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BIO200H5 (22)
Final

# Formula Sheet-2003-05-07-8pg.pdf

8 Pages
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School
University of Toronto Mississauga
Department
Biology
Course
BIO200H5
Professor
Dax Urbszat
Semester
Spring

Description
Reference Guide & Formula Sheet for Physics Dr. Hoselton & Mr. Price Page 1 of 8 #20 Heating a Solid, Liquid or Gas #3 Components of a Vector Q = m•c•∆T (no phase changes!) Q = the heat added if V = 34 m/sec∠ 48° then c = specific heat. V = 34 m/se•(cos 48°);andV = 34 m/se•(sin 48°) ∆ T = temperature change, K i J #21 LinMeaormentum #4 Weight = m•g momentum =p = m•v = mass • velocity g = 9.81m/sec²near the surface of the Earth momentum is conserved in collisions = 9.795 m/se² in Fort Worth, TX #23 Center of Mass – point masses on a line Density = mass / volume xcm = Σ(mx) / Mtotal ρ = m unit :kg /m 3 #25 Angular Speed vs. Linear Speed V Linear speed = v = rω = r • angular speed #7 Ave speed = distance / time = v = d/t Ave velocity = displacement / time = v = d/t #26 Pressure under Water Ave acceleration = change in velocity / time P =ρ•g•h h = depth of water #8 FricFtornce ρ = density of water F F= µF #28 Universal Gravitation N If the object is not moving, you are dealing with static m 1 2 friction and it can have any value fros Nero up to µ F F = G 2 If the object is sliding, then you are dealing with kinetic r friction and it will be constant and equal to µ F G = 6.67 E-11 N m² / kg² K N #9 Torque #29 MechaniE cnlergy PE Grav P = m•g•h τ = F•L•sin θ KE = K = ½•m•v² Where θ is the angle between F and L; unit: Nm Linear #30 Impulse = Change in Momentum #11 Newton's Second Law F• t =∆(m•v) Fnet= Σ FExt= m•a #31 SneLll'sw #12 Work = F•D•cos θ n1•sinθ1= n2•sinθ2 Where D is the distance moved and Index of Refraction θ is the angle between F and the n = c / v direction of motion, c = speed of light = 3 E+8 m/s unit : J #32 Ideal Gas Law #16 Power = rate of work done P•V = n•R•T n = # of moles of gas Power = Work time unit : watt R = gas law constant = 8.31 J / K mole. Efficiency = Work / Energy #34 PerioWdiaves out in Mechanical Advantage = force out /force in v = f •λ M.A. = F out Fin f = 1 / T T = period of wave #35 Constant-Acceleration Circular Motion #19 Constant-Acceleration Linear Motion v = vο+ a•t x ω = ω ο α •t θ (x-x ) = v •t + ½•a•t² v θ−θ ο= ωο•t + ½α •t² ω ο ο 2 2 v ² = ο ² + 2•a• (xο- x ) t ω = ωο + 2•α (θ−θ ο t (x-xο) = ½•( ο + v) •t a θ−θ ο ½•(ω ο ω )•t α (x-x ) = v•t - ½•a•t² v θ−θ ο ω •t - ½α •t² ω ο ο ο Version 5/12/2005 Reference Guide & Formula Sheet for Physics Dr. Hoselton & Mr. Price Page 2 of 8 #53 ResisCtoormbinations #36 Buoyant Force - Buoyancy SERIES F B •ρ•g = m Displaced fluideightDisplaced fluid R eq= R 1 R 2 R +3 . . ρ = density of the fluid PARALLEL V = volume of fluid displaced 1 1 1 1 = + + K + = Req R 1 R 2 Rn #37 Ohm L'sw V = I•R #54 Newton's Second Law and V = voltage applied Rotational Inertia I = current τ = torque = Iα R = resistance I = moment of inertia = m•r²for a point mass) (See table in Lesson 58 for I of 3D shapes.) Resistance of a Wire R = •ρ / A x #55 Circular Unbanked Tracks ρ = resistivity of wire material mv 2 L = length of the wire = µmg A x cross-sectional area of the wire r #56 Continuity of Fluid Flow #39 Heat of a Phase Change A in inA •out out Q = m•L L = Latent Heat of phase change #58 Moment of Inertia - cylindrical hoop m•r #41 HookL e'sw solid cylinder or disk ½ m•r F = k•x solid sphere / m•r 5 Potential Energy of a spring hollow sphere ⅔ m•r W = ½•k•x² = Work done on spring thin rod (center) 112m•L thin rod (end) ⅓ m•L #42 Electricwer P = I²•R = V ² / R = I•V #59 Capacitors Q = C•V Q = charge on the capacitor #44 Speed of a Wave on a String C = capacitance of the capacitor mv 2 V = voltage applied to the capacitor T = RC Circuits (Discharging) L −t/RC V c V •o T = tension in string V − I•R = 0 m = mass of string c L = length of string #60 Therm Eaxlpansion #45 Projectile Motion Linear: ∆L = L α ∆ T : l a t n o z i r o H x-xο= vο•t + 0 o Vertical: y-yο = vο•t + ½•a•t² Volume: ∆V = V o ∆• T #46 CentripeFtalce #61 BernoulE l'suation 2 P + ρg•h + ½• ρv ² = constant F = mv = mω r 2 QVolume Flow Rate1v 1 A 2v 2 constant r #62 Rotational Kinetic Energy (See LEM, pg 8) #47 Kirchhoff’s Laws 2 KE rotational•I•ω = ½•I• (v / r) Loop Rule: ΣAround any looi= 0 KE = ½•m•v + ½•I• Node Rule: Σ at any node i rolling w/o slipping Angular Momentum = L = I• = mωv•r•sin #51 Minimum Speed at the top of a Angular Impulse equals VCertrooarp CHANGE IN Angular Momentum v = rg ∆L = τorquet = (I•ω) Version 5/12/2005 Reference Guide & Formula Sheet for Physics Dr. Hoselton & Mr. Price Page 3 of 8 #75 Thin Lens Equation #63 Period of Simple Harmonic Motion f = focal length m 1 1 1 1 1 i = image distance T = 2 where k = spring constant = + = + k f D o D i o i o = object distance f = 1 / T = 1 / period #64 Banked Circular Tracks Magnification v = r• •tan θ M = − / D = −i /o = H / H i o i o #66 First Law of Thermodynamics Helpful reminders for mirrors and lenses ∆U = Q Net+ W Net Focal Length of: positive negative Change in Internal Energy of a system = mirror concave convex +Net Heat added to the system lens converging diverging +Net Work done on the system Object distance =ll bjects Object height o Hlolbjects Flow of Heat through a Solid Image distance =eal virtual ∆Q / t = k•A• T / L Image height =iH virtual, upright real, inverted k = thermal conductivity Magnification virtual, upright real, inverted A = area of solid L = thickness of solid #76 CoulomL b'sw q q #68 Potential Energy stored in a Capacitor F = k 1 2 r 2 P = ½•C•V² 2 k = 1 =9E9 N ⋅ RC Circuit formula (Charging) 4πε C 2 − t / RC o V = V cell − e ) #77 CapaciC toormbinations c PARALLEL R•C = =τtime constant V - Vcapacitor•R = 0 C eq= C 1 C +2C +3… cell SERIES 1 1 1 1 n 1 #71 SimP plndulum = + + K + = ∑ Ceq C 1 C 2 C n = 1 i L and f = 1/ T T = π g #78 Work done on a gas or by a gas W = P• ∆V #72 Sinusoidal motion x = A•cos(ω•t) = A•cos( 2 πf •t) #80 Electric Field around a point charge q ω = angular frequency E = k 2 f = frequency r #73 DoppE lefect 1 N ⋅ 2 Toward k = =9 E 2 343 ±Away vo 4πε o C f′= f 343 mTowardv #82 Magnetic Field around a wire Away s v = velocity of observer v = velocity of source µoI o s B = 2πr #74 2 ndLaw of Thermodynamics Magnetic Flux Φ = B•A• cos θ The change in internal energy of a system is ∆U = Q Added W Done On QlostW Done By Force caused by a magnetic field Maximum Efficiency of a Heat Engine on a moving charge (CCayrce)t (Temperatures in Kelvin) F = q•v•B•sin θ T % Eff = (1− c )⋅100% #83 Entropy change at constant T T ∆ S = Q / T h (Phase changes only: melting, boiling, freezing, etc) Version 5/12/2005 Reference Guide & Formula Sheet for Physics Dr. Hoselton & Mr. Price Page 4 of 8 #95 Relativistic Time Dilation #84 Capacitance of a Capacitor ∆ t =∆to/ β C = κ εA / d o κ = dielectric constant #96 Relativistic Length Contraction A = area of plates ∆ x = β ∆ o d = distance between plates εo = 8.85 E(-12) F/m Relativistic Mass Increase m = m / β o #85 Induced Voltage N = # of loops ∆Φ #97 Energy of a Photon or a Particle Emf = N E = h•f = m•c2 ∆t Lenz’s Law – induced current flows to create a B-field h = Planck's constant = 6.63 E(-34) J sec opposing the change in magnetic flux. f = frequency of the photon #98 Radioactive Decay Rate Law #86 Inductors during an increase in current − k t V = V •e − t / (L / R) A = A oe = (1/2n)•A0 (after n half-lives) L cell Where k = (ln 2) / half-life − t / (L / R) I = (Vcell•[ 1 - e ]
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