FORMULAS

Question 1

Universal Gravitation Equation

Answer 1

F = G (m₁ * m₂) / r², where G = 6.67 x 10^-11

Question 2

Kinetic Friction Equation

Answer 2

F_k = μ_k * N

Question 3

Kinematics (no displacement)

Answer 3

v = v_i + (a * t)

Question 4

Kinematics (no final velocity)

Answer 4

x = (v_i * t) + ((a * t²) / 2)

Question 5

Kinematics (no time)

Answer 5

v² = v_i² + (2 * a * x)

Question 6

Kinematics (no acceleration)

Answer 6

x = v_bar * t

Question 7

Centripetal Force

Answer 7

F_c = (m * v²) / r

Question 8

Torque

Answer 8

τ = r * F = r * F * sinθ

Question 9

Kinetic Energy

Answer 9

K = (1/2) * m * v²

Question 10

Gravitational Potential Energy

Answer 10

U = m * g * h

Question 11

Elastic Potential Energy

Answer 11

E = (1/2) * k * x²

Question 12

Total Mechanical Energy

Answer 12

E = Kinetic Energy + Potential Energy

Question 13

Definition of Work (mechanial)

Answer 13

W = F * d = F * d * cosθ

Question 14

Definition of Work (isobaric gas-piston system)

Answer 14

W = P * ΔV

Question 15

Definition of Power

Answer 15

P = W / t = ΔE / t

Question 16

Work-Energy theorem

Answer 16

W_net = ΔK = K_f - K_i

Question 17

Mechanical Advantage

Answer 17

F_out/ F_in

Question 18

Efficiency

Answer 18

W_out / W_in =
((load) * (load distance)) / ((effort) * (effort distance))

Question 19

Temperature Conversions (Farenheit -> Celcius, Kelvin -> Celcius)

Answer 19

F = (9 / 5) * C + 32
K = C + 273

Question 20

Thermal Expansion

Answer 20

ΔL = α * L * ΔT

Question 21

Volume Expansion

Answer 21

ΔV = β * V * ΔT

Question 22

First Law of Thermodynamics

Answer 22

ΔU = Q - W

Question 23

Heat Gained or Lost (with temperature change)

Answer 23

q = m * c * ΔT

Question 24

Heat Gained or Lost (phase change)

Answer 24

q = m * L

Question 25

Entropy and Heat

Answer 25

ΔS = Q_rev / T

Question 26

Second Law of Thermodynamics

Answer 26

ΔS_universe = ΔS_system + ΔS_surroundings > 0

Question 27

Density

Answer 27

ρ = m / V

Question 28

Weight of a Volume of Fluid

Answer 28

F_g = ρ * V * g

Question 29

Specific Gravity

Answer 29

SG = ρ / (1g / cm³)

Question 30

Pressure

Answer 30

P = F / A

Question 31

Absolute Pressure

Answer 31

P = P₀ + (ρ * g * z)

Question 32

Gauge Pressure

Answer 32

P_gauge= P - P_atm= (P₀ + (ρ * g * z)) - P_atm

Question 33

Pascal's Principle

Answer 33

P = F₁ / A₁ = F₂ / A₂

Question 34

Buoyant Force

Answer 34

F_buoy = ρ_fluid * V_{fluid displaced}* g = ρ_fluid* V_submerged * g

Question 35

Poiseuille's Law

Answer 35

Q = (π * r⁴ * ΔP) / (8 * η * L)

Question 36

Critical Speed

Answer 36

v_c= (N_r * η) / (ρ * D)

Question 37

Continuity Equation

Answer 37

Q = v₁ * A₁ = v₂ * A₂

Question 38

Bernoulli's Equation

Answer 38

P₁ + ((1/2) * ρ * v₁²) + (ρ * g * h₁) = P₂ + ((1/2) * ρ * v₂²) + (ρ * g * h₂)

Question 39

Coulomb's Law

Answer 39

F_e = (k * q₁ * q₂) / r²

Question 40

Electric Field

Answer 40

E = F_e / q = (k * Q) / r²

Question 41

Electric Potential Energy

Answer 41

U = (k * Q *q) / r

Question 42

Electric Potential (from electric potential energy)

Answer 42

V = U / q

Question 43

Electric Potential (from source charge)

Answer 43

V = (k * Q) / r

Question 44

Voltage

Answer 44

ΔV = V_b - V_a = W_ab / q

Question 45

Electric Potential Near a Dipole

Answer 45

V = ((k * q * d) / r²) * cosθ

Question 46

Dipole Moment

Answer 46

p = q * d

Question 47

Electric Field on the Perpendicular Bisector of a Dipole

Answer 47

E = (1 / (4 * π * ε₀)) * (p / r³)

Question 48

Torque on a Dipole in an Electric Field

Answer 48

τ = p * E * sinθ

Question 49

Magnetic Field from a Straight Wire

Answer 49

B = (μ₀* I) / (2 * π * r)

Question 50

Magnetic Field from a Loop of Wire

Answer 50

B = (μ₀ * I) / (2 * r)

Question 51

Magnetic Force on a Moving Point Charge

Answer 51

F_B = q * v * B * sinθ

Question 52

Magnetic Force on a Current-Carrying Wire

Answer 52

F_B = I * L * B * sinθ

Question 53

Current

Answer 53

I = Q / Δt

Question 54

Krichhoff's Junction Rule

Answer 54

I_{into junction} = I_{leaving junction}

Question 55

Krichhoff's Loop Rule

Answer 55

V_source = V_drop

Question 56

Definition of Resistance

Answer 56

R = (ρ * L) / A

Question 57

Ohm's Law

Answer 57

V = I * R

Question 58

Voltage and Cell emf

Answer 58

V = E_cell - (i * r_int)

Question 59

Definition of Power

Answer 59

P = W / t = ΔE / t

Question 60

Electric Power

Answer 60

P = I * V = I²* R = V² / R

Question 61

Voltage Drop Across Circuit Elements (series)

Answer 61

V_p = V₁ + V₂ + V₃ + ... + V_n

Question 62

Voltage Drop Across Circuit Elements (parallel)

Answer 62

V_p = V₁ = V₂ = V₃ = ... = V_n

Question 63

Equivalent Resistance (series)

Answer 63

R_s = R₁ + R₂ + R₃ + ... + R_n

Question 64

Equivalent Resistance (parallel)

Answer 64

1/R_p = (1/R₁) + (1/R₂) + (1/R₃) + ... + (1/R_n)

Question 65

Definition of Capacitance

Answer 65

C = Q / V

Question 66

Capacitance Based on Parallel Plate Geometry

Answer 66

C = ε₀ * (A / d)

Question 67

Electric Field in a Capacitor

Answer 67

E = V / d

Question 68

Potential Energy in a Capacitor

Answer 68

U = (1 / 2) * C * V₂

Question 69

Capacitance with a Dielectric Material

Answer 69

C' = κ * C

Question 70

Equivalent Capacitance (series)

Answer 70

1/C_s = (1/C₁) + (1/C₂) + (1/C₃) + ... + (1/C_n)

Question 71

Equivalent Capacitance (parallel)

Answer 71

C_p = C₁ + C₂ + C₃ + ... + C_n

Question 72

Wave Speed

Answer 72

v = f * λ

Question 73

Period

Answer 73

T = 1 / f

Question 74

Angular Frequency

Answer 74

ω = 2 * π * f = (2 * π) / T

Question 75

Speed of Sound

Answer 75

v = sqrt(B / ρ)

Question 76

Doppler Effect

Answer 76

f' = f * ((v +/- v_D) / (v -/+ v_S))

Question 77

Intensity

Answer 77

I = P / A

Question 78

Sound Level

Answer 78

β = 10 * log(I / I₀)

Question 79

Change in Sound Level

Answer 79

β_f = β_i + 10 * log(I_f / I_i)

Question 80

Beat Frequency

Answer 80

f_beat = |f₁ - f₂|

Question 81

Wavelength of a Standing Wave (strings + open pipes)

Answer 81

λ = (2 * L) / n

Question 82

Frequency of a Standing Wave (strings + open pipes)

Answer 82

f = (n * v) / (2 * L)

Question 83

Wavelength of a Standing Wave (closed pipes)

Answer 83

λ = (4 * L) / n

Question 84

Frequency of a Standing Wave (closed pipes)

Answer 84

f = (n * v) / (4 * L)

Question 85

Speed of Light from Frequency and Wavelength

Answer 85

c = f * λ, where c = 3.00 x 10^8 in

Question 86

Law of Reflection

Answer 86

θ₁ = θ₂

Question 87

Optics Equation

Answer 87

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

Question 88

Magnification

Answer 88

m = (-i / o)

Question 89

Index of Refraction

Answer 89

n = (c / v)

Question 90

Snell's Law

Answer 90

n₁ * sinθ₁ = n₂ * sinθ₂

Question 91

Critical Angle

Answer 91

θ_c= sin^-1(n₂ / n₁)

Question 92

Lensmaker's Equation

Answer 92

(1 / f) = (n - 1) * ((1 / r₁) - (1 / r₂))

Question 93

Power of Lens

Answer 93

P = (1 / f)

Question 94

Focal Length of Multiple Lens System

Answer 94

(1 / f) = (1 / f₁) + (1 / f₂) + (1 / f₃) + ... + (1 / f_n)

Question 95

Power of Multiple Lens System

Answer 95

P = P₁ + P₂ + P₃ + ... + P_n

Question 96

Magnification of Multiple Lens System

Answer 96

m = m₁ * m₂ * m₃ * ... * m_n

Question 97

Positions of Dark Fringes in Slit-Lens Setup

Answer 97

a * sinθ = n * λ

Question 98

Positions of Dark Fringes in Double-Slit Setup

Answer 98

d * sinθ = (n + (1 / 2)) * λ

Question 99

Energy of a Photon of Light

Answer 99

E = h * f, where h = 6.6 x 10^-34 J / s

Question 100

Maximum Kinetic Energy of an Election in the Photoelectric Effect

Answer 100

K_max = (h * f) - W

Question 101

Work Function (minimum energy to eject election)

Answer 101

W = h * f_T

Question 102

Mass Defect and Energy

Answer 102

E = m * c²

Question 103

Rate of Nuclear Decay

Answer 103

Δn / Δt = -λ * n

Question 104

Exponential Decay

Answer 104

n = n₀ * e^{(-λ * t)}

Question 105

Decay Constant

Answer 105

λ = (ln2 / T_1/2) = (0.693 / T_1/2)

Question 106

Michaelis-Menten Equation

Answer 106

v = (v_max * [S]) / (K_m + [S])

Question 107

Turnover Number

Answer 107

v_max = [E] * k_cat

Question 108

Gram Equivalent Weight

Answer 108

GEW = Molar mass / n

Question 109

Equivalents from Mass

Answer 109

Equivalents = Mass of Compound / Gram Equivalent Weight

Question 110

Rate Law

Answer 110

rate = k[A]^x * [B]^y

Question 111

Arrhenius Equation

Answer 111

k = A * e^{-E_a / (R * T)}

Question 112

Gibbs Free Energy

Answer 112

ΔG = ΔH - (T * ΔS)

Question 113

Standard Gibbs Free Energy from Equilibrium Constant

Answer 113

ΔG^°_rxn = -R * T * lnK_eq

Question 114

Gibbs Free Energy From Reaction Quotient

Answer 114

ΔG_rxn = ΔG^°_rxn + (R * T * lnQ) = R * T * ln(Q / K_eq)

Question 115

Ideal Gas Law

Answer 115

P * V = n * R * T

Question 116

Henry's Law

Answer 116

[A] = k_H * P_A or [A]₁ / P₁ = [A]₂ / P₂ = k_H

Question 117

Osmotic Pressure

Answer 117

Π = i * M * R * T

Question 118

Freezing Point Depression

Answer 118

ΔT_f = i * K_f * m

Question 119

Boiling Point Elevation

Answer 119

ΔT_b = i * K_b * m

Question 120

Henderson-Hasselbalch Equation (acid buffer)

Answer 120

pH = pK_a + log([A^-] / [HA])

Question 121

Henderson-Hasselbalch Equation (base buffer)

Answer 121

pOH = pK_b + log([B⁺] / [BOH])

Question 122

p scale value approx.

Answer 122

-log(n * 10^-m) = m - log(n) p value = m - 0.n

Question 123

Nernst Equation (simplified when T = 298 K) for determining a cell's emf deviating standard conditions

Answer 123

E_cell = E^°_cell - (R * T) / (n * f) * lnQ = E^°_cell - (0.0592) / (n * f) * lnQ

Question 124

Nernst Equation (simplified when T = 310 K) for determining membrane potential

Answer 124

E = (R * T) / (z * F) * ln([ion]_outside / [ion]_inside) = (61.5 / z) * log([ion]_outside / [ion]_inside)

Question 125

Body Mass Index

Answer 125

BMI = mass / height²

Question 126

Goldman-Hodgkin-Katz voltage equation

Answer 126

V_m = 61.5 * log((P_Na+ * [Na+]_outside + P_K+ * [K+]_outside + P_Cl- * [Cl-]_inside) / (P_Na+ * [Na+]_inside + P_K+ * [K+]_inside + P_Cl- * [Cl-]_outside))