formulas for physics

8/6/2019 Formulas for Physics

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Formulas

Kinematics

Distance=Speed/Time

Displacement

Total Displacement

5 Key Equations


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Newtons Laws

Force of Gravity

First Law net external force is 0, object will be at rest or continue to move at constant velocity

Third Law every action force, there is a simultaneous reaction force that is equal in magnitude, but

opposite in direction

Coefficient of friction ()

G in the equation above is always 6.67x10^-11

Km/h ---- m/s is divided by 3.6


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Sound & Waves

Vibration cyclical motion of an object about an equilibrium point

o All Vibrations need a medium to transfer wavesMechanical Wave transfer of energy through a material due to vibration

o Vibration is caused by disturbance in mediumMedium material that permits transfer the transmission of energy through vibrations (s,l,g)

NetMotion displacement of a particle over a certain time interval; difference bet. particless initialpoint & final positions.

Elastic property of a medium that returns to its original shape after being disturbed

TranslationalMolecularMotion straight-line motion of molecule; is typically gases bec. particles in

liquids & solids are not free to move in this manner

Speed if a wave & distance it can travel depend on composition of medium. Rigid medium allows a wave

to travel faster & longer than less rigid medium. Less rigid disperses more energy, thus reducing speed &

distance wave can travel.

Types of Waves

Transverse wave wave in which particle vibrate perpendicular to the direction of the flow of energy

Longitudinal wave wave in which particles vibrate parallel to the direction of the flow of energy

In a fluid, longitudinal waves transfer energy through regions of higher & lower pressure. These regionsare called compressions & rarefactions.

Compression region in a longitudinal wave in which the mediums particles are closer together

Rarefaction region in a longitudinal wave in which the mediums particles are farther apart

Sound a form of energy produced by rapidly vibrating objects detectable by sensory organs such as the

ear

Many wave motions are a combo of longitudinal & transverse motion

Wave Characteristics

- Based on both wave shape & behavior of a wave in timeAmplitude max displacement of a wave from its equilibrium point

Waveform shape of a wave when graphed

Crest max point of transverse wave


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Trough min point of transverse wave

Wavelength () the distance between 2 similar points in successive identical cycles in a wave, such as

from crest to crest or trough to trough

Phase in a continuous transverse or longitudinal wave, x-coordinate of a unique point of the wave

Phase Shift a shift of an entire wave along the x-axis with respect to an otherwise identical wave

In Phase state of 2 identical waves that have same phase shift

Out ofPhase - state of 2 identical waves that have different phase shifts

Frequency (f) number of complete cycles that occur in unit time, usually 1s (Hz)

Period(T) time for a vibrating particle to complete one cycle

Wave Speed(v) rate at which a wave is travelling through a medium; also a measure of how fast energy

is moving (m/s)

Single HarmonicMotion (SHM) any motion that repeats itself during intervals

Wave Speed

Universal WaveEquation relates speed of a wave to its frequency & wave length. Universal equation

applies to all waves Linear Density () mass per unit distance of a string (kg/m)

Equation for speed of a wave along string depends on linear density of string & strings tension

FT = Tension of String (Newtons)

= linear density (kg/m)


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More rigid intermolecular forces allow for faster transfer of energy, therefore, higher wave speed in

medium

Waves travel faster in hotter gases than cooler gases bec. of increased molecular motion caused by higher

temp. in a hotter gas

Properties of Sound Waves

Audible SoundWave sound wave in the range of human hearing (20 Hz 20 kHz)

Infrasonic Wave sound wave with frequency below 20 Hz (Earthquakes)

Ultrasonic Wave sound wave with frequency above 20 kHz (Medical)

SpeedofSound

Mach Number(M) ratio of airspeed of an object to the local speed of sound

Pressure(p) - the force per unit area

SoundIntensity the amount of sound energy being transferred per unit area; unit W/m2

Decibal(dB

) the unit of sound level used to describe sound intensity level

Human hearing can detect a range of sound intensities over many magnitudes in intensity

Loudness levels are usually described on the decibal scale, which is more convenient than the range of

values for sound intensity. Loudness levels are depenedent on the distance from the source of the sound

Sound levels in industry & recreation must be kept to a reasonable level to avoid hearing damage


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Wave Interactions

Interference of Waves

Interference the process of generating a new wave when 2 or more waves meet

Principle ofSuperposition at any point the amplitude of 2 interfering waves is the sum of the

amplitudes of the individual waves

Constructive Interference the process of forming a wave with a larger amplitude when 2 or more waves

combine

Destructive Interference the process of forming a wave with a smaller amplitude when 2 or more

waves combine

Vibrating particles in a medium react to the sum of all forces on them. Their motion is caused by the sum

total of forces on them.

Humans can design technologies to take advantage of wave properties. An example of such a technology

is noise canceling headphones.

Waves at Media Boundaries

Media Boundary the location where 2 or more media meet

Free-endReflection a reflection that occurs at a media boundary where the second medium is less

dense than the first medium; reflections have an amplitude with the same orientation as the original wave

Fixed-endReflection a reflection that occurs at a media boundary where one end of the medium is

unable to vibrate; reflections are inverted

Transmission the motion of a wave through a medium, or motion of a wave from one medium to

another medium

Standing Wave an interference pattern produced when incoming & reflected waves interfere with each

other; the effect is a wave pattern that appears to be stationary

Node In a standing wave, the location where the particles of the medium are at rest

Antinode In a standing wave, the location where the particles of the medium are moving with the

greatest speed; the amplitude will be twice the amplitude of the original wave

Wave Characteristics

- Based on both wave shape & behavior of a wave in timeAmplitude max displacement of a wave from its equilibrium point

Waveform shape of a wave when graphed


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Crest max point of transverse wave

Trough min point of transverse wave

Wavelength () the distance between 2 similar points in successive identical cycles in a wave, such as

from crest to crest or trough to trough

Phase in a continuous transverse or longitudinal wave, x-coordinate of a unique point of the wave

Phase Shift a shift of an entire wave along the x-axis with respect to an otherwise identical wave

In Phase state of 2 identical waves that have same phase shift

Out ofPhase - state of 2 identical waves that have different phase shifts

Frequency (f) number of complete cycles that occur in unit time, usually 1s (Hz)

Period(T) time for a vibrating particle to complete one cycle

Wave Speed(v) rate at which a wave is travelling through a medium; also a measure of how fast energy

is moving (m/s)

Single HarmonicMotion (SHM) any motion that repeats itself during intervals

Wave Speed

Universal WaveEquation relates speed of a wave to its frequency & wave length. Universal equation

applies to all waves Linear Density () mass per unit distance of a string (kg/m)

Equation for speed of a wave along string depends on linear density of string & strings tension

FT = Tension of String (Newtons)


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= linear density (kg/m)

More rigid intermolecular forces allow for faster transfer of energy, therefore, higher wave speed in

medium

Waves travel faster in hotter gases than cooler gases bec. of increased molecular motion caused by higher

temp. in a hotter gas

The Doppler Effect

DopplerEffect when a source of sound approaches an observer, the observed frequency of the sound


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Electricity & Magnetism

Electrical power(P) the rate of transformation of electrical energy

Power is expressed in watts(W) or (J/s)

Time (s)

Energy (J)

Kilowatthour(kWh) measure of electrical energy

1 kWh = 3.6 million J

Mechanical energy, thermal energy, and radiant energy are transformed into electrical power plants

Electrical energy us measured in units of kWh for homes & megawatt hours (MWh) for power plants

Improving efficiency of power plants can decrease our use of resources

Electrical Potential Difference

Electric potential the amount of electric potential energy associated with charges; measured in (J/C)

aka volt (V)

Electric potentialdifference the change in electric potential energy associated with charges at 2

different points in a circuit

V = electric potential difference (J/C) or(V), E= change in electric potential energy (J), Q = amount of

charge (electrons) (columbs)

Sources cause increase, Loads cause decrease

Electric Current

DirectCurrent(DC) The movement of electrons in only one direction

I = current (A), Q amount of charge (C), t = time interval


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irchoffs Laws

VoltageLaw (KVL) In any complete path in an electric circuit, total electric potential increase at the

source is equal to the total potential decrease throughout the rest of the circuit

CurrentLaw (KCL) In a closed circuit, the amount of current enterig a junction is equal to the amount

of current

Laws

OhmsLaw The voltage in a conductor is proportional to the current if the temperature remains

constant. So V = constant * I

Also known as

Power is

mA divided by 1000 equals Amps

Equivalent Resistance total resistance of a group of resistors connected in series or parallel

Electromagnetic Induction

Electromagnetic Induction the production of electric current in a conductor moving through a magnetic

field

Induction means that one action causes another action to happen, often without direct contact

Law ofelectromagnetic induction Any change in the magnetic field near a conductor induces a voltage

in the conductor, causing an induced electric current in the conductor


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Increasing number of loops in a solenoid produces stronger magnetic field for a given current. Same

application for induced current

Faradays ring is a device that demonstrates electromagnetic induction. A current in the primary coil

creates a magnetic field in the ring. The magnetic field in the ring then induces a current in the secondary

coil

Lenzs Law

Lenzs Law If a changing magnetic field induces a current in a coil, the electric current is in such a

direction that its own magnetic field opposes the change that produced it

Tip coil opposes whatever the magnet is trying to do. If north is moving in, the coil repels it with a

north. If north is moving out, the coil attracts it back with a south.

Alternating Current

AlternatingCurrent an electric current that periodically reverses direction

AC frequency in NA is 60 Hz in power grids

Some appliances require AC, others use DC

Homes require a certain amount of voltages of 120 V & 240 V

Circuits in the house are protected by fuses, circuit breakers, ground fault circuit interrupters & arc fault

circuit interrupters

Electricity Generation

Electric Generator a device that transforms other forms of energy into electrical energy

AC Generators are designed with loops of a conductor that spin in a magnetic field. The ends of the loops

are connected to 2 different slip rings, allowing them to produce AC.

Coiling the conductor around an armature increases the strength of the induced magnetic field, making the

generator produce more current.

Spinning the armature more quickly or using a stronger external magnetic field also increases the current

produced by the generator

DC generators are designed like a DC motor except energy is put into the motor to cause it to spin

Transformers

Transformer an electromagnetic device that can raise or lower voltage

Step-down Transformer a transformer with fewer secondary windings than primary windings

Step-up Transformer a transformer with more secondary windings than primary windings


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p = primary & s secondary

Turns into

Grouping them

Np is the # of windings on primary coil & Ns is the # of windings on secondary coil

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