Q2 SPH4U0-C Formula Sheet PDF

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SPH4U: Physics, Grade 12, University Preparation

CONSTANTS AND EQUATIONS

CONSTANTS g == 9.8 m/s

2

6

me = 9 .11× 10 -31 k g

rearth = 6.38× 10 m

G == 6.67 × 10− 11

N ⋅m 2 kg 2

m p = 1.67 × 10 -27 kg

m earth == 5.98 × 10 24 kg

e = 1 .6 ×10 -19 C

k = 9 .0× 10 9 N ⋅ m 2 /C 2

c = 3 .0 × 10 8 m/s

µ 0 = 4π ×× 10 −7 T ⋅ m / A

CONVERSIONS f = 10−−15

p = 10 −12 n == 10 −9

µ = 10 −6

m = 10 −3

k = 10

3

M = 10 6 G = 10 9

T == 10

12

P = 10

15

MATHEMATICAL EQUATIONS b2+ c2 − a2 2bc

c 2 = a 2 + b 2 − 2ab cos C cos A =

FORMULAS Kinematics  d ∆d  v av = v av = ∆t ∆t Dynamics

  FNet = ma

 ∆v  a av = ∆t

  Fg = mg

sin A sin B sin C = == a b c

 (v + v 2 ) d= 1 t 2

  Fk = µ k F N

Wtotal = ∆ EK

EK =

o h

cos θ =

a h

  1  d = v2 t − at 2 2

   v2 = v1 + at

tan θ =

o a

A = πr 2

  1 d = v1 t + at 2 2

C = 2π r

 2  2 v 2 − v1 = 2ad

  Fs ,max = µ S F N

Circular Motion and Universal Gravitation  Gm 1m 2   v2 4π 2 r   Fc = ma c Fg = ac = ac = 2 r2 r T  T = 1/ f ac = 4π 2 rf 2 Work and Energy   W = F ⋅ ∆d

sin θ =

1 mv 2 2

vs =

GmE r

E G = mgh

g=G

m r2

  ETH = F f ⋅ ∆d

G = 6.67 × 10-11 N·m 2 /kg2

ES =

1 2 kx 2

F S = − kx

Momentum    J = Fnet ∆ t = ∆ p

  p = mv

    m1 v1 + m2 v 2 = m1v '1 +m 2 v ' 2

Electrostatics kq1 r2  F a= E m 

E E = qV

ε =

q = Ne  FE = qε

 kq q FE = 12 2 r

EE =

kq1q 2 r

V =

  m − m2    v1 v 1′ =  1  m1 + m 2 

kq1 r

  v 1 

k = 9 .0 × 10 9 N ⋅ m 2 /C 2 e = 1 .6 × 10-19 C m e = 9 .11× 10-31 k g

V = ε⋅d

m p = 1.67 × 10 -27 kg

Magnetism

Φ B == BA cos θ   FM = qvB sinθ

 2 m1  v ′2 =   m1 + m2

µ 0 = 4 π × 10 −−7 T ⋅ m / A  F M == ILB sinθ

 FM µ 0 I 1 I 2 = L 2 πd

V =−

∆Φ ∆t

B=

µ0 I 2πr

B=

µ 0 NI L

Waves and Light n=

c v

c = λf

v =λ f

c = 3.0 × 10 8 m/s

Two Point Sources and Double Slit Diffraction

1  Pn S 1 − Pn S 2 =  n − λ , n== 1,2 ,3,... 2  xn 1λ  = sin θn =  n −  , n = 1,2 ,3,... 2 d L  Single Slit Diffraction

xn nλ , n = 1,2,3,... ≈≈ sinθθn == L w 1  m + λ xm 2 ≈≈ sin θ m =  , m = 1,2,3,... L w Reflection from Thin Films

Pm S 1 − Pm S 2 = mλ , m == 0 ,1,2,... mλ xm ≈ sinθ m = , m = 0 ,1,2,... d L Diffraction Gratings

 1λ sin θ n =  n −  , n = 1,2 ,3,... 2 d 

sin θ m =

mλ , m = 0 ,1,2,... d

Transmission through Thin Films

Note: In these equations, the subscript ‘n’ represents minima or nodes; whereas, ‘m’ represents maxima or anti-nodes....