Equations

Question 1

Linear Motion Equations (5)

Answer 1

v = v₀ + at

x = v₀t + ½at²

v² = v₀² + 2ax

v_avg = (v + v₀)/2

x = (v_avg)t

Question 2

Static Friction

Answer 2

0 < f_s < μ_sF_N

Question 3

Kinetic Friction

Answer 3

f_k = µ_kF_N

Question 4

SI Unit: Newton

Answer 4

(kg • m) / s²

Question 5

SI Unit: Joule

Answer 5

N • m

Question 6

Work

Answer 6

W = Fd cos θ

Question 7

Power

Answer 7

P = W / Δt

Question 8

Kinetic Energy

Answer 8

K = ½mv²

Question 9

SI Unit: Watt

Answer 9

J / s

Question 10

Newton’s Third Law

Answer 10

F_b = -F_a

Question 11

Newton’s Law of Gravitation

Answer 11

F = (Gm₁m₂)/ r²

Question 12

Centripetal Acceleration

Answer 12

a_c = v² / r

Question 13

Centripetal Force

Answer 13

F_c = (mv²) / r

Question 14

Total Mechanical Energy

Answer 14

E = U + K

Question 15

Work - Energy Theorem

Answer 15

W = ΔE

Question 16

Conservation of Energy

Answer 16

ΔE = ΔU + ΔK = 0

Question 17

Thermal Expansion

Answer 17

ΔL = αLΔT

Question 18

Volume Expansion

Answer 18

ΔV = βVΔT

if not given, estimate β = 3α

Question 19

Heat Gained or Lost by an object (q)

Answer 19

q = mcΔT

provided no phase change

Question 20

Specific Heat (c)

Answer 20

c = q / mΔT

SI Units: cal / g•K

Question 21

Heat of Transformation

Answer 21

Q = mL

provided with phase change

Question 22

Adiabatic Process

Answer 22

Q = 0

ΔU = -W

Question 23

Constant Volume

Answer 23

W = 0

ΔU = Q

Question 24

Isothermal

Answer 24

ΔU = 0

Q = W

Question 25

Density

Answer 25

ρ = m / V

Question 26

SI Unit: Pascal

Answer 26

N / m²

Question 27

Pressure

Answer 27

P = F / A

Question 28

Weight

Answer 28

W = ρgV

Question 29

Specific Gravity

Answer 29

ρ_substance / ρ_{water ρwater} = 10³ kg/m³ or 1 g/cm³

Question 30

Pressure (of fluid with uniform density in a sealed vessel)

Answer 30

P = ρgz

Question 31

Absolute Pressure

Answer 31

P = P₀ + ρgz

Question 32

Gauge Pressure

Answer 32

P_g = P - P_atm

Question 33

Continuity Equation

Answer 33

A₁v₁ = A₂v₂

Question 34

Dynamic Pressure of a Fluid

Answer 34

½ρv²

Question 35

Static Pressure of a Fluid

Answer 35

P₁ + ρgh₁

Question 36

Bernoulli's Equation

Answer 36

½pv²₁ + P₁ + ρgh₁ = ½pv²₂ + P₂ + ρgh₂

Question 37

Buoyant Force

Answer 37

F_b = ρ_fluidgV_submerged = ρ_fluidgV_{fluid displaced}

Question 38

Pascal's Principle Equations

Answer 38

P = F₁ / A₁ = F₂ / A₂ A₁d₁ = A₂d₂ W = F₁d₁ = F₂d₂

Question 39

Coulomb's Law

Answer 39

F = kq1q2/ r2 SI Unit: Newtons

Question 40

Electric Field

Answer 40

E = F_e / q = kQ / r²

Question 41

SI Units: Electric Field

Answer 41

N / C or V / m

Question 42

Electric Potential Energy

Answer 42

U = qΔV = qEd = kQq / r

Question 43

Electric Potential

Answer 43

V = U / q

Question 44

Potential Difference (Voltage)

Answer 44

Voltage = W / q = kQ / r

Question 45

SI Unit: Volt

Answer 45

J / C

Question 46

Current

Answer 46

I = Q / Δt

Question 47

SI Units: Ampere

Answer 47

C / s

Question 48

Ohm's Law

Answer 48

V = IR

Question 49

Resistance

Answer 49

R = ρL / A in Ω (ohms)

Question 50

Series Circuits Equations

Answer 50

R_eq = R₁ + R₂ + R₃ + ... V_T = V₁ + V₂ + V₃ + ... I_T = I₁ = I₂ = I₃

Question 51

Parallel Circuits

Answer 51

1/R_eq = 1/R₁ + 1/R₂ + 1/R₃ + ... V_T = V₁ = V₂ = V₃ = ... I_T = I₁ + I₂ + I₃ + ...

Question 52

Power Dissipated by Resistors

Answer 52

P = IV = V² / R = I²R

Question 53

Capacitance

Answer 53

C = Q / V

Question 54

Capacitors in Parallel

Answer 54

C_eq = C₁ + C₂ + C₃ + ...

Question 55

Energy Stores by Capacitors

Answer 55

U = ½QV = ½CV² = ½Q² / C

Question 56

Capacitors in Series

Answer 56

1/C_eq = 1/C₁ + 1/C₂ + 1/C₃ + ...

Question 57

Wave Formulas

Answer 57

f = 1/T v = fλ

Question 58

Angular Frequency

Answer 58

ω = 2πf = 2π / T

Question 59

String Wave Formulas

Answer 59

λ = 2L / n (n = nodes = 1, 2, 3...) f = nv / 2L (n = nodes = 1, 2, 3...)

Question 60

Open Pipe Formulas

Answer 60

λ = 2L / n (n = nodes = 1, 2, 3...) f= nv / 2L (n = nodes = 1, 2, 3...)

Question 61

Closed Pipes Formulas

Answer 61

λ = 4L / n (n = nodes = 1, 3, 5...) f = nv / 4L (n = nodes = 1, 3, 5...) End of a closed pipe is always a node

Question 62

Intensity of Sound

Answer 62

I = P / A

Question 63

SI Units: Intensity

Answer 63

W / m²

Question 64

Sound Level

Answer 64

β = 10 log (I/I₀) in decibel = dB

Question 65

Increase in dB

Answer 65

Increase of 10 dB is an increase in intensity by a factor of 10 -- an increase of 20 dB is an increase in intensity by a factor of 100

Question 66

Doppler Effect

Answer 66

f' = f (v +- v_D) / (v +- v_S) Stationary source: v_S = 0 Stationary detective: v_D = 0

Question 67

Doppler Effect: observer and detector moving closer

Answer 67

+ sign in the numerator - sign in denominator

Question 68

Doppler Effect: observer and detector moving apart

Answer 68

- sign in numerator + sign in denominator

Question 69

Refraction

Answer 69

n = c / v speed of light = 3 x 10⁸ m/s

Question 70

Snell's Law

Answer 70

n₁sinθ = n₂sinθ when n₂ \> n₁ light bends towards the normal when n₂ \< n₁ light bends away from the normal

Question 71

Diffraction- location of dark fringes

Answer 71

αsinθ = nλ | (n = 1, 2, 3...)

Question 72

Optics Equation

Answer 72

1/f = 1/o + 1/i

Question 73

Magnification

Answer 73

m = -i / o |m| \< 1 - image reduced |m| \> 1 - image enlarged |m| = 1 - image same size inverted image has a negative m; erect image has a positve m

Question 74

Photoelectric Effect

Answer 74

E = hf = hc / λ K = hf - W

Question 75

Half Life

Answer 75

n = n₀e^-λt

Question 76

Alpha Decay

Answer 76

Question 77

Beta-Minus Decay

Answer 77

Question 78

Beta-Plus Decay

Answer 78

Question 79

Components of Gravity on an Inclined Plane

Answer 79

F_g,parallel = mgsinθ F_{g, perpendicular} = mgcosθ

Question 80

Torque (τ)

Answer 80

τ = r x F = rFsinθ

Question 81

Center of Mass Calculation

Answer 81

Question 82

Dot Product: Multiplying vectors to create scalar quantity

Answer 82

A • B = |A| • |B| cosθ

Question 83

Cross Product: Multiplying vectors to generate a vector

Answer 83

A x B = |A| • |B| sinθ

Question 84

Convex Mirrors What type of image is formed by a convex mirror regardless of the position of the object?

Answer 84

Virtual Upright

Question 85

Concave Mirrors: What is the image formed when an object is placed inside the focal length?

Answer 85

Enlarged and Virtual behind the mirror

Question 86

Converging Lenses: 1. What is the image formed when an object is placed beyond the focal length? 2. What is the image formed when an object is placed inside the focal length? 3. What is the image formed if an object is placed at the focal point?

Answer 86

1. Real and Inverted 2. Virtual, Upright and Enlarged 3. No image formed

Question 87

Right Hand Rule: resultant of cross product

Answer 87

1. Start by pointing thumb in the direction of vector A 2. Extend your fingers in the direction of vector B 3. Your palm will then point in the direction of the resultant C

Question 88

Graviational Potential Energy

Answer 88

U = mgh

Question 89

Springs: Elastic Potential Energy

Answer 89

U = ½kx²

Question 90

Pulley System Efficiency

Answer 90

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

Question 91

Mechanical Advantage of Simple Machines

Answer 91

Ratio of magnitudes of the force exerted on an object by a simple machine (F_out) to the force actually applied on the simple machine (F_in) F_out / F_in

Question 92

Temperature Conversions

Answer 92

F = 9/5C + 32 K = C + 273

Question 93

SI Unit: Ohm (Ω)

Answer 93

V / A

Question 94

SI Unit: Farad

Answer 94

C / V

Question 95

SI Unit: Tesla

Answer 95

N / A•m

Question 96

1. 3^½ 2. 2^½

Answer 96

1. 1.7 2. 1.4

Question 97

Critical Speed

Answer 97

v_c = N_Rη / ρD N_R is a dimensionless constant that will be given, η is the viscocity of the fluid, ρ is the density of the fluid, and D is the diameter of the pipe/tube

Question 98

Poiseuille's Law (flow rate Q)

Answer 98

Q = πr⁴ΔP / 8ηL Q is the flow rate, r is the radius of the tube, ΔP is the pressure gradient, η is the viscocity of the fluid and L is the length of the pipe

Question 99

Dipole Moment

Answer 99

p = qd

Question 100

Magnetic Field of a Straight Wire

Answer 100

B = μ₀I / 2πr

Question 101

Magnetic Field of a Loop Wire

Answer 101

B = μ₀I / 2r

Question 102

Magnetic Force on a moving point charge

Answer 102

F_B = qvBsinθ

Question 103

Μagnetic Force on a current-carrying wire

Answer 103

F_B = ILBsinθ

Question 104

Voltage and Cell emf

Answer 104

V = E_cell - ir_int where r_int is internal resistance

Question 105

Electric field in a capacitor

Answer 105

E = V/d

Question 106

Capacitance with a dielectric material

Answer 106

C' = κC

Question 107

Kirchoff's Junction Rule

Answer 107

At any point or junction in a circuit, the sum of currents directed into that point equals the sum of currents directed away from that point I_{into junction} = I_{leaving junction}

Question 108

Kirchoff's Loop Rule

Answer 108

Around any closed circuit loop, the sum of voltage sources will always be equal to the sum of voltage drops (potential drops) V_source = V_drop

Question 109

Change in Sound Level

Answer 109

β_f = β_i + 10log I_f/I_i

Question 110

Focal Length of multiple lens system

Answer 110

1/f = 1/f₁ + 1/f₂ + 1/f₃ + ...

Question 111

Magnification of multiple lens system

Answer 111

m = m₁ x m₂ x m₃...

Question 112

Electron Capture

Answer 112

Opposite of beta-negative decay- lies in reactants

Question 113

Mass defect and energy

Answer 113

E = mc²

Question 114

log_A1 =

Answer 114

0

Question 115

log A^B =

Answer 115

B log A

Question 116

log_A A =

Answer 116

1