formula physics

7/28/2019 formula physics

http://slidepdf.com/reader/full/formula-physics 1/77

Prepared by:Joselito DL. Torculas, EcE



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.



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.



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”.





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.



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.


SI UNITS OF

MEASUREMENTS



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.


SI UNITS OF

MEASUREMENTS



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)


SI UNITS OF

MEASUREMENTS







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.


SI UNITS OF

MEASUREMENTS



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-



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



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



3. Which of the following is equivalent to the unit“lux”?

a. lumen/m2 c. lux/steradian

b. footcandle/steradian d. lumen/steradian



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



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



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…



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



VECTOR IN SPACE:

Magnitude:

k A j Ai A A z y x

222

z y x A A A A



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



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



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



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





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



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:



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)



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



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.


281.9;..

s

m g mghwh E P

2

2

1.. mv E K



POWER – is the time rate of doing work.

Units conversions for Power:


Fvt

Fd

t

W

P

ergs s

J

W

7

1011

sec5507461

lb ft W hp



11. Who coined the term energy in 1807?

a. William Thomson c. Lord Kelvin

b. Thomas Young d. Ydnar Odalla



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.



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



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



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



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.



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.



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



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



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



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


proportional to its diameter.

2211 l f l f

2211 d f d f



c. Law of Tensions

the frequency of a vibrating string is directly

proportional to the square root of the tension.

d. Law of Densities


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



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.



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





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



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



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.



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.



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).



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)




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.




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.






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



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:


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



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.


receding if

vv

vv f

g approachinif vv

vv f

f

s

o s

s

o s

;

;

'



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







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



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!!!



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



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).





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



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.




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.




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



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





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.



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



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



Documents

formula physics