Download - 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