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Phys12-C00-equationSheet

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EQUATIONS AND CONSTANTS FOR GRADE 12 PHYSICS
These equations make doing homework and exams a bit easier, but they are not an excuse for not learning the course
material. If you don’t know what these equations mean and how to use them, they will not help you at all.
KINEMATIC EQUATIONS:
𝑣®avg =
Δ𝑑®
Δ𝑑
π‘Ž®avg =
Į𝑣
Δ𝑑
1
Δ𝑑® = 𝑣®1 Δ𝑑 + π‘ŽΔ𝑑
® 2
2
1
Δ𝑑® = 𝑣®2 Δ𝑑 − π‘ŽΔ𝑑
® 2
2
𝑣®1 + 𝑣®2
Δ𝑑® =
Δ𝑑
2
𝑣 22 = 𝑣 21 + 2π‘ŽΔ𝑑
𝑣®2 = 𝑣®1 + π‘ŽΔ𝑑
®
SYMMETRIC PROJECTILES:
2𝑣 𝑖 sin πœƒ
Total time: 𝑇 =
𝑔
2
𝑣 sin(2πœƒ)
Range: 𝑅 = 𝑖
𝑔
2
𝑣 sin2 πœƒ
Max height: 𝐻 = 𝑖
2𝑔
LAWS OF MOTION:
First law: 𝐹®net = 0® → π‘Ž® = 0®
Δ π‘®
Second law: 𝐹®net = π‘š π‘Ž® =
Δ𝑑
Third law: 𝐹®AB = −𝐹®BA
MOMENTUM & IMPULSE
𝑝® = π‘š®π‘£
𝐽® = 𝐹Δ𝑑
𝐽®net = Δ π‘®
COLLISIONS:
∑︁
∑︁
𝑝®π‘– =
𝑝®π‘–′ (all collisions)
𝑖
∑︁
𝐾𝑖 =
𝑖
𝑖
∑︁
𝐾𝑖′ (elastic only)
CONSERVATION OF ENERGY:
∑︁
𝐸 mech = 𝐾 +
π‘ˆπ‘–
𝑖
𝐸 sys = 𝐸 mech + 𝐸 int
Δ𝐸 sys = π‘Šext
πΊπ‘š 1 π‘š 2
π‘Ÿ2
πΊπ‘š 𝑠
𝑔= 2
π‘Ÿ
π‘ˆπ‘” = −
𝐹𝑔 =
πΊπ‘š 1 π‘š 2
π‘Ÿ
𝐹®π‘” = π‘š 𝑔®
𝑖
1D ELASTIC COLLISION:
𝑣 1 (π‘š 1 − π‘š 2 ) + 2π‘š 2 𝑣 2
𝑣 1′ =
π‘š1 + π‘š2
𝑣
(π‘š
− π‘š 1 ) + 2π‘š 1 𝑣 1
2
2
𝑣 2′ =
π‘š1 + π‘š2
ELECTROSTATICS:
π‘˜π‘ž 1 π‘ž 2
π‘Ÿ2
π‘˜π‘ž 𝑠
𝐸= 2
π‘Ÿ
π‘˜π‘ž 𝑠
𝑉=
π‘Ÿ
πΉπ‘ž =
π‘ˆπ‘ž =
π‘˜π‘ž 1 π‘ž 2
π‘Ÿ
𝐹®π‘ž = π‘ž 𝐸®
Δ𝑉 =
Δπ‘ˆ
π‘ž
FORCES:
parallel plate:
Gravity 𝐹®π‘” = π‘š 𝑔®
Static friction: 𝐹𝑠 ≤ πœ‡ 𝑠 𝐹𝑁
Kinetic friction: πΉπ‘˜ = πœ‡ π‘˜ 𝐹𝑁
Hooke’s Law: 𝐹®π‘  = −π‘˜ π‘₯®
1
Drag: 𝐹𝐷 = πœŒπ‘£ 2∞𝐢𝐷 𝐴ref
2
𝐸=
𝜎
Δ𝑉
=
πœ€0
𝑑
MAGNETISM:
πΉπ‘š = π‘žπ‘£π΅ sin πœƒ
πΉπ‘š = 𝐼𝑙 𝐡 sin πœƒ
CIRCULAR MOTION:
π‘Ž®π‘ ⊥ 𝑣®
π‘Žπ‘ =
𝑣2
π‘Ÿ
π‘šπ‘£ 2
𝐹𝑐 = π‘šπ‘Ž 𝑐 =
π‘Ÿ
2πœ‹π‘Ÿ
1
𝑇=
𝑓 =
𝑣
𝑇
𝑣2
tan πœƒ =
π‘Ÿπ‘”
WORK & ENERGY:
π‘Š = 𝐹Δ𝑑 cos πœƒ (constant force)
1
π‘Šnet = Δ𝐾
𝐾 = π‘šπ‘£ 2
2
1
π‘ˆπ‘” = π‘šπ‘”β„Ž
π‘ˆπ‘’ = π‘˜π‘₯ 2
2
π‘Š = −Δπ‘ˆ (conservative forces)
GRAVITY:
ORBITAL MOTION:
√οΈ‚
𝐺𝑀
𝑣 orb =
π‘Ÿ
√οΈ‚
2𝐺 𝑀 √
𝑣 esc =
= 2𝑣 orb
π‘Ÿ
𝐺 π‘€π‘š 1 2
𝐾orb =
= π‘šπ‘£ orb
2π‘Ÿ
2
𝐺 π‘€π‘š
π‘ˆorb = −
= −2𝐾orb
π‘Ÿ
𝐺 π‘€π‘š
𝐸 tot = 𝐾orb + π‘ˆπ‘” = −
= −𝐾orb
2π‘Ÿ
𝑇2
= constant
π‘Ÿ3
1
TRAVELLING WAVE:
𝑣 = π‘“πœ† =
πœ†
𝑇
REFRACTION:
𝑛1 sin πœƒ 1 = 𝑛2 sin πœƒ 2
𝑐
𝑛=
𝑣
ONE-SLIT DIFFRACTION:
Bright fringes:
1
π‘š+
πœ† = π‘Š sin πœƒ
2
1 πœ†πΏ
π‘¦π‘š = π‘š +
π‘š = 1, 2, 3 · · ·
2 π‘Š
Dark fringes:
π‘šπœ† = π‘Š sin πœƒ
π‘šπœ†πΏ
π‘¦π‘š =
π‘Š
π‘š = 1, 2, 3 · · ·
TWO-SLIT INTERFERENCE:
Bright fringe:
π‘›πœ† = 𝑑 sin πœƒ
π‘›πœ†πΏ
𝑦𝑛 =
𝑑
Δ𝑦𝑑
πœ†≈
π‘₯
𝑛 = 0, 1, 2, 3 · · ·
1 eV = 1.602 × 10−19 J
𝐸 = β„Žπ‘“
(
β„Žπ‘“ −πœ‘
𝐾max =
0
𝑛 = 0, 1, 2, 3 · · ·
OPTICAL RESOLUTION:
Rectangular: πœƒ min
Circular: πœƒ min
πœ†
=
π‘Š
1.22πœ†
=
𝐷
THIN-FILM INTERFERENCE:
One phase shift
1
Constructive: 2𝑛𝑑 = π‘š −
πœ†
2
Destructive: 2𝑛𝑑 = π‘šπœ†
Two phase shifts
if β„Ž 𝑓 > πœ‘
otherwise
𝐸 β„Žπ‘“
β„Ž
=
=
𝑐
𝑐
πœ†
β„Ž
πœ†=
π‘šπ‘£
β„Ž
πœŽπ‘ 𝜎π‘₯ ≥
4πœ‹
1 km/h = 0.278 m/s
1 m/s = 3.6 km/h
1 ly = 9.461 × 1015 m
SPECIAL RELATIVITY:
𝐢 = 2πœ‹π‘Ÿ
𝐴 = πœ‹π‘Ÿ 2
SI UNIT PREFIXES:
tera
giga
mega
kilo
centi
milli
micro
nano
pico
femto
1012
109
106
103
10−2
10−3
10−6
10−9
10−12
10−15
T
G
M
k
c
m
πœ‡
n
p
f
Spheres:
𝑆 = 4πœ‹π‘Ÿ 2
4
𝑉 = πœ‹π‘Ÿ 3
3
π‘š
𝑉
Small angles: tan πœƒ ≈ sin πœƒ ≈ πœƒ
Density: 𝜌 =
USEFUL CONSTANTS:
Universal gravitational constant: 𝐺 = 6.674 × 10−11 N · m2 /kg2
Coulomb’s constant: π‘˜ = 8.988 × 109 N · m2 /C2
Electron rest mass: π‘š 𝑒 = 9.110 × 10−31 kg
Proton rest mass: π‘š 𝑝 = 1.673 × 10−27 kg
Elementary charge: 𝑒 = 1.602 × 10−19 C
1
1−
MATHEMATICAL FORMULAS:
Circles:
Acceleration to to gravity: 𝑔 = 9.81 m/s2 (near surface of Earth)
Constructive: 2𝑛𝑑 = π‘šπœ†
1
Destructive: 2𝑛𝑑 = π‘š −
πœ†
2
Speed of light in vacuum: 𝑐 = 2.998 × 108 m/s
𝑣 2
Planck’s constant: β„Ž = 6.626 × 10−34 J · s
𝑐
= 4.136 × 10−15 eV · s
𝑑 ′ = 𝛾𝑑
𝐿
𝐿′ =
𝛾
′
π‘š = π›Ύπ‘š
π‘š Earth = 5.972 × 1024 kg
π‘Ÿ Earth = 6.371 × 106 m
π‘š Sun = 1.989 × 1030 kg
′
𝑝=π‘šπ‘£
π‘Ÿ Sun = 6.957 × 108 m
𝐸 0 = π‘šπ‘2
′ 2
1 kW · h = 3.6 × 106 J
𝑝=
Dark fringes:
1
𝑛+
πœ† = 𝑑 sin πœƒ
2
1 πœ†πΏ
𝑦𝑛 = 𝑛 +
2 𝑑
𝛾 = √οΈ‚
UNIT CONVERSIONS:
QUANTUM MECHANICS:
𝐸𝑇 = π‘š 𝑐 = π›Ύπ‘šπ‘
π‘š Moon = 7.348 × 1022 kg
2
π‘Ÿ Moon = 1.737 × 106 m
𝐾 = 𝐸𝑇 − 𝐸 0 = (𝛾 − 1)π‘šπ‘2
𝑑Earth-to-moon = 3.844 × 108 m
2
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