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

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University of Toronto Mississauga

Biology

BIO200H5

Dax Urbszat

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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