Physics - Oak Park USD



Physics Annotated Formula SheetFormulaSymbol and UnitsDisplacementd = x – xo + or – depending on directiond = displacement in m (meter)x = position in mvav = average velocity in m/st = change in time in s (second)a = acceleration in m/s2v = instantaneous velocity in m/sConstant velocityvav = d/tAccelerated motiona = (vt – vo)/tKinematic formulasd = vot + ?at2d = ?(vo + vt)tvt = vo + atvt2 = vo2 + 2adGraphing constant velocity in one dimensiondvatttGraphing accelerated motion in one dimension259080-22288500dvatttVector addition68580011303000 y Rx Bx= Bcos?B217170070485001828800704850010287007048500102870070485001028700704850018288007048500 By = Bsin?B B 217170012446000102870012446000 Ry R A Ay = Asin?A10287003873500 Ax = Acos?A6870702857500 xAx + Bx = RxAy + By = RyR = (Rx2 + Ry2)? tan ? = Ry/Rx ??? = tan-1(Ry/Rx)add 180o to ? when Rx is negativeProjectile motion (g = gravitational acceleration, -10 m/s2)vertical motion use accelerated motion formulashorizontal motion use constant velocity formuladirectiondvovtatverticaldyvyovyt-gthorizontaldxvxUniform circular motionvc = 2?r/Tac = vc2/rac is directed toward center vc = perimeter velocity in m/sr = radius of circle in mT = period of motion in sac = centripetal acceleration in m/s2Newton's Laws of MotionObject stay in same motion unless acted upon by a forceAcceleration if proportional to force/massFor every action there is an equal, but opposite reaction Accelerating forceF|| = maF = force in N (Newton)m = mass in kg (kilogram)a = acceleration in m/s2Spring forceFs = kxFs = spring force in Nk = spring constant in N/mx = distance stretched in mForce of gravity (weight)Fg = mgFg = force of gravity in Nm = mass in kgg = 10 m/s2FormulaSymbol and UnitsNormal force, Fn, is the ? force on the object by the surfaceForce of frictionFor static friction: Ff ???sFnFor kinetic friction: Ff = ?kFnFf = force of friction in N? = coefficient of friction Fn = force normal in NAccelerating forces problems. Fn Fp25158706985001601470698500 16002003873500 Fp-?125857012700091567069850001601470698500016014709842500 Ff Fp-||6858006731000 Fg Fn17037052730500185166010985500 Fp556260546100014859006032500194754560325001851660755650018516607556500139446075565001600200317500014903452603500 Ff ? Fg Fg 18516601587500 Fg-||56070511049000 ?Label all forcesresolve non-||, non-? forces into || and ? components? F|| = ma (m is all moving mass)? F? = 0Masses hanging from a pulley, where mA > mB(mA – mB)g = (mA + mB)am = mass of A and B in kgg = 10 m/s2a = acceleration of system in m/s2Centripetal forceFc = mac = mv2/rFc = centripetal force in Nm = mass in kgac = centripetal acceleration in m/s2v = perimeter velocity in m/sr = radius of circle in mForce of gravity between planetsFg = GMm/r2Fg = force of gravity in NG = 6.67 x 10-11 N?m2/kg2M, m = mass in kgr = distance between centers in mv = perimeter velocity in m/sForce of gravity is centripetalGMm/r2 = mv2/rCenter of masscm = m1r1 + m2r2 + ... (m1 + m2 + ...)cm = center of mass in mm = mass in kgr = distance from 0 position in mNon-accelerating force problems where forces act through cm.Draw free body diagramResolve all forces into x-components and y-components? Fx = 0? Fy = 03 forces, two of which are perpendicular: draw vector sum diagram and solve for missing sides of right triangleNon-accelerating force problems where forces act away from cm.Draw free body diagramDetermine axis of rotation that eliminates an unknown??F x r = ??F x r (torque)??F? = ? F ?? F ? = ? F ???FormulaSymbol and UnitsWork: W = F||d+ or – , but no directionW = work in J (Joule)F|| = force in Nd = distance parallel to F in m P = power in W (Watt)K = kinetic energy in Jm = mass in kgv = velocity in m/sUg = gravity potential energy in Jg = 10 m/s2h = height above surface in mG = 6.67 x 10-11 N?m2/kg2M = planet mass in kgr = distance center-center in mUs = spring potential energy in Jk = spring constant in N/mx = distance stretched in mPower: P = W/t = FvavW can be any energy formKinetic energy: K = ?mv2Gravitational potential energy near a surfaceUg = mghGravitational potential energy between planetsUg = -GMm/rSpring potential energyUs = ?kx2 Energy problems1.determine initial energy of the object, Eo2.determine energy +/– due to a push or pull: Wp = ±F||d3.determine energy removed by friction: Wf = Ffd 4.determine resulting energy, E' = Eo ± Wp – Wf5.determine d, h, x or v6.general equation: K + U ± Wp – Wf = K' + U' ?mv2 + mgh + ?kx2 ± Fpd – Ffd = ?mv'2 + mgh' + ?kx'2 Linear momentump = mvp = linear momentum in kg?m/sm = mass in kgv = velocity in m/sJ = impulse in N?sF = force in Nt = time in sK = kinetic energy in JImpulseJ = F?t = m?v = ?pKinetic energy to momentumK = p2/2mStationary ? separation0 = mAvA' + mBvB'Inelastic collisionmAvA + mBvB = (mA + mB)v'conservation of p, but not KElastic collisionmAvA + mBvB = mAvA' + mBvB'vA + vA' = vB + vB'conservation of p and KCollision in two dimensionspx: mAvAx + mBvBx = (mA + mB)vx' or mAvAx' + mBvBx'py: mAvAy + mBvBy = (mA + mB)vy' or mAvAy' + mBvBy'Ballistic pendulum problemsbullet strikes block and sticksmvm + 0 = (m + M)v'block swings or slides2061845-51371500swing (K = Ug): ?(m + M)v'2 = (m + M)gh ? h = v'2/2gslide (K = Wf): ?(m + M)v'2 = ?(m + M)gd ? d = v'2/2?gMoment of Inertia (angular inertia): I = mr2point mass in a circular orbitI = moment of inertia in kg?m2m = mass in kgr = radius of circular path in mL = angular momentum in kg?m2/s? = angular velocity in rad/sp = linear momentum in kg?m/sv = linear velocity in m/sAngular momentumL = I? = rp = rmvpoint mass in a circular orbitConservation of angular momentum: r1v1 = r2v2Matter energy equivalenceE = mc2E = energy in Jm = mass in kgc = 3 x 108 m/sBinding energy, BEmnuclide + mBE = mp + mnNuclear reactionsproton: 11p, neutron 10n, electron 0-1e, positron 01ealpha: ? = 42He, beta: ? = 0-1econservation of mass # & charge: 23892U ? 42He + 23490Thnuclear process: mproducts – mreactants = mBE < 0 (E = ?mc2)half life: 1 ? ? ? ? take same amount of time t?FormulaSymbol and UnitsSimple harmonic motion (SHM)2438406604000Time to complete one cycleT = 2?(m/k)?T = period in sm = mass in kgk = spring constant in N/mA = amplitude in mvo = velocity at midpoint in m/sdisplacement0±Avelocity, vvo = 2?A/T = A(k/m)?vA = 0acceleration, aao = 0aA = vo2/A = A(k/m)potential energy, UUo = 0UA = ?kA2kinetic energy, KKo = ?mvo2KA = 0Period of a simple pendulumT = 2?(L/g)?T = period in sL = length of pendulum in mg = gravity acceleration in m/s2Mechan-5524511176000ical waveamplitude, A: maximum height of a crest or depth of a trough measured from the midpoint (m)wavelength, ?: distance between any two successive identical points of the wave (m)frequency, f: the number of complete waves that pass a given point per unit time (Hz or s-1)period, T: the time it takes for one wave to pass (s)T = 1/fvelocity, vw: speed of the waveform, vw = ?/T = ?f (m/s)transverse wave (string): disturbance ? wave ?longitudinal wave (sound): disturbance ? wave ?Interferenceamplitudes combine (superposition principle)constructive interference when amplitudes are addeddestructive interference when amplitudes are subtractedbeats, fbeats = |fA – fB|Velocity of a wave on a stringvw = (Ft/?)?vw = velocity of wave in m/sFt = force of tension in N? = linear density in kg/mHarmonicsDetermining nth harmonic?n = 2L/nfn = nf1? = wavelength in mL = length of string in mn = number of harmonicf = frequencyDoppler effectf’ = f(vw ± vo)/(vw ± vs)approaching: f' > f (+vo, –vs)receding: f' < f (–vo, +vs)approximation formula ?f/f ? v/vwapproaching: f’ = f + ?freceding: f’ = f – ?ff' = perceived frequency in s-1f = generated frequency in s-1vw = wave velocity in m/svo = observer velocity in m/svs = source velocity in m/sFormulaSymbol and UnitsAngle of reflection?i = ?rphase shift when ni < nr?i = incoming ray ? to surface?r = reflected ray ? to surfacen = index of refractionWave velocity in a vacuumc = f?c = 3 x 108 m/sf = frequency of wave in s-1 (Hz)? = wavelength in mn = index of refraction (no units)vn = velocity at n in m/sRefraction within a mediumvn = c/nfn = f1?n = ?1/nAngle of refraction (Snell's law)nisin?i = nRsin?Rni < nR: bend toward normalni > nR: bend away from normalni = source medium n?i = incident angle ? to surfacenR = refracting medium n?R = refracted angle ? to surfacen ? to f ? color separation = dispersion (prism)total reflection when ni > nR and ?i ? ?c = nlow/nhighParabolic mirror radius of curvaturer = 2fr = radius of curvature in mf = focal length in mlens/mirror equation1/do + 1/?di = 1/±f+di for real image (-di virtual)+f for converging (-f diverging)do = object distance to l/m in mdi = image distance to l/m in mf = focal length in mM = magnification (no units)hi = height of image in mho = height of object in mmagnification equationM = hi/ho = -di/dodo > +fdo < +f–fInterference with two slitstan? = x/Lsin?c = m?/dsin?d = (m + ?)?/d?c for bright band (?d for dark)? = angle from slits to band in mx = center to band distance in mL = slits to screen distance in mm = band order (no units)? = wavelength of light in md = distance between slits in mW = width of light spotd' = width of slitInterference with one slitW = 2?L/d'Thickness of a film, T (?f = ?1/n)Interferenceni < nf < nrnf > ni and nrBrightT = ??fT = ??fDarkT = ??fT = ??fEM RadiationHigh energy has short ?, high f (low energy has long ?, low f) Transverse wave ?polarizableDoppler shift: moving away = shift to longer ? (red shift) Photon energyE = hf = mc2 UV > violet ... red > infraredE = Energy in Jh = 6.63 x 10-34 J?sf = frequency in s-1m = relativistic mass in kgc = 3 x 108 m/s? = wavelength in mp = momentum in kg?m/sPhoton momentump = mc = h/? = E/cParticle wavelength (De Broglie)?particle = h/pAtomic energy levels (Bohr model)En = -B/n2En = electron energy in eVB = 13.6 eV for hydrogenn = energy level (1, 2, etc.)EeV = photon energy in eV?nm = wavelength in nmEnergy absorbed by an atomEeV = En-high – En-lowEeV = 1240 eV?nm/?nmPhotoelectric effectKelectron = Ephoton - ?Kelectron = kinetic energy in eVEphoton = 1240 eV?nm/?nm? = work function in eVme = 9.11 x 10-31 kgv = electron velocity in m/sKinetic energy of an electronKelectron = ?mev2FormulaSymbol and UnitsDensity? = m/V? = density in kg/m3m = mass in kgV = volume in m3?kg/m3 = ?g/cm3 x 103Specific gravitys.g. = mair/(mair – mfluid)?object = s.g. x ?fluids.g. = specific gravity (no units)mair = mass measured in airmfluid = submerged massPressure on a surfaceP = F/AP = pressure in Pa (Pascals)F = force in NA = Area in m2PPa = Patm x 105Force on a hydraulic pistonFin/Ain = Fout/AoutPressure in fluid at a depthP = ?fghP = pressure in Pa?f = density of fluid in kg/m3g = 10 m/s2h = depth in mUpward force on a submerged object (Archimedes principle)Fb = ?fgVoFb = buoyant force in N?f = density of fluid in kg/m3g = 10 m/s2Vo = object's submerged volumeFluid flow in a pipeV/t = Av = ConstantV/t = volume flow rate in m3/sA = area at a position in m2v = velocity at a position in m/sSolve plumbing, lift & tank leak problems (Bernoulli's equation)P + ?gy + ??v2 = ConstantP = pressure on fluid in Pa? = density of fluid in kg/m3g = 10 m/s2y = elevation in mv = velocity in m/sThermal expansion?L = ?Lo?T?L = change in length in m? = expansion coefficient in o C-1Lo = original length in m?T = temperature change in o CKinetic energy of gasesK = 3/2RTK = kinetic energy in JR = 8.31 J/mol?KT = Temperature in Kv = velocity in m/sM = molar mass in kgP = pressure in PaV = volume in m3n = number of molesTK = ToC + 273Velocity of gas moleculesv = (3RT/M)?Ideal gas lawPV = nRTPV diagram+Win (-Wout) toward y-axis, -Win (+Wout) away from y-axis+?T and +?U away from origin (P x V)PV (heat engine) problems?U = 3/2nR?T = 3/2?PV = 3/2P?VWin = -P?V = Area?U = Qin + WinFor complete cycle: ?U = 0?U = internal energy change in Jn = number of molesR = 8.31 J/mol?KQin = heat added to system in JWin = work on the system in JProcess?T ?U = Qin + WinIsometric?(?V = 0)?PV/nR3/2?PV?U0Isobaric?(?P = 0)P?V/nR3/2P?V?U – Win-P?VIsothermic (?T = 0)00-Win-QinAdiabatic (Q = 0)?Win0?UEfficiency of a heat engineec = (Thigh – Tlow)/Thighe = |Wcycle|/Qinec = ideal efficiency (no units)T = temperature in Ke = actual efficiency (no units)Rate of heat flow through a barrierQ/t ? A(TH – TL)/LQ/t = rate of heat flow in J/sA = area of barrier in m2TH = high temperature in o CTL = low temperature in o CL = thickness of barrierQ = heat in Jm = mass in kgc = specific heat in J/kg?KHeat gain/loss by a materialQ = mc?TFormulaSymbol and UnitsConducting sphere: excess charge on outer surface, E = 0 insideElectric force between chargesFe = k|Qq|/r2attract for unlike (repel for like)Fe = electric force in Nk = 9 x 109 N?m2/C2Q, q = charge in C (Coulombs)r = Q1 to Q2 distance in mE = electric field in N/C or V/mElectric field around a chargeE = k|Q|/r2away from +Q (toward -Q)Electric field around multiple chargesCalculate E for each chargeCombine E (add for same direction, subtract for opposite direction, use Pythagorean and tan? = y/x for ? fields)E = 0 between like charges and closer to lesser |Q|E = 0 outside unlike charges and closer to lesser |Q|Force on q in electric field EFe = |q|E+q: E ? , Fe ???–q: E ?, Fe ?Fe = electric force in Nq = charge in CE = electric field in N/CElectric potential energy between charges Ue = kQq/r+Ue for like (-Ue for unlike)Ue = electric potential energy in Jk = 9 x 109 N?m2/C2Q, q = charge in C (Coulombs)r = Q1 to Q2 distance in mV = potential (voltage) in V (volts)Electric potential (voltage) around a charge V = kQ/r+V for +Q (-V for –Q)Electric potential around multiple chargesCalculate V for each charge Combine V (add +V and subtract -V)V = 0 between unlike charges and closer to lesser |Q|V = 0 infinitely far away from like chargesElectric potential energy on a charge in an electric potentialUe = qVUe = electric potential energy in Jq = charge in CV = voltage (potential) in Vm = mass in kgv = velocity in m/sKinetic energy equals loss in UeK = -?Ue?mv2 = |q?V|Current flowI = Q/tI = current in A (amperes)Q = charge in Ct = time in sResistance in wiresR = ?L/AR = resistance in ? (ohms)? = resistivity in ??mL = length in mA = cross-section area in m2Battery terminal voltage V = E ± IR+ when battery is recharging– when battery is dischargingV = terminal voltage in VE = emf in VI = current in AR = internal resistance in ? Voltage loss (Ohm's law)V = IRV = voltage in VI = current in AR = resistance in ?P = power in watts WPower consumedP = IV = V2/R = I2RCapacitor capacitanceC = ?oA/dC = capacitance in F (farads)?o = 8.85 x 10-12 C2/N?m2A = plate area in m2d = plate separation in mQ = charge in CV = voltage in VUC = stored energy in joules JCapacitor store chargeQ = CVCapacitor store energyUC = ?QV = ?CV2 = ?Q2/C Electric field between capacitor platesE = V/dDirection is from Vhigh ? VlowE = electric field in V/mV = voltage in Vd = distance between platesVariable Capacitor problemsAdjust A or dCapacitanceBattery ConnectionArea(A)Distance(d)C = ?oA dConnectedDisconnected Q = C x V Q = C x V??????????????FormulaSymbol and UnitsCircuit Element SymbolsBatteryCapacitorResistorSummary Chart for Circuit Elements in Series and ParallelElementS/PFormulaConstantVariableResistorSeriesRs = R1 + R2IsVn = IsRnParallel1/Rp = 1/R1 + 1/R2VpIn = Vp/RnCapacitorSeries1/Cs = 1/C1 + 1/C2QsVn = Qs/CnParallelCP = C1 + C2VpQn = CnVpKirchhoff’s Circuit Rulesloop rule: ?V = 0 for any complete circuitjunction rule: Iin = Iout for any junctionGeneral steps for solving a circuit problemDetermine overall resistance: combine Rp until all RsDetermine the overall current of the circuit: I = Vtot/RtotDetermine voltage loss in series resistors: V = ItotRDetermine voltage in parallel components: Vp = Vtot – ? VsDetermine I and P for each resistor: I = V/R, P = IVDetermine Q and UC for each capacitor: Q = CV, Uc = ?QVMeasuring I and VI: place ammeter between battery and circuit element (series)V: attach voltmeter to each side of circuit element (parallel)Magnetic force on a moving charge: FB = qvBFB = force in Nq = charge in Cv = velocity in m/sB = magnetic field in Tm = mass in kgr = radius of circular path in mI = current in AL = length of wire in mMagnetic forces are centripetalqvB = mv2/rpalm toward center of circle pathMagnetic force on current wireFB = ILB99060033020009906003302000Direction F B766445120650099060011303000 I, vMagnetic field near a wireI out ????I in B??? B = k'I/r ???BB = magnetic field in T (teslas)k' = 2 x 10-7 T?m/AI = current in Ar = ? distance from wire m?o = 4? x 10-7 T?m/AN = number of turnsL = length in mMagnetic field in a solenoidB out B in I??? B = ?oI(N/L) ???IMagnetic force between wiresFB = k'I1I2L/rDirection: I1 ? I2 = attractionPermanent MagneticsMagnetic field lines go from north pole to south poleEarth's north magnetic pole is at the south geographic poleMagnetic flux?B = A x B?B = flux in Wb (weber)A = enclosed area ? to B in m2B = magnetic field in TE = emf in V??B = change in flux in Wbt = time in sv = velocity of rod in m/sL = distance between rails mB = magnetic field in TInduced emf in a wire loopE = ??B/tInduced emf in a moving rodE = vLBDirection of induced currentBthumb??(increase: flip, decrease: no flip)Induced CurrentI = E/RUpincrease (rotate || to ?, move B closer)clockwisedecreasecounter clockwiseDownincreasecounter clockwisedecreaseclockwise ................
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