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MCAT EK Physics and Chemistry Equations
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Gravity
Terms in this set (131)
speed =
distance/time
velocity =
displacement/time
acceleration =
change in velocity/time
v(avg) =
1/2 (vf + v0)
Kinematic equation 1:
Δx = vot + 1/2at^2
Kinematic equation 2:
vf^2 = v0^2 + 2aΔx
Kinematic equation 3:
vf = v0 + at
Kinematic equation 4:
Δx = 1/2 (v0 + vf)t
vertical velocity of projectile =
srroot (2gh)
Force =
ma
Gravitational Force between two objects =
G (m1m2) / r^2
Gravitational force acting on object on incline plane =
mgsinθ
Normal force acting on object on incline plane =
mgcosθ
µ(k or s) of incline plane=
µ(k or s) = sinθ/cosθ
Hook's Law: Force =
-kΔx
Force of static friction =
µsF(normal)
Force of kinetic friction =
µkF(normal)
torque =
Frsinθ
Kinetic Energy =
1/2mv^2
Gravitational potential energy =
mgh
Elastic potential energy (eg spring) =
1/2kx^2
First Law of thermodynamics
E(total) = W + q (q = heat)
Work-Kinetic Energy theorem:
W = ΔK
If ΔE(internal) = 0 then
W + q = ΔK + ΔU
Work =
Fdcosθ
Power =
Work/time
Power 2 =
ΔE / time (where E is energy)
Instantaneous Power =
Fvcosθ (where v is velocity)
Law of conservation of mechanical energy
K1 + U1 = K2 + U2
if no heat, Work =
ΔK + ΔU
Mechanical advantage
F(input)d(input) = F(output)d(output)
Mechanical advantage 2
F(output)/F(input) = d(input)/d(output)
density =
mass/volume
specific gravity =
density of substance / density of water
Pressure =
Force / Area
Pressure of fluid at rest in sealed container =
ρgy
Pressure of fluid at rest open to air =
ρgy + P(atm)
Buoyant force =
ρ(fluid)Vol(fluid)g
Buoyant force 2 =
m(fluid)g
apparent weight lost of object
ρ(fluid) / ρ(object) * 100%
Volume rate flow Q =
Av
Continuity equation
A1v1 = A2v2
mass flow rate I =
ρQ = ρAv
Bernoulli's Equation
P1 + 1/2ρv1^2 + ρgh1 = P2 + 1/2ρv2^2 + ρgh2
velocity of fluid coming from spigot
v = sqrroot(2gh) where height is height of spigot
change of pressure in horizontal pipe with constant cross sectional area
ΔP = QR (where R is resistance)
Coulomb's Law (force between two charged objects)
F = k(q1q2) / r^2
Electric Field E =
kq1/r^2
Force on charge due to electric field
F = qE (where q is charge and E is Electric Field)
Potential energy of a charge in an electric field
U = qEd (where d is displacement)
electric potential energy
U = k(q1q2)/r
another electric potential energy
U = qV
Voltage V =
V = Ed (E is electric field)
Voltage due to a point charge =
Kq1/r
Resistivity R of substance =
ρL/A
Current i =
V/R where R is resistance
Electric field in a parallel plate capacitor
E = Q / (kAε0)
Capacitance
C = Q/V (where Q is charge and V is voltage)
Potential energy of capacitor
U = (1/2)QV
Potential energy of capacitor 2
U = (1/2)CV^2
Potential energy of capacitor 3
(1/2)Q^2/C
Resistors in series
R(eff) = R1 + R2 + R3...
Resistors in parallel
1/R(eff) = 1/R1 + 1/R2 + 1/R3...
Capacitors in series
1/C(eff) = 1/C1 + 1/C2 + 1/C3...
Capacitors in parallel
C(eff) + C1 + C2 + C3...
Force on a charge due a magnetic field
F = qvBsinθ
Force on a charge due to a magnetic field as a centripetal force
F = qvBsinθ = mv^2/r
Power 1 =
P = iV
Power 2 =
P = V^2/R
Power 3 =
P = i^2/R
velocity of sound wave
v = sqrroot (B/ρ) where B is Bulk modulus (measure of elasticity) and ρ is density (measure of inertia)
decibels
β = 10log (I/I0) where I0 is the threshold intensity of hearing, I is intensity
Doppler effect
FO = Fs (c ± vO/ c ± vs) where vO is velocity of object and vs is velocity of source
Doppler approximation 1
Δf/fs = v/c
Doppler approximation 2
Δλ/λs = v/c
Doppler approximation 1 after you've calculated Δf
fo = fs ± Δf
Doppler approximation 2 after you've calculated Δλ
λo = λs ± Δλ
Diffraction equation
dsinθ = mλ
Lens/mirror equation
1/p + 1/i = 1/f
Power of lens
P = 1/f (where f is in meters!! unit is diopters, which is m-1)
magnification 1
m = h'/h
magnification 2
m = - (i)/p
focal length =
f = 1/2r
Snell's law
n1sinθ1 = n2sinθ 2
critical angle formula
θ c = sin-1(n2/n1)
ΔE of photon
ΔE = hf
wavelength of photon
λ = h/mc (h is Plank's constant)
KE of photon
KE = hf - φ (where φ is work function)
percent yield
actual yield/theoretical yield * 100
rate constant k =
k = Ae^(-E(a) / RT) where E(a) is activation energy, R is gas constant, T is temperature)
rate law
rate(forward) = k[A]^a[B]^b
Law of Mass Action
K = [C]^c[D]^d/[A]^a[B]^b
Heisenberg's Uncertainty Principle
ΔxΔp ≥ h/2
KE(avg) for a mole of molecules in any fluid
KE(avg) = (3/2)RT where R is gas constant and T is temp
PV Work =
Work = -PΔVat constant pressure
Enthalpy ΔH =
ΔH = ΔU + PΔV (at constant pressure)
Enthalpy 2 ΔH = (if only PV work is performed)
ΔH = q (where q is heat)
ΔfHo(reaction) =
ΔfHo(reaction) = ΔfHo(products) - ΔfHo(reactants)
Gibbs free energy
ΔG = ΔH - TΔS
Q =
products/reactants (not at equilibrium)
Gibbs free energy not at equilibrium
ΔG = ΔG^o + RTln(q)
Gibbs free energy at standard conditions
ΔG^o = -RTln(K)
Ideal Gas Law
PV = nRT
Ideal gas law for constant pressure
V1/T1 = V2/T2
Ideal gas law for constant temp and pressure
V1/n1 = V2/n2
Ideal gas law for constant moles
P1V1/T1 = P2V2/T2
Deviations from ideal gas law: volume
V(real) > V(ideal)
Deviations from ideal gas law: pressure
P(real) < P(ideal)
Partial pressure
P(a) = χ(a)P(total) where χ(a) is the mole fraction of gas a
Dalton's law for partial pressures
P(total) = P1 + P2 + P3...
Heat capacity C
C = q/ΔT (where q is heat)
heat by using specific heat c
q = mcΔT
heat by using specific heat c written another way to make analyzing phase change diagram easier
ΔT = (1/mc)q
Molarity
moles of solute / volume of solution
molality
moles of solute/ kilograms of solvent
χ (mole fraction)
χ = moles of solute / total moles of all solutes and solvents
mass %
Mass % = mass of solute/total mass of solution * 100%
ppm
ppm = mass of solute/total mass of solution * 10^6
heat of solution ΔHsol
ΔHsol = ΔH1 + ΔH2 + ΔH3...
Vapor pressure of solution P(v) =
P(v) = χ(a)P(a) (where P(a) is pressure of pure liquid)
Vapor pressure of solution P(v) with volatile solute
P(v) = χ(a)P(a) + χ(b)P(b)
Gibbs free energy for cell potential
ΔG = -nFE(max) where F is Faraday's constant and E is voltage
Nernst equation
E = E^o - (.06/n)log(Q)
pH =
pH = -log[H+]
Kw
Kw = [H30+][OH-]
Ka =
Ka = [H3O+][A-]/[HA]
Kb
Kb = [OH-][HA]/[A-]
Kw again =
Kw = KaKb
14 = (at 25 degrees C)
14 = pKa + pKb
Henderson-Hassalbach
pH = pka + log[A-]/[HA]
pH of weak acid =
pH = (1/2)pka - (1/2)log[HA]
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