Compilation of Engineering physics 2 topic.

1. ENGINEERING
PHYSICS 2
Prepared by: Grail Papat-iw

2. PERIODIC MOTION
– repeated pattern of motion.
1) Cycle – one complete rotation.
2) Period – time to complete one cycle.
3) Frequency – number of cycles per unit
time.
4) Amplitude – maximum displacement.
SIMPLE HARMONIC MOTION
– a periodic motion that obeys Hookes Law.
• Hookes Law – the restoring force(fr) is
directly proportional to the displacement(x).
•Restoring Force – a force that pulls the
object back to the equilibrium position.
Fr =
𝑘
𝑥
where: k = spring content in
𝑁
𝑀

3. 2 OBJECTS THAT UNDERGO SHM
1) Spring Mass System
• Period of a spring mass system
T = 2 𝜋
𝑚
𝑘
, 1 sec where: m = mass in
k = spring constant in
𝑁
𝑀
Acceleration:
am =
𝐴−𝐾
𝑚
,
𝑚
𝑠2 maximum at any displacement, x :
am =
𝑋. 𝐾
𝑚
,
𝑚
𝑠2

4. Speed:
vm = A
𝐾
𝑚
,
𝑚
𝑠
at any displacement:
vx = (𝐴2−𝑋2 )
𝑘
𝑚
.
𝑚
𝑠
2) Simple Pendulum
L = length of string
m = Mass of pendulum
𝑇 = 2𝜋
𝐿
𝑔
g = gravitational acceleration
(9.8 𝑚/𝑠2 𝑜𝑟 980 𝑐𝑚/𝑠2)

5. WAVES:
- disturbance thru a medium.
• Medium – any material in which the waves travel (ex.
water, air, land).
2 TYPES OF WAVES
1) Transverse – particles of the wave and the motion of the wave
are perpendicular.

6. 2) Longitudinal or Compressional
– the particles of the wave and the motion are parallel.
• Compression – particles are very near each other.
• Rarefaction – particles are far from each other.
Speed of a Transverse Waves
1) V = XF where: v = speed in m/s
f = frequency in cps
λ = wavelength in m
• Wavelength – distance between two common points of
waves.

7. 2) V =
𝑇𝑒
𝑚/𝑙
where: Te = tension in the cord or string in
newton.
M = mass of the string kg
L = length of the string m
SPEED OFA TRANSVERSE WAVE:
V= f ℓ V =
𝑇𝑅
𝑚/𝑙
where: TR = tension of the string in N.
m = mass of a string
l = length of string
ℓ = wavelength

8. Example: 1) A string is made to vibrate at 120hz . If it has a
transverse wave of 31cm wavelength, find:
a) Speed b) Tension of the mass of the string is 1.20N.
Solution:
a) v = λ f b) v =
𝑇𝑒
𝑚/𝑙
=
120 𝑐𝑦𝑐𝑙𝑒𝑠
𝑠𝑒𝑐
𝑣2 =
𝑇𝑒
𝑚/𝑙
v =
3720 𝑐𝑦𝑐𝑙𝑒𝑠/𝑠𝑒𝑐
100
Te = 𝑣2
(m/l)
v = 37.20 m/s = 37.2 m/s
0.59 ∗
1 𝑘𝑔
1000𝑔
50𝑐𝑚 ∗
10𝑚
100𝑐𝑚
= 1.3838 N

9. Standing Waves:
– waves created whenever two or more waves coming
from opposite ends of a string meet.
Sound Waves:
– are compressional waves in a material medium such as air
water, land.
Speed of Sound in Air (v)
V = 331 m/s at 0˚ celcium temperature.
* A change of 0.6m/s happens for every 1˚C change in
temperature.

10. DOPPLER:
– change in the frequency of sound heard by a observer due
to a moving wave source.
Freq. fo = fi
𝑣 ± 𝑣𝑜
𝑣 ±𝑣𝑠
fo = frequency heard by observer
fs = frequency emitted by observer
vo = speed by observer
vs = speed of sound source

11. ELECTROSTATIC:
– study of electricity at rest.
LAWS ON ELECTROSTATIC:
1) “Like charges repel and unlike charges attract”.
CHARGES
1. Positive – proton (+)
2. Negative – electron (–)
Force of repulsion
Force of attraction

12. 2) COULOMBS LAW (Charles Agustin de Coulumb)
– the force between two charges is directly proportional
to the product of the two charges and inversely proportional
to the square of the distance between them.
F =
𝐾 𝑄1, 𝑄2
𝑟2
where : F = force of attraction or repulsion , N
Q1, Q2 = charges in Coulomb (c)
r = distance between the two charges
k = constant of proportionality
9 ∗ 109 𝑁.𝑚2
𝑐2

13. Example: 1) Two charges, Q1 = 5 ∗ 10−6 𝐶 and Q2 =
10 ∗ 10−6 𝐶 are placed 5cm apart.
a) Find the force between them
b) If the force between them increased by 10%, what should
be the distance between them?
Solution:
a) F =
𝐾𝑄1,𝑄2
𝑟2 b) F = 180 + 10% (180)
=
9∗109(5∗10−6)(10∗10−6)
(0.05)2 = 198 N
= 180 N r =
𝑘𝑄1,𝑄2
𝐹
=
9∗10−9(5∗10−6)(10∗10−6)
198
= 0.0477 m

14. ELECTRIC FIELD
- an imagenary region sorrounding a changed object.
∈ =
𝐾𝑄
𝑟2 ,
𝑁
𝐶
OR ∈ =
𝐹
𝑄
Potential Difference (v)
- work done in moving a charge from one point to another
within an electric field.
- also called electromotive force (emf) and voltage.
v =
𝑤
𝑞
,
𝑗𝑜𝑢𝑙𝑒
𝑐
𝑜𝑟 𝑣𝑜𝑙𝑡
w = Vq = (Va – Vb)q – from point B to point A
= (Vb – Va)q – from point A to point B

15. CAPACITOR
- a device the temporarily stores electric charge.
CAPACITANCE (C)
- increase the amount of charge stored in a capacitor.
c =
𝑄
𝑉
,
𝑐𝑜𝑢𝑙𝑜𝑚𝑏 𝑐
𝑣𝑜𝑙𝑡 (𝑣)
or farad (f)
Electrical Power (p)
- product of current and voltage.
P = IV , P =
𝑉2
𝑅
, 𝑃 = 𝐼2
𝑅 in watt or
horsepower(HP) = 746 watts
Electrical Energy (w)
- product of power of times.

16. W = p.t , juole = watt-sec or kilowatthour (kwHr) 3.6 ∗ 106
joules
*After 1 day (20 hrs)
wt= Pztr
=
1792 (24 ℎ𝑟𝑠)
1000
= 43,008 kwHr
Cost of Electricity
- total energy in kwHr * cost kwHr
Cost if c/kwHr is : ₱8.00
Cost : 43.008 kwHr *
₱8.00
𝑘𝑤𝐻𝑟
= ₱344.064

17. DYNAMIC ELECTRICITY
- continuous movement of charge.
3 Basic Electrical Quantities
1. Current (I)
- ratio of charge over time.
I =
𝑄
𝑡
,
𝐶
𝑆
𝑜𝑟 𝐴𝑚𝑝𝑒𝑟𝑒
2. Potential Difference, Voltage or Electromotive Force
(EMF)
- source of electrical energy in volts.
3. Resistance (R)
- property of a material to resist current flow.
unit : OHMS (Ώ)

18. OHM’S LAW (by GEORGE SIMON OHM)
- “The current is directly proportional to voltage but
inversely proportional to the resistance.”
I =
𝑉
𝑅
Electric Circuit
- path of current flows.
3 Important Elements
v R electrical load
connecting wire (conductor)
voltage source

19. Series Resistances
Char:
R1 1. 𝐼 𝑇 = 𝐼1 = 𝐼2 = 𝐼3
2. 𝑅 𝑇 = 𝑅1 = 𝑅2 = 𝑅3
R2 3. 𝑉𝑇 = 𝑉1 + 𝑉2 + 𝑉3
R3
Ι

20. Parallel Resistance
V 𝐼 𝑇 𝑅1 𝑅2 𝑅3
𝐼1 𝐼2 𝐼3
Char:
1. 𝑅 𝑇 =
1
1
𝑅1
+
1
𝑅2
+
1
𝑅3
2. 𝐼 𝑇 = 𝐼1 + 𝐼2 + 𝐼3
3. 𝑉𝑇 = 𝑉1 + 𝑉2 + 𝑉3

21. 2 Kinds of Current
1. DC (Direct Current)
- direction is only one.
2. AC (Alternating Current)
- current direction reverses
2 Kinds of Current Direction
1. Electron Flow
- negative (‒) to pasitive (+)
2. Connection Flow
- positive (+) to neagative (‒)

22. KIRCHHOFFS LAW (Gustav Robert Kirchhoff)
- used to analyze circuits with more than one voltage
source.
1. Current Law (KCL)
- “The algebraic sum of currents entering and leaving
the same node is zero.”
Node – junction/point where two or three branches meet.
2. Voltage Law (KVL)
- “The algebraic sum of the voltage sources around a
closed path is zero.”

23. FORCES IN MAGNETIC FIELDS
- an imaginary region surrounding a magnet.
Magnet - a material that possesses magnetism and can
attract small pieces of iron/metals.
2 Kinds of Magnetism
1. Permanent
2. Temporary
- magnetism is created whenever current passes thru a
wire.
Ex: Wire – known as electromagnetism
S N

24. Forces exists in a magnetic field whenever:
a) A charge moves through it
F = qVßsinθ
F = force in newton
q = charge in coulomb
v = speed of charge in m/s
ß = magnetic field in Tesla
θ = angle between the magnetic field and speed

25. b) Current in a magnetic field
F = ßILsinθ
Where: I = current
L = length of conductor
θ = angle between I and ß
Direction of Force
- determined using RIGHT –HAND RULE (RHR)
Thumb – V/I direction
Index
Magnetic filed
Middle -Force
Y
X