum%c=speed of lightPCA photoelectricEff Zž505@€<)ųI)ąI€2’@ų"’ E ”{ćlF x5QØ R@@RØ€@łģPPhotoelectric effect phi=work function, the amount of energy that needs to be overcome so %that an electron can be .freed from the metal7h=plank's constant@f=frequency of incid.lightP$A deBroglie ,-0 &*RdDŠĄŒ@@@Ą@’@€€’’Å ąģ2bBDˆš€€Ph=planck's constant p=momentumlambda=wavelength%any moving object has a .wavelength (wave nature)P+A mass-energyEquiv W0Hü@„@„  (  x@ ĢĀšąAUB2‚ A¦B B BĢ‚@BąBˆ‚@DB BD?ļš'ż„8 PMass-energy equivalent c=speed of lightdelta m=rest massdelta E=energyPSTDYųQ¼