MCAT Essential Equations

linear motion

v = v₀ + at

linear motion (terms of x/distance)

x = v₀t + (at²)/2

linear motion (change in distance,time,velocity)

∆x = ∆t • 1/2(v_i+v_f)

y-component of force

F_g = mgsin𝜃

x-component of force

F_g = mgcosθ

parallel force on an incline

∥F_g = mgsin𝜃 (sin is sliding down)

perpendicular force on an incline

⟂F_g = mgcos𝜃

force between two objects

F=G(m1m2)/r²

kinetic friction

fk = μkN

center of mass

x = (m₁x₁ + m₂x₂ +… ) / (m₁ + m₂ + … )

work

W = Fdcos𝜃 [1 J = 1 Nm]

power

P = Work/time [1 Watt = 1 J/s]

kinetic energy

KE = 1/2mv²

average molecular speeds

K=1/2mv²=3/2KbT

gravitational potential energy

U = mgh

elastic potential energy

U = 1/2kx²

Hooke's Law

F = -kx

Total Mechanical Energy

E = U (potential) + K (kinetic)

work due to pressure and volume

W = P∆V; area under a pressure x volume graph

mechanical advantage

F(out)/F(in)

efficiency

work out/work in

Efficiency

(load x load distance)/(effort x effort distance)

torque

𝜏 = rFsinθ [Nm]

centripital force (Fc)

F = (mv²)/r

density

ρ = m/v

specific gravity

ρ_(object)/ρ_(water)

absolute pressure

P = P_o + pgz

gauge pressure

P_(gauge) = P_(absolute) - P_(atm)

Pascal's Principle

P = F1/A1 = F2/A2

Archimedes' Principle

F_(buoy) = ρ_(fluid)V_{(fluid displaced)}g = ρ_(fluid)V_(submerged)g

equation of continuity

A1V1=A2V2

Bernoulli's Equation

P₁+ ρgh₁+ 1/2ρv₁² = P₂+ ρgh₂+ 1/2ρv₂²

Poiseuille's equation

Q = (π)r⁴ΔP/8ηL

Coulomb's Law

F=K q₁*q₂/r², magnitude of force between two charges

Electric field

E = kQ/r² [N/C]

electric potential energy

U = kQq/r [J]

electric potential

V = kQ/r [1Volt=J/C]

Shortcut for Coulomb's Law, Electric Potential Energy, Electric Field and Electric Potential

Left to Right: multiply by “r”; Top to Bottom: divide by “q”

magnetic field in a straight wire

B = uI/2(π)r [T]

magnetic field in the center of a circular wire

B = uI/2r [T]

magnetic force on point charge

F = qvBsinθ [T]

magnetic force on a current carrying wire

F = ILBsinθ [T = 1Ns/Cm]

Current

I = ΔQ/Δt [ampere=C/s]

Resistance

R = ρL/A (rePLAy)

Ohm's Law

V = IR

Capacitance

C = Q/V [Farad]

Propagation of Speed

v = fλ

Period

T = 1/f

intensity of sound wave

I = Power/Area

Decibel Scale

10log(I/I0)

Focal Length Relationship (thin lens equation)

1/f = 1/o + 1/i = 2/r

Magnification

m = -d_i/d_o = h_i/h_o

total magnification

m1 x m2 x m3

Lens Power

P = 1/f (diopters)

index of refraction

n = c/v

Snell's Law

n₁sinθ₁ = n₂sinθ₂

Dark fringes in single slit diffraction

a*sin𝜃= nλ

Dark Fringes in Double Slit diffraction

dsin𝜃 = (n + 1/2)λ

Energies of photons and frequencies (Rydberg Formula)

E = hf

wavelength and frequency

c = fλ (light) OR v=fλ

% Yield

actual/theoretical x 100%

% Error

| actual - theoretical / actual | x 100%

Centripetal Acceleration

a_c = v²/r

Michaelis-Menten Equation

V₀ = V_max x [S] / K_m+[S]

Catalytic Efficiency

K_cat/K_m

osmotic pressure

π =iMRT

Arrhenius Equation

k = A*e^(E_a/RT)

Gibbs Free Energy (standard conditions)

ΔG˚ = −RT ln (K_eq)