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7/28/2019 formula physics
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Prepared by:Joselito DL. Torculas, EcE
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PHYSICS
is a branch of science which deals with the study of
matter, energy, force and motion and the way theyrelate to each other.
is an “experimental science” wherein we observe
the phenomena and nature and try to find patterns
and principles that relate these phenomena.
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MEASUREMENT
is the process of determining the amount, quantity,degree or capacity by comparison with an accepted
standard.
PRECISION – is a measure of the consistency or
repeatability of measurements.
ACCURACY – is the degree of exactness of a
measurement compared to the expected value, or
the most probable value of the variable being
measured.
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THE TWO SYSTEM OF
MEASUREMENTS
1. ENGLISH SYSTEM
also called the BRITISH SYSTEM.
used only in the United States and some African
countries.
the system of unit used is the FPS or the “foot-
pound-second”.
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THE SEVEN FUNDAMENTAL
SI UNITS OF
MEASUREMENTS
1. METER (m)
the unit of length.
in 1960, a meter is measured using the
wavelength of the orange-red light emitted by
atoms of krypton in a glow discharge tube.
but in November 1983, the length standard was
changed again: a meter is the distance that
light travels in a vacuum in 1/299792458
second.
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2. KILOGRAM (kg)
the unit of mass.
is defined to be the mass of a particular cylindrical slab of platinum-iridium alloy.
this cylinder is kept at constant temperature and
humidity in a dustless vault in Sevres near Paris,
France.
THE SEVEN FUNDAMENTAL
SI UNITS OF
MEASUREMENTS
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3. SECOND (s) the unit of time.
from 1889 until 1967, it was defined as a certainfraction of the mean solar day, the average time
between successive arrivals of the sun at its highestpoint in the sky.
from 1967 up to present, a second is based on anatomic clock, which uses the energy difference betweenthe two lowest energy states of the cesium-133atom.
when bombarded by microwaves of precisely theproper frequency, cesium atoms undergo a transitionfrom one of these states to the other.
a second is defined as the time required
for 9192631770 cycles of this radiation.
THE SEVEN FUNDAMENTAL
SI UNITS OF
MEASUREMENTS
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4. KELVIN (K)
the unit of temperature.
named after William Thomson, commonly
known as Lord Kelvin, the 1st baron of Kelvin.
the standard is based on the point at which solid,
liquid and gaseous water coexist simultaneously
(the “triple point” which has an assigned value of
273.16 K)
THE SEVEN FUNDAMENTAL
SI UNITS OF
MEASUREMENTS
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7. MOLE (mol)
the unit for number of particles. the standard is based on the number of atoms
contained in a 0.012 kilogram of carbon-12
isotope.
THE SEVEN FUNDAMENTAL
SI UNITS OF
MEASUREMENTS
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SI PREFIXES FOR POWERS OF
10
POWER OF TEN PREFIX POWER OF TEN PREFIX
10-24 yocto- 1024 yotta-
10-21 zepto- 1021 zetta-
10-18 atto- 1018 exa-10-15 femto- 1015 peta-
10-12 pico- 1012 tera-
10-9 nano- 109 giga-
10-6
micro- 106
mega-10-3 milli- 103 kilo-
10-2 centi- 102 hecto-
10-1 deci- 101 deka-
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1. One newton is equivalent to?
a. 1 kg-m c. 1 kg-m/s
2
b. 1 kg-m/s d. 1 m/s2
CONVERSION FACTORS:
1 lbf = 4.45 N ; 1 dyne = 10-5 N
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2. A weight of 1 x 10-15 gram is also equivalent to
a. 1 femtogram c. 1 picogram
b. 1 attogram d. 1 yoctogram
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3. Which of the following is equivalent to the unit“lux”?
a. lumen/m2 c. lux/steradian
b. footcandle/steradian d. lumen/steradian
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4. What refers to the mass which is accelerated atthe rate of one foot per second per second whenacted on by a force of one pound?
a. 1 slug c. 1 dyne
b. 1 erg d. 1 BTU
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5. The size of the largest atom is in the order of
a. centimeter c. nanometer
b. millimeter d. micrometer
size of some bacteria and living cells is in the order of
MICROMETERS
diameter of the point of a ballpen is in the order of MILLIMETERS
diameter of our little finger is in the order of CENTIMETERS
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VECTOR AND SCALAR QUANTITIES
SCALAR QUANTITY
is a physical quantity which has magnitude only.
examples are volume, temperature, height, mass,age, speed, distance, etc…
VECTOR QUANTITY
is a physical quantity which has both magnitudeand direction.
examples are force, velocity, displacement,
momentum, weight, acceleration, etc…
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VECTOR IN A PLANE:
where:
a. Magnitude:
b. Angle with the horizontal (direction):
j Ai A A y x
sin
cos
A A
A A
y
x
22 y x A A A
x
y
A
A1
tan
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VECTOR IN SPACE:
Magnitude:
k A j Ai A A z y x
222
z y x A A A A
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OPERATION ON VECTORS
If you are given two vectors in space:
We can perform these operations:
1. ADDITION
2. SUBTRACTION
k A j Ai A A z y x
k B j Bi B B z y x
k B A j B Ai B A B A z z y y x x
k B A j B Ai B A B A z z y y x x
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3. MULTIPLICATION
a. DOT PRODUCT (SCALAR PRODUCT)
b. CROSS PRODUCT (VECTOR PRODUCT)
OPERATION ON VECTORS
cos B A B A B A B A B A z z y y x x
z y x
z y x
B B B
A A Ak ji
B A
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RESULTANT OF TWO OR MORE
VECTORS
Magnitude:
Direction (for plane vectors only)
k F j F i F R z y x
222
z y x F F F R
x
y
F
F 1tan
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6. It is simply a vector whose magnitude is 1.
a. moment vector c. unit vector
b. tensor d. vector unity
k A j Ai A A z y x
222 z y x
z y x
A A A
k A j Ai Aa
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8. Determine the magnitude of the resultant of thefollowing forces: A = 600 N @ 40o, B = 800 N @ 1600 and C = 200 N @ 300o.
a. 532.78 N c. 522.68 N
b. 435.94 N d. 627.89 N
j F i F R y x
22
y x F F R
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9. A rope is stretched between two rigid poles 40 ft apart.A load of 100 lbs was placed at the midpoint of the ropethat caused it to sag 5 ft. What is the approximatetension in the rope in lbs?
a. 190 c. 206
b. 180 d. 215
0;0 y x F F
First Condition for Equilibrium:
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10. Two perpendicular vectors are given in terms of their components by U = Uxi – 4j + 6k and V = 3i + 2j– 3k. Determine the component Ux.
a. 5.67 c. 7.67
b. 6.67 d. 8.67
cos B A B A B A B A B A z z y y x x
DOT PRODUCT (SCALAR PRODUCT)
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WORK, ENERGY and POWER
WORK – is defined as the product of the force and
displacement in the direction of the force.
where:
F : force
d : displacementθ : angle between the force and displacement
)0(;cos if Fd W Fd W
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ENERGY – is the capability to do work.
a. POTENTIAL ENERGY – is the energy possessed by an
object by virtue of its position or configuration.
b. KINETIC ENERGY – is the energy possessed by an
object by virtue of its motion.
WORK, ENERGY and POWER
281.9;..
s
m g mghwh E P
2
2
1.. mv E K
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POWER – is the time rate of doing work.
Units conversions for Power:
WORK, ENERGY and POWER
Fvt
Fd
t
W
P
ergs s
J
W
7
1011
sec5507461
lb ft W hp
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11. Who coined the term energy in 1807?
a. William Thomson c. Lord Kelvin
b. Thomas Young d. Ydnar Odalla
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12. The sum of potential and kinetic energies present in
a system is called what?
a. kinetic energy c. rest energy
b. potential energy d. mechanical energy
POTENTIAL ENERGY – is the energy possessed by an object by virtue of
its position or configuration.
KINETIC ENERGY–
is the energy possessed by an object by virtue of itsmotion.
REST ENERGY – the energy something possesses by virtue of its mass.
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13. A force of 200 lbf
acts on a block at an angle of 28o with respect to horizontal. The block is pushed 2feet horizontally. What is the work done by thisforce?
a. 320 J c. 476 J
b. 540 J d. 215 J
cos Fd W
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14. At her highest point, a girl on the swing is 7 feetabove the ground, and at her lowest point, she is3 feet above the ground. What is her maximumvelocity?
a. 10 fps c. 14 fps
b. 12 fps d. 16 fps
.... E K E P
2
2
1mvmgh
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15. A 0.25 hp motor is used to lift a load at the rate of 5cm/s. How great a load can it lift at this constantspeed?
a. 381 kg c. 421 kg
b. 350 kg d. 400 kg
Fvt
Fd
t
W P
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WAVE
is a vibratory disturbance that moves through a
medium.
they are produced in all forms of matter even in
empty space where ordinary matter does not
exist.
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TYPES OF WAVES
1. TRANSVERSE WAVE a wave in which the vibration direction is
perpendicular to the direction of the wave
propagation.
examples are water waves, waves in strings under tension, electromagnetic waves (light and radio
waves).
in a transverse wave, the maximum upward
displacement is known as CREST and the maximum
downward displacement is known as TROUGH.
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2. LONGITUDINAL WAVE
a wave in which the vibration direction is parallel to
the direction of propagation.
examples are sound waves, waves in rods and in
vibrating helical spring.
in a longitudinal wave, the area of maximum
compression is called CONDENSATION while the
area of maximum separation is called
RAREFACTION.
TYPES OF WAVES
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WAVE EQUATIONS:
1. WAVE VELOCITY – the distance through whicheach wave moves per second.
a. Velocity of a Transverse Waveson a stretched string:
b. Velocity of Longitudinal Waves
in solids and liquids:
c. Velocity of Longitudinal Waves
in gases:
f t
v
linear
F m Fl v
E v
MW
kRT v
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2. FUNDAMENTAL FREQUENCY OF A STRETCHEDSTRING
For the nth harmonic:
linear
F
l m
Fl
l l
v
f 2
1
2
1
21
1 f n f n
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3. LAWS OF VIBRATING STRING
a. Law of Lengths
the frequency of a vibrating string is inversely
proportional to its length.
b. Law of Diameters
the frequency of a vibrating string is inversely
proportional to its diameter.
2211 l f l f
2211 d f d f
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c. Law of Tensions
the frequency of a vibrating string is directly
proportional to the square root of the tension.
d. Law of Densities
the frequency of a vibrating string is inversely
proportional to the square root of its density.
3. LAWS OF VIBRATING STRING
2
1
2
1
F F
f f
1
2
2
1
f
f
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16. What refers to the scattering of a wave behind anobstruction?
a. dispersion c. refraction
b. reflection d. diffraction
DISPERSION – occurs when a beam containing more than one
frequency is split into corresponding number of different beams when
refracted.
REFLECTION – is a phenomenon of wave motion in which a wave isreturned after impinging on a surface.
REFRACTION – is the bending of light rays as they pass obliquely from
one medium to another medium of different optical densities.
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17. A wave that needs a material medium throughwhich it can travel as it transfers energy is called
a. radiowave c. microwave
b. mechanical wave d. EM wave
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19. What is the speed of sound in neon gas attemperature of 18oC considering that the molecularmass of this gas is 20.18 g/mol? Neon is monoatomic,use cp/cv = 1.67.
a. 321.7 m/s c. 447.5 m/s
b. 478.6 m/s d. 543.7 m/s
VELOCITY OF LONGITUDINAL WAVES IN GASES:
MW
kRT v
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20. A string of length 4 meters was initially vibrated atits fundamental frequency, which is 60 Hz. Whatwill be the new length of this string (other factorsconsidered to be the same) at its 8th harmonic?
a. 0.5 m c. 0.75 m
b. 0.67 m d. 1 m
LAW OF LENGTHS:
2211 L f L f
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SOUND is a disturbance or vibration whose energy must be
communicated into a medium.
is an example of a longitudinal wave.
definition is completed by these three very important
things: (1) there must be a vibrating body (2) there
must be a medium to transmit the vibration and (3)
there must be a receiver to detect the sound.
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Nature of Sound Waves
1. INFRASONIC WAVES – sound with frequencies
below 20 Hz.
2. SONIC WAVES – sound with frequencies from
20 Hz to 20 kHz.
3. ULTRASONIC WAVES – sound with frequencies
above 20 kHz.
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Characteristics of Sound
1. PITCH
is the highness or lowness of a note or tone.
is the property of sound which depends on the
frequency of the waves received by the ear.
subjected unit is MEL (as proposed by Stevens,
Volkmann and Newman in 1937).
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2. LOUDNESS
is an observer’s auditory impression of the
strength of the sound and is associated with therate at which energy is transmitted to the ear.
it depends on the amplitude of the vibration of
sound.
subjected unit is SONE (as proposed by StanleySmith Stevens in 1936)
Characteristics of Sound
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3. INTENSITY
refers to the power carried by the sound through a
unit area erected perpendicular to the direction of
propagation of the wave.
it depends on many factors: amplitude and area of
the vibrating body, distance of the source of sound
from the receiver and density of the medium
through which sound is transmitted. unit is in W/m2.
Characteristics of Sound
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4. TIMBRE
the quality of sound related to harmonic
structure.
the characteristic of sound which enables us to
distinguish between two sound produced by two
different person or two different musical
instrument.
Characteristics of Sound
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b. SOUND INTENSITY LEVEL (IdB)
where:
I 0
: threshold of hearing (1 x 10-12 W/m2)
Formulas in Relation to Sound
0log10 I
I
I dB
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c. SPEED OF SOUND (v)
i. in AIR
Speed of sound v1 and v2 at absolute
temperatures T1 and T2:
ii. in IDEAL GAS:
iii. in other materials:
Formulas in Relation to Sound
C T
T
C T T
vC
K
C C
20;273
45.331
20;607.045.331
2
1
2
1
T
T
v
v
MW
kRT v
E v
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d. DOPPLER EFFECT
proposed by Austrian physicist Christian Johann Doppler in1842.
is the apparent rise and fall in pitch of the sound of a sounding
body as the sounding body or observer approaches/leaves the
observer or sounding body.
Formulas in Relation to Sound
receding if
vv
vv f
g approachinif vv
vv f
f
s
o s
s
o s
;
;
'
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21. When a person tells you that the pitch of yourvoice is high, he is referring to
a. the intensity of your voiceb. the number of sound waves you are sending
out per second
c. the loudness of your voice
d. the quality of your voice
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23. What part of the human ear where sound energy is
converted into electrical energy?
a. ear drum c. tympanum
b. cochlea d. ear canal
COCHLEA
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24. Two cars A and B are traveling toward each other atspeeds of 45 kph and 70 kph respectively. If A blowsits horn, what is the relative pitch heard by apassenger in B considering that the velocity of sound is 344 m/s?
a. 1.043 c. 1.096
b. 1.021 d. 1.078
DOPPLER EFFECT!!!
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25. An explosion occurs at a distance of 4 km from theobserver. How long after the explosion does aperson hear if the temperature is 18oC?
a. 14.58 secs c. 11.69 secs
b. 12.45 secs d. 17.54 secs
C T if T v oC 20;6.045.331
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LIGHT
is an electromagnetic radiation with a wavelength
that is visible to the unaided eye.
is any electromagnetic radiation ranging from 700
nm (red light) to 400 nm (violet light).
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2. CORPUSCULAR THEORY
also called the PARTICLE THEORY of light.
proposed by Isaac Newton.
describes light as being composed of tiny particles
called corpuscles sent out by luminous bodies and
which behave like tiny elastic balls.
however, most scientists did not favor this theory for it
can explain the reflection of light but not the refractionof light.
Theories about the Nature of Light
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3. ELECTROMAGNETIC THEORY
proposed by James Clerk Maxwell.
explains that light is the result of the oscillations of the
electrically charged particles of the atoms.
Theories about the Nature of Light
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4. QUANTUM THEORY
proposed by Max Planck.
it advanced the idea that light is energy called photonsor quanta which are transmitted in small bundles or
quantities from luminous bodies and which, upon
entering the eyes, make us able to see.
Theories about the Nature of Light
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Formulas in Relation to Light
a. Wavelength of Light in a Medium
b. Snell’s Law of Refraction
i. in terms of speed of light:
ii. in terms of refractive index:
n f
c 0
r i cc sinsin 21
r i nn sinsin 21
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c. Energy of a photon
d. Malus’ Law
the intensity of light that passed through the polarizer is
equal to the product of the maximum intensity and the
square of the cosine of the polarizing angle.
Formulas in Relation to Light
f h E
20 cos I I
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27. One of the common defects of vision called farsightedness is more technically termed as
a. astigmatism c. myopia
b. hyperopia d. presbyopia
ASTIGMATISM – defect of vision caused by the cornea having
different curvatures in different planes.
MYOPIA – defect of vision commonly called as nearsightedness.PRESBYOPIA – defect of vision caused by aging.
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28. What is the wavelength of yellow light whosefrequency is 500 THz?
a. 800 nm c. 600 nmb. 200 nm d. 700 nm
f c
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29. What is the angle of refraction of light as the beamof parallel light enters a block of ice at an angle of incidence of 30o? (the index of refraction of ice is 1.31and that of air is 1.0).
a. 45o c. 30o
b. 22o d. 28o
SNELL’S LAW
2211 sinsin nn