ENGINEERING

PHYSICS
Correlation Course
RONALD RENON S. QUIRANTE, REE, RMP
Simple Harmonic Motion of
a Spring
𝑇 =2 𝜋
√ 𝑚
𝑘
𝑇=
1
𝑓

𝐹 =𝑘𝑥 Hooke’s Law

𝐹 =𝑚𝑎 Newton’s 2nd Law

𝑉 𝑚𝑎𝑥 = 𝐴 𝜔 𝑎 𝑚𝑎𝑥 = 𝐴 𝜔2
Problem #1
A body hangs from an ideal spring. What is the
frequency of oscillation of the body if its mass m, is
0.015 kg, and k is 0.5 N/m?
A. 0.62 Hz
B. 0.76 Hz
C. 0.84 Hz
D. 0.92 Hz
Problem #2
A 2.5 kg mass undergoes SHM has a maximum
acceleration of 8π m/s2 and a maximum speed of 1.6
m/s. Find the period.
A. 0.2 s
B. 0.3 s
C. 0.4 s
D. 0.5 s
Problem #3
A 2.5 kg mass undergoes SHM and makes 3 vibrations
each second. Compute the acceleration when its
displacement from the equilibrium position is 5 cm.
A. 17.76 m/s2
B. 15.67 m/s2
C. 11.22 m/s2
D. 19.35 m/s2
Simple Harmonic Motion of
a Pendulum

𝑇 =2 𝜋
𝐿
𝑔 √
Where:
T = Time Period
L = Length of string
g = Gravity
Problem #4
On a planet with an unknown value of gravitational
acceleration g, the period of a 0.65 m long pendulum is
2.8 s.
A. 3.27 m/s2
B. 2.21 m/s2
C. 6.67 m/s2
D. 5.15 m/s2
Fundamentals in
Wave Motion

𝑉
𝜆=
𝑓

Where:
λ = wavelength
V = velocity
f = frequency
Problem #5
Waves whose crests are 30 m apart reach an anchored
boat once every 3 s. The wave velocity is ___.
A. 15 m/s
B. 20 m/s
C. 10 m/s
D. 12.5 m/s
Transverse Wave

𝑉=
𝐹𝐿
𝑚 √
Where:
F = tension force
L = length of string
m = mass of string
Problem #6
A rope of length 5 m is stretched to a tension of 80 N. If
its mass is 1 kg, at what speed would a 10 Hz transverse
wave travel down string?
A. 20 m/s
B. 18 m/s
C. 22 m/s
D. 15 m/s
Longitudinal Wave

𝑉=
𝐸
𝜌 √
Where:
V = velocity
E = Young’s Modulus
ρ = density
Problem #7
Compute the speed of sound in steel if its density
is 7900 kg/m3 and its Young’s modulus is 275 GPa.
A. 3500 m/s
B. 4100 m/s
C. 5900 m/s
D. 6700 m/s
Standing Waves in a
Stretched String

𝑓 𝑛 =𝑛
𝑉
2𝐿 ( )
Where:
f = frequency
V = velocity
L = length of string
n = fundamental tone: 1st harmonic, n
= 1; 2nd harmonic (1st overtone), n = 2;
3rd harmonic (2nd overtone), n = 3 …
Problem #8
A 1.5 m long rope is stretched between two supports
with a tension that makes the speed of transverse waves
48 m/s. What is the frequency of the second overtone?
A. 48 Hz
B. 36 Hz
C. 56 Hz
D. 62 Hz
Problem #9
A string has a length of 0.4 m and a mass of 0.16 g. If the
tension in the string is 70 N. Determine the fundamental
frequency of the wave it can produce when plucked?
A. 523 Hz
B. 391 Hz
C. 774 Hz
D. 633 Hz
Speed of Sound in Air

𝑉 𝑎𝑖𝑟 =331+0.6 ( Δ ° 𝐶 )
Problem #10
Find the wavelength in air of a sound wave
whose frequency is 440 Hz.
A. 0.52 m
B. 0.67 m
C. 0.78 m
D. 0.99 m
Problem #11
At 25oC, a sound wave takes 3 s to reach a receiver.
How far away is the receiver from the source?
A. 1000 m
B. 1038 m
C. 1192 m
D. 882 m
Standing Wave in Air
Columns (Open Pipe)

𝑓 𝑛 =𝑛
𝑉
2𝐿 ( )
Where:
f = frequency
V = velocity
L = length of string
n = fundamental tone: 1st harmonic, n
= 1; 2nd harmonic (1st overtone), n = 2;
3rd harmonic (2nd overtone), n = 3 …
Problem #12
The fundamental frequency of a pipe that is open
at both ends is 594 Hz. How long is the pipe?
A. 0.12 m
B. 0.45 m
C. 0.29 m
D. 0.61 m
Standing Wave in Air Columns
(Open-Closed Pipe)

𝑓 𝑛 =𝑛
𝑉
4𝐿 ( )
Where:
f = frequency
V = velocity
L = length of string
n = fundamental tone: 1st harmonic, n
= 1; 2nd harmonic (1st overtone), n = 2;
3rd harmonic (2nd overtone), n = 3 …
Problem #13
An organ pipe that’s closed at one end has a length of
17 cm. If the speed of sound through the air inside is
340 m/s, what is the pipe’s fundamental frequency?
A. 400 Hz
B. 600 Hz
C. 500 Hz
D. 650 Hz
 Sound Intensity
Level or Loudness
𝑃2
𝐼= → Watts/m2 unit
2𝜌 𝑉

𝐵=10 log
( )
𝐼
𝐼𝑜
→ in Decibels (dB) unit

Where:
I = sound intensity
P = pressure
ρ = density; 1.3 kg/m3 or 1.2 kg/m3
V = velocity of sound 343 m/s
Io = 1 x 10-12 W/m2
Problem #14
What is the sound intensity in decibels of a
source with a sound power of 5 x 10-10 watts/m2?
A. 27 dB
B. 36 dB
C. 43 dB
D. 50 dB
Problem #15
What is the intensity level in dB of a sound wave
in air whose pressure amplitude is 0.2 Pa?
A. 56.1 dB
B. 66.7 dB
C. 76.5 dB
D. 88.3 dB
 dB Difference of Two
Sound Intensity Levels
𝐵1=10 log
( )
𝐼1
𝐼𝑜
𝐵2=10 log
( )
𝐼2
𝐼𝑜

𝐵2 − 𝐵1=10 log
( )
𝐼2
𝐼1
Problem #16
How many times more intense is a 50 dB sound
than a 40 dB sound?
A. 6 times
B. 7 times
C. 9 times
D. 10 times
Propagation of Sound

𝑃 2
𝐼 = → 𝐴=4 𝜋 𝑟
𝐴

𝐼2 𝑟 12
=
𝐼1 𝑟2
2
Problem #17
To be effective, an alarm must be heard at a minimum
level of 70 dB. If it is to be effective 60 m away, what is
most nearly the minimum power required?
A. 0.23 W
B. 0.36 W
C. 0.45 W
D. 0.57 W
Problem #18
An observer is 2 m from a source of sound waves. By
how much dB will the sound level decrease if the
observer moves a distance of 20 m?
A. 20 dB
B. 30 dB
C. 40 dB
D. 50 dB
 Doppler Effect

𝑓𝐿 𝑓𝑠
=
𝑉 +𝑉 𝐿 𝑉 −𝑉 𝑠

Where:
VL = listener velocity
Vs = source velocity
V = 343 m/s

𝑉 𝐿 =+→ 𝑡𝑜𝑤𝑎𝑟𝑑𝑠 𝑡h𝑒 𝑠𝑜𝑢𝑟𝑐𝑒 𝑉 𝑠 =+→𝑡𝑜𝑤𝑎𝑟𝑑𝑠 𝑡h𝑒𝑙𝑖𝑠𝑡𝑒𝑛𝑒𝑟

𝑉 𝐿 =−→ 𝑚𝑜𝑣𝑖𝑛𝑔 𝑎𝑤𝑎𝑦 𝑡h𝑒 𝑠𝑜𝑢𝑟𝑐𝑒 𝑉 𝑠 =−→ 𝑚𝑜𝑣𝑖𝑛𝑔 𝑎𝑤𝑎𝑦 𝑡h𝑒 𝑙𝑖𝑠𝑡𝑒𝑛𝑒𝑟
Problem #19
A train whistle emits sound at a frequency of 555 Hz. A person
standing next to the train track hears the whistle at a
frequency of 488 Hz. What is the speed of the approaching
train?
A. 22 m/s
B. 28 m/s
C. 38 m/s
D. 47 m/s
Problem #20
A railroad train is traveling at 30 m/s in still air. The frequency of
the note emitted by the train whistle is 262 Hz. What frequency
is heard by a passenger on a train moving in the opposite
direction to the first at 18 m/s and receding from the first?
A. 190.22 Hz
B. 228.28 Hz
C. 244.34 Hz
D. 315.31 Hz
 Beat Frequency
The difference in the frequency of a given two waves.
Problem #21
Two organ pipes, open on one end but closed at the other, are
each 1.14 m long. One is now lengthened by 2 cm. Find the
frequency of the beat that they produce when playing
together their fundamental.
A. 1.2 Hz
B. 1.4 Hz
C. 1.1 Hz
D. 1.3 Hz
Illumination

𝐼 𝜙
𝐸= 2 → 𝐼=
𝑟 4𝜋
Problem #22
What is the illumination on a surface 3 m below a 150-
watt incandescent lamp that emits a luminous flux of
2275 lm?
A. 18.20 lx
B. 20.12 lx
C. 22.32 lx
D. 24.62 lx
Law of Refraction of Light
(Snell’s Law)

𝑐
𝑛=
𝑉

Where:
c = speed of light (3 x 108 m/s)
Problem #23
What is the approximate speed of light in water?
A. 1.25 x 108 m/s
B. 1.75 x 108 m/s
C. 2.00 x 108 m/s
D. 2.25 x 108 m/s
Problem #24
A beam of light enters a plate of flint glass (n = 1.63) at
angle of incidence of 40o. Find the angle of refraction.
A. 19.15o
B. 27.33o
C. 30.26o
D. 23.23o
Quantum Theory of Light

𝐸 =h𝑓

𝑐
𝜆=
𝑓
Where:
h = Planck’s constant (6.63 x 10-34 J-s)
Problem #25
What is the energy (in electron-volt) of a violet
photon if the wavelength of the light is 470 nm?
A. 1.75 eV
B. 2.65 eV
C. 3.15 eV
D. 4.02 eV
Problem #26
A 19.62-N block moving along a horizontal surface at 10
m/s is acted by upon by a 5 N force of friction. The time
required to bring the block to rest is approximately __.
A. 3.0 s
B. 3.5 s
C. 4.5 s
D. 4.0 s
Problem #27
An object A has a mass of 5 kg and is moving horizontally with velocity
of 5 m/s. Object A is hit by another object, which causes it to reverse
direction. If its new velocity is 10 m/s and the objects were in contact
with each other for 0.02 s, find the average force exerted on object A.
A. 3750 N
B. 4250 N
C. 3910 N
D. 4090 N
Problem #28
A 40 kg skater traveling at 4 m/s overtakes a 60 kg skater
traveling at 2 m/s in the same direction and collides with each
other. If two skater remain in contact, what is their final
velocity?
A. 3.2 m/s
B. 3.7 m/s
C. 2.8 m/s
D. 2.3 m/s
Problem #29
A 1-kg ball moving at 12 m/s collides head-on with a 2-kg ball
moving in the opposite direction at 24 m/s. Determine the
speed of the 1 kg ball after impact if the coefficient of
restitution is equal to 0.667.
A. 28 m/s
B. 4 m/s
C. 12 m/s
D. 24 m/s
 Bodies Bouncing
Back and Forth

2𝑛
h𝑛 =h 0 𝑒

e = coefficient of restitution
Problem #30
A rubber ball is dropped on the ground from a height of
5 m. If the coefficient of restitution is 0.7, find the
height of the 4th rebound.
A. 0.67 m
B. 1.02 m
C. 0.41 m
D. 0.29 m
 Work

𝑊𝑜𝑟𝑘=𝐹𝑜𝑟𝑐𝑒⋅ 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒

𝑊 =𝐹𝑆
Problem #31
A box is dragged across a frictionless floor by a rope which
makes an angle of 60o with the horizontal. If the tension in the
rope is 100 N while the box is dragged 15 m, how much work is
done?
A. 0.75 kJ
B. 1.25 kJ
C. 1.50 kJ
D. 0.56 kJ
Problem #32
A 10-lb block slides 6 ft down a plane inclined 40o with
horizontal. Determine the total work done by all forces acting
on the block. The coefficient of sliding friction is 0.40.
A. 19.112 lb-ft
B. 20.178 lb-ft
C. 22.614 lb-ft
D. 17.951 lb-ft
 Gravitational Potential
Energy
The energy stored in an object due to its positive above
Earth’s surface.

𝑃𝐸=𝑚𝑔h
Problem #33
In raising a 200-kg bronze statue, 10 kJ of work is
performed. How high was it raised?
A. 4.22 m
B. 6.67 m
C. 5.10 m
D. 3.33 m
Elastic Potential Energy
(Spring)

1 2
𝑃𝐸= 𝑘 𝑥
2

′
𝐹 =𝑘𝑥 → 𝐻𝑜𝑜𝑘𝑒 𝑠 𝐿𝑎𝑤
Problem #34
A woman weighing 600 N steps on a bathroom scale
containing stiff spring. Find the work done on the spring
if the spring is compressed 1 cm under her weight.
A. 1 J
B. 2 J
C. 3 J
D. 4 J
 Kinetic Energy
(Linear Motion)
The energy that objects possess due to their motion.

1 2
𝐾𝐸 = 𝑚 𝑉
2
Problem #35
What is most nearly the kinetic energy of a 3924
N motorcycle travelling at 40 kph?
A. 20.1 kJ
B. 18.6 kJ
C. 24.7 kJ
D. 29.3 kJ
 Kinetic Energy
(Rotational Motion)
The energy that objects possess due to their motion.

1 2
𝐾𝐸 = 𝐼 𝑊
2
I = Mass of Inertia
1 2 2 2 2 2
𝐼 = 𝑚 𝑟 →𝐶𝑦𝑙𝑖𝑛𝑑𝑒𝑟 𝑜𝑟 𝐷𝑖𝑠𝑘 𝐼 = 𝑚 𝑟 → 𝑆𝑜𝑙𝑖𝑑 𝑆𝑝h𝑒𝑟𝑒 𝐼 = 𝑚 𝑟 → 𝑇h𝑖𝑛− 𝑤𝑎𝑙𝑙𝑒𝑑 𝐻𝑜𝑙𝑙𝑜𝑤𝑒𝑑 𝑆𝑝h𝑒𝑟𝑒
2 5 3
Problem #36
A 1-kg phonograph turntable has a diameter of 34 cm.
What is its kinetic energy when it rotates at 45 rpm?
A. 0.16 J
B. 0.67 J
C. 0.25 J
D. 0.42 J
Problem #37
What is total kinetic energy of a 3 kg ball whose
diameter is 15 cm, if it rolls across a level surface with a
speed of 2 m/s?
A. 3.1 J
B. 1.9 J
C. 2.4 J
D. 4.5 J
 Rest Energy

2
𝐸 =𝑚 𝑐

c = speed of light (3 x 108 m/s)

Problem #38
What mass of fuel is used in a nuclear power plant that
produces nuclear energy at the rate of 1 gigawatt during
the whole year?
A. 0.45 kg
B. 0.35 kg
C. 0.28 kg
D. 0.58 kg
Power Needed to Move an
Object Horizontally

𝑃=𝐹𝑉
Problem #39
An automobile uses 74.6 kW to maintain a uniform
speed of 96 kph. What is the thrust force provided by
the engine?
A. 2.21 kN
B. 2.79 kN
C. 3.54 kN
D. 3.92 kN
Power Needed to Move an
Object Vertically

𝑚𝑔h
𝑃=
𝑡
Problem #40
By the use of a pulley a man raises a load of 50 kg to a
height of 15 m in 65 s. Find the average power required.
A. 98 W
B. 156 W
C. 81 W
D. 113 W
 Law of Conservation
of Energy
Energy cannot be created nor destroyed, but it can be
change from one form to another.

𝑃𝐸 1+ 𝐾𝐸 1=𝑃𝐸 2+ 𝐾𝐸 2

1 2 1 2
𝑚𝑔h1 + 𝑚 𝑉 1 =𝑚𝑔h 2+ 𝑚 𝑉 2
2 2
Problem #41
A 3 kg frictionless cart moves with velocity of 2.5 m/s
towards a 30o ramp. How far up the ramp does the cart
travel before stopping?
A. 0.55 m
B. 0.75 m
C. 0.83 m
D. 0.64 m
Problem #42
A ball is being whirled vertically at a constant energy at the
end of an 80-cm string. If the ball’s speed at the top of the
circle is 3 m/s, what is its speed at the bottom of the circle?
A. 6.36 m/s
B. 5.75 m/s
C. 8.42 m/s
D. 4.33 m/s
Problem #43
A spring loaded toy cannon has a spring constant with k =
5 N/m, which is compressed 20 cm. When it is released, a
0.2 kg plastic ball will attain a muzzle velocity of ___.
A. 0.5 m/s
B. 1.0 m/s
C. 1.5 m/s
D. 2.0 m/s
Problem #44
A 2-kg block is dropped from a height of 40 cm onto a
spring whose force constant is 1960 N/m. Find the
maximum distance the spring will be compressed.
A. 10 cm
B. 15 cm
C. 18 cm
D. 20 cm
Relationship between
Work and Energy

1 2 1 2
𝐹𝑆= 𝑚𝑉 + 𝑚 𝑉 0
2 2
Problem #45
A pool cue striking a stationary billiard ball (mass = 0.25 kg)
gives the ball a speed of 2 m/s. If the average force of the cue
on the ball was 200 N, over what distance did this force act?
A. 0.15 cm
B. 0.20 cm
C. 0.25 cm
D. 0.30 cm
Torque (Newton’s Law
on Angular Motion)

𝑇 =𝐼 𝛼

𝑇 =𝑟𝐹 sin 𝜃
 Power Developed by the
Exerting Torque

2 𝜋 𝑁𝑇
𝑃=
𝑘

k = 60 when N = rpm and T = N-m

= 44,760 when N = rpm and T = N-m (P = hp unit)
= 33,000 when N = rpm and T = lb-ft (P = hp unit)
Problem #46
Determine the torque needed to bring a turbine
whose moment of inertia is 60 slugs-ft2 to rest in 12 s
from an initial speed of 764 rpm
A. 250 lb-ft
B. 350 lb-ft
C. 400 lb-ft
D. 430 lb-ft
Problem #47
A flywheel whose moment of inertia is 6 kg-m2 is acted
upon by a constant torque of 50 N-m. How long does it
take to go from rest to a velocity of 90 rad/s?
A. 8.6 s
B. 7.4 s
C. 9.5 s
D. 10.8 s
 Newton’s Law of
Universal Gravitation
Gravitational Acceleration at any point above earth:

𝐺 𝑚𝑒
𝑔= 2
𝑅
G = Gravitational constant = 6.667 x 10-11 Nm2/kg2
me = mass of Earth = 6 x 1024 kg
Re = radius of Earth = 6400 km
Problem #48
Find the weight of an 80-kg person at an altitude
of 2000 km.
A. 393.1 N
B. 453.6 N
C. 481.4 N
D. 367.3 N
 Newton’s Law of
Universal Gravitation
Velocity of Satellite Revolving about Earth:

𝑉=
𝐺 𝑚𝑒
𝑅 √
G = Gravitational constant = 6.667 x 10-11 Nm2/kg2
me = mass of Earth = 6 x 1024 kg
Re = radius of Earth = 6400 km
Problem #49
An artificial satellite is to be put in orbit at an altitude of
15,000 km. What speed must be given to make it go on
a circular orbit?
A. 4324.45 m/s
B. 4611.63 m/s
C. 3952.12 m/s
D. 3689.71 m/s
 Newton’s Law of
Universal Gravitation
Period of a Revolving Satellite:

𝑇=
2𝜋 𝑅
𝑉
=2 𝜋
𝑅
𝑔
G = Gravitational constant = 6.667 x 10-11 Nm2/kg2
me = mass of Earth = 6 x 1024 kg
√
Re = radius of Earth = 6400 km
Problem #50
Suppose that a satellite is placed in a circular point orbit
100 miles above the earth’s surface. Determine the time (in
hour) required for one complete revolution of the satellite?
A. 3.33
B. 2.78
C. 1.48
D. 1.02