SPH3U Formula Sheet
Quadratic Formula
Sine/Cosine Laws
2
2
2
c = a + b − 2 ab cos C
sin A
sin B
=
a
sin C
=
b
a ave =
∆d
=
∆E h = mc∆t
∆t
v ave =
∆v
=
∆t
q = Ne
I =
∆t
a∆t
1
2
2
∆t
=
V
R1
I
R2
L1
=
L2
P = IV = I R =
2
4π r
2
c = fλ
=
r
T
2
= 4π rf
2
2
v AB = v AC + v CB
n=
A2
A1
v1
λ2
v2
GMm
r
2
Fg = mg
G = 6.67 × 10
g=
−11 Nm 2
1
VT = V1 + V2 + ...
VT = V1 = V2 = ...
I T = I1 = I 2 = ...
I T = I1 + I 2 + ...
1
=
RT
1
R2
+
1
f
1
=
do
1
P=
=
sin θ1
r
2
Bcoil = µ 0
F f = µ FN
F net = ma
F1
Work, Energy and Power
W = F ∆d cos θ = ∆E
E g = mgh
Ek =
1
2
mv
∆E g = mg ( h2 − h1 )
2
∆E k =
1
2
2
m ( v2
Ek 2 = Ek 1 + W
P=
W
∆t
=
∆E
∆t
P = Fvave
1
mv1 +
2
mgh1 =
∆Ek = −∆E g
F2
V1
V2
L
=
N2
=
N1
N2
I1
µ 0 = 4π × 10
coil
I2
=
I2
I1
s
n2
nsmall
nbig
f1 = f2
n1
+
1
transformers
−7
Tm
A
hi
m=
di
ho
=−
di
do
(diopters)
# images =
360
0
−1
θ
Waves and Sound
vs = 332
f1v s
f2 =
f1
f2
fbeat = f2 − f1
v s ± vo
intensity =
=
d2
=
+ 0.59T
m
s
power
I1
area
I2
L2
d1
=
L1
T1
T2
=
2
=
r2
2
r1
ρ2
ρ1
two free ends or two fixed ends
L=
n
λ
fn = nf1
2
one fixed end one free end
Conservation of Energy
2
−
2
v1 )
=
N1
NI
8 m
sin θ crit =
=
sin θ 2
v = fλ
Electromagnetism
c = 3.00 × 10
f
+ ...
R2
cost of electricity = cost per kWh or MJ × energy used
kg 2
GM
c
Optics
parallel
RT = R1 + R2 + ...
λ1
=
Dynamics
Fg =
T
n1 sin θ1 = n2 sin θ 2
R
2
N
Waves and Light
2
series
∆t
1
f =
v
=
V
∆t
T =
C
q
2
v 2 = v1 + 2 a∆ d
ac =
∆V
−19
∆Ee
2
∆ d = v 2 ∆t − 12 a∆t
v
e = 1.602 × 10
N
f =
∆ d = v1 ∆t +
2
q
R=
2
∆E h = Lv m
v 2 + v1
∆d =
Frequency and Period
Electricity
v 2 = v1 + a∆t
measure1+ measure 2
2
× 100%
2
| measure1 − measure 2 |
% difference =
m1c1 ∆t1 = − m2 c2 ∆t 2
∆E h = L f m
v 2 + v1
useful output energy
× 100%
accepted
total input energy
∆t
measured − accepted
% error =
2a
efficiency =
v 2 − v1
b − 4 ac
Error Formulae
∆t
−b ±
x=
Efficiency and Heat
c
Kinematics
d 2 − d1
v ave =
2
for 0 = ax + bx + c
2
2
1
mv2 + m2 gh2
2
L=
(2 n − 1)
4
λ
f n = (2 n − 1) f1
× 100%