Physics AS Complete
Energy in a closed system
In a closed system, the total energy remains constant.
Standing waves in a both-ends-open pipe
In a pipe, they have an antinode at both ends, unless one end is closed, in which case there is a node at that end but not at the other.
Standing waves in a one-end-open pipe
In a pipe, they have an antinode at both ends, unless one end is closed, in which case there is a node at that end but not at the other.
Requirement for superposition
In order to observe a steady interference pattern, you need to have two waves of the same frequency that maintain a constant phase difference over a period of time. Two sources that produce such waves a known as coherent sources.
Combining Resistors in Paralell
In parallel, the additional resistor provides another path, so the total resistance drops, and the total current increases as there are more branches added. IT = I1 + I2... according to Kirchhoff's 1st law, and so V/R_T =V/R_1 +V/R_2 ... and as V is the same in all branches (equal to emf), the resistance becomes: 1/R_T =1/R_1 +1/R_2 ...
Work function
In the photoelectric effect formula, φ represents the work function of the metal. This is an intrinsic property of a metal, and it is the amount of energy required for the electrons to escape the metal. If the energy of the incident radiation (hf) is less than the work function, photoelectrons will not be released. The point at which they begin to be released is known as the threshold frequency, it is where KE = 0, so hf=φ.
Amplitude definition
Maximum displacement of a particle (peak or trough)
Number density in metals
Metals - Each atom in the metal lattice supplies at least one free electron to form the bond which holds the positive ions together. These free electrons can move within the lattice and so can be used for conduction. Metals have a slower drift velocity, in mm/s.
Moments equation
Moment (Nm)=Perpendicular Force (N) × Distance (m)
Elastic collisions
Momentum conserved, total energy conserved, KE conserved
Inelastic collisions
Momentum conserved, total energy conserved, KE not conserved
Frequency definition
Number of cycles per second. Measured in Hertz (Hz)
Bodies/Extended objects
Objects that are not point objects are called 'bodies' or 'extended objects'.
Percentage difference
Once you have a final value, the % difference from the actual value (known constant such as g or manufacturers value for resistance etc) can be worked out be doing % "Difference"= "Your Value - Actual Value" /"Actual Value" ×100%. The lower this is, the closer you are to the true value and so the more accurate your experiment is.
Torque of a couple
One of the forces x the perpendicular distance between them.
Velocity
Rate of change of displacement.
Snapshot Graph
Snapshot Graph - A snapshot of the entire wave at one moment in time. The distance between successive waves/crests is the wavelength.
Gamma ray's wavelength
<10⁻¹⁶m (100 am) - 10⁻¹⁰m (100 pm)
Electron drift velocity
Equation for electron drift velocity: I=Anev
Percentage Error
Found by: % error= (absoulute error)/value×100%
Displacement
The direct measurement from the start point to the end point, a straight line.
Consideration of pd and current in potential divider circuits
The example to the right shows that when using V=IR, the part in parallel needs to be considered using pd, not current. The pd is the same in both branches, so it can be considered as 'one resistor'.
Impulse of an object
The force on the object x the time it takes to act
Archimedes' Principle
The upthrust that an object that is floating or submerged feels is equal to the mass of the fluid displaced by the object.
Polymeric materials
These won't stretch much to start with, then they'll stretch quickly and then stop stretching much at the end. When it unloads after the force has been released, it does the same, but a bit lower on the stretch axis. It will generally not take much stress at all.
IV graph: bulb
This produces a symmetrical but curved line, so I NOT α V. Therefore, it doesn't obey Ohm's law. As the PD (and hence I) increases, the filament heats up, causing increased resistance. The graph is symmetrical, so there is reverse bias on the negative area (it behaves the same no matter the polarity). It behaves like an ohmic conductor at small PDs.
Kirchhoff's Second Law
This states that: in any circuit, the sum of the electromotive forces (emfs) is equal to the sum of the pds around a closed loop. Therefore Σε_in=ΣV around a closed loop. This is conservation of energy.
Directly proportional graphs
Will produce a straight line through the origin
Photons
."Energy of photon " (J)= "Planck's Constant " (Js^(-1) )× "Frequency " (Hz "or " s^(-1) ).E=hf.f=v/λ=c/λ. Therefore, E=hc/λ.
When calculating a resultant force...
... use a force triangle to work out where that force will act
Remember to include that velocity/acceleration is the... (when describing)
...gradient of the graph when describing the shape.
Remember to comment on air resistance being... (when commenting on the validity of a model)
...greater at higher speeds if taking about the validity of a model
There is no acceleration...
...if there is no force acting (and vice-versa)
A distance time graph will always have a... (gradient)
...positive or zero gradient, never negative.
Energy and Power
.P=VI, P=I^2 R, P=V^2/R, W=VIt,
Microwaves wavelength
10⁻³ (1 mm) - 10⁻¹ (100 mm)
Radio waves wavelength
10⁻¹ (100 mm) - >10⁶ (1Mm)
X-rays wavelength
10⁻¹³m (100 fm) - 10⁻⁸m (10 nm)
Ultraviolet wavelength
10⁻⁸m (10 nm) - 4×10⁻⁷ (400 nm)
Visible wavelength
4×10⁻⁷ (400 nm) - 7×10⁻⁷ (700 nm)
Infrared wavelength
7×10⁻⁷ (700 nm) - 10⁻³ (1 mm)
Newton's 1st law
A body will remain at rest or at a constant velocity if there is no net force acting upon it. If a force is applied, the body will accelerate, change direction, spin or change shape.
Couple
A couple is a pair of forces that apply a moment or a turning effect to a body. It is a pair of forces that produce rotation only. They have the same magnitude and act at the same distance from the midpoint.
Ductile materials
A ductile material follows the Young Modulus until it reaches its yield strength, where its molecules begin to rearrange. This is the limit of proportionality. From here, it begins to permanently stretch, called strain hardening. Here, it is deforming plastically. It then reaches its ultimate tensile strength, after which it undergoes necking, becoming weaker until it fractures.
Centre of mass
A freely suspended body will come to rest with its centre of gravity vertically below the point of suspension. This is what a plumb-line does, it suspends the body so that its centre of mass can be found by where it hangs.
Amps and Coulombs
Amps is the measure of the total electrons passing, but one electron is too small to be the basic unit of charge. Therefore, coulombs are used - one electron has a charge of 1.6x10-19 Coulombs (C). 1 amp is a flow of 6.25x1018 electrons per second (1/1.6x10-19). 1 coulomb is the charge of one amp in one second, coulombs are amp seconds. 0.25A of charge for 20 seconds = 0.25x20 = 5C
Electron volts
An electronvolt (eV) is the amount of energy transferred to a single electron if it is accelerated through a PD of 1V. It is just a small measure of energy that can be used on the atomic level when the joule is too big. Therefore, 1eV=1.6×〖10〗^(-19) J and so 1J=6.25〖×10〗^18, which is 1/ the joules per eV. 1 electron accelerated across 1 volt = 1Ev. W=VQ.∴W=Ve, the voltage x the charge on an electron (constant of 1.6×〖10〗^(-19).
IV graph: thermistor
As temperature increases, the resistance of a thermistor decreases. The resistance rises slowly at first before speeding up. This property makes thermistors useful in temperature sensitive circuits, for example in an oven, a thermostat or to monitor temperatures.
Internal Resistance Equation
Because of Kirchhoff's second law (K II), the sums of pds around a closed loop = the sum of emfs around the same loop. Therefore, ε=IR+Ir and so ε=I(R+r) and V=IR so ε=V+Ir. I = circuit current, V = pd from rest of circuit the terminal voltage of the battery, ε = emf of battery, R = resistance of rest of circuit and r = internal resistance. Therefore, V=-Ir+ε, and as y=mx+c, the gradient of a plot of terminal voltage against current gives internal resistance and emf.
Brittle materials
Brittle materials will stretch a little bit, but will then rapidly weaken and fracture. These materials tend to have a high ultimate tensile strength, but will then very quickly fracture.
Two source interference experiment
By setting up a 3cm microwave emitter in front of 3 sheets with 2 gaps between them, both 3cm wide, you can study this. A microwave receiver is put on a straight line with a ruler on it, and then slowly moved up and down, continuously logging the results to study the interference pattern.
Coherent Light
Coherent light is light with the same wavelength, so they have a constant phase difference.
Connecting cells
Connecting cells in series increases the available emf, but also the internal resistance, limiting the current that the combination can produce. Connecting them in parallel produced the same emf as one cell, but a much lower internal resistance, so a greater current.
Density equation
Density (kgm-3) = Mass (kg) /Volume (m3) . ρ=m/v
Evidence for waves
Diffraction; Refraction; Reflection; Polarisation; Interference
Potential Divider example
E) A 270Ω resistor and a 170Ω resistor are connected as part of a potential divider circuit with a 36V supply. The output is connected over the 270Ω resistor. Calculate the voltage supplied to the rest of the circuit (Vout). V_out=R_2/(R_1+R_2 )×V_in ; V_out=270/(170+270)×36 ; V_out=270/440×36 ; V_out=22.1V
Electric Current
Electric current is the flow of electric charges - electrons or sometimes ions
Electrical power
Electrical power is the rate of energy transfer, this is measured in Watts. Power=(Energy Transferred)/(Time Taken),P=W/t. Kilowatt hours are used to measure household electricity usage as a joule is way too small. One kilowatt-hour is equal to 3.6MJ (3.6 million J)
Wave model prediction: Low intensity light should take some time to give off electrons.
Electrons are emitted as soon as the light is shone. --- A single photon is enough to release one electron, so they are release immediately.
Wave model prediction: Low intensity light should have no effect at all.
Electrons are still emitted, although fewer --- Each photon causes one electron to be released, so fewer photons of lower intensity light just mean fewer electrons will be released.
Polycrystalline diffraction
Electrons fired by an electron gun at successive planes of atoms in polycrystalline graphite give a constructive interference pattern. This is because the wavelength of a fast-moving electron is around 10-10m, around the same size as the space between atoms in a solid. This is why some electrons can be diffracted by planes of atoms. The wave model is used when the wavelength of the electrons is similar to the width of the gap. This experiment demonstrates how electrons can behave as particles when being accelerated by the high PD of the electron gun, and then as a wave when they diffract.
EMF and PD
Emf is electromotive force. A source of emf is a device which can supply energy to an electric current. A cell provides an emf by converting chemical energy into electrical energy. It's joules per coulomb, so J/C so emf is measured in volts. PD is work done moving charges around the circuit, i.e. energy used within the circuit. Emf is energy supplied to the circuit. All energy provided by the power supply must be used in the circuit. Batteries and power supplies supply electrical energy to a circuit. Devices within this circuit transduce this energy: bulbs produce heat and light, resistors produce heat.
Homogenous Equations
Equations are homogenous if the units on each side are the same. Correct equations must be homogenous.
Newton's 3rd law
Every action force has an equal and opposite reaction force. The reaction force is of the same magnitude, but is in the opposite direction, acts on a different object and is the same type of force.
IV graph: resistor
For a fixed resistor, the graph of V against I is a straight line through the origin, so V α I, it is a directly proportional relationship. Therefore, fixed resistors obey Ohm's law and have constant resistance, these are considered Ohmic components.
Area of a liquid or gas
For an object in a liquid or gas, the surface area of the inside of the container is used as the area. Therefore p=F/SA.
Conditions of equilibrium
For an object to be in equilibrium, the resultant force must be zero and the sum of the moments must be zero.
Upthrust formula and derivation
For any object, F=pA. Therefore, for an object underwater, F=hρgA at the top of the object, and F=(h+x)ρgA at the bottom of the object. Therefore, the resultant upwards force F=xρgA. This force is called upthrust. "Upthrust" = Axρg. Here, the volume of the fluid = Ax and the mass = Axρ. Therefore, the upthrust is equal to the weight (Axρ)g of the fluid displaced by the block of wood. A = Cross sectional area of object at top and bottom. X = Height of object. Ρ = Density of liquid. g = gravitational constant.
Hooke's Law
Force (F/N) = Extension (x/m) X Spring Constant (k/Nm-1) . F∝kx so F=kx.
Stationary waves formation
Formed when you have two waves of the same frequency and wavelength and similar amplitude which are travelling in opposite directions in the same medium. This usually occurs when a wave is reflected back at one end, but not always, there can be two sources. Stationary waves differ from progressive waves in that energy is stored in the wave instead of being transmitted from one point to another. Destructive interference occurs at a node, so the amplitude is 0. Constructive interference occurs at an antinode so the amplitude is maximum. The distance from one node to the next is λ/2, so double this distance to find the wavelength.
Terminal velocity
Friction is particles colliding with a moving object. Therefore, air resistance (air particles) and water resistance (water particles) are both classes as friction.
Wave model prediction: Greater intensity radiation means more energy, so more electrons should be released.
Greater intensity releases electrons at a greater rate. --- Greater intensity means more photons per second, so more electrons released per second.
Other electric currents (ions)
Having more electrons than protons gives a negative charge and vice versa. A charge of -2 would have a charge of 2x1.6x10-19 C = 3.2x10-19 C. A flow of ions in a liquid can be a current in the same way a flow of electrons is.
Double slit diffraction
Here, each slit produces a similar diffraction pattern in the same direction. However, the maximum of the diffraction pattern is now seen to be crossed by a number of bands, and they must be produced by the interference between light from each slit.
Two source interference equation
Here, λ=ax/D, where λ = wavelength, a = gap spacing, x = fringe spacing (max-min) and D = distance from gap to measurement plane. The 1st order maxima has phase difference 1, the 2nd order maxima has phase difference 2 etc. The central maxima has phase difference 0. The 1st order minima has phase difference 0.5, and the 2nd order minima has phase difference 1.5 etc.
History Graph
History Graph - This shows what a single particle does with time. The x-axis shows time, and so the distance between successive crests and troughs is the time period (T).
Photoelectric effect
If a beam of photons is shone at a metal, it causes electrons to be emitted from the metal. This is the photoelectric effect. Each photon causes one photoelectron to be emitted, and the kinetic energy that this photon has is dependent on the frequency of the incident radiation. This can be calculated using the formula 〖KE〗_max=hf-ϕ.
Momnents definition
If a force acts on an object at a distance from a pivot, it will have a turning effect. The size of the turning effect is called the moment of the force. The size of the moment depends on both the size of the force and the perpendicular distance from the line of action of the force to the pivot.
Limit of proportionality
If a spring is stretched too far, it will reach the limit of proportionality, where it no longer conforms to Hooke's Law.
Adding bulbs in series and paralell
If an extra bulb is added in series, it decreases the current and therefore the charge. An extra bulb in parallel would increase the current and therefore the charge.
Elastic limit
If it is then stretched further, it will reach the elastic limit, where the spring will no longer return to its original shape. This is known as plastic deformation.
Bodies in equilibreum
If the resultant force on the body is 0, and it is not rotating, then it is in equilibrium. In this case the sum of all the moments in the object (C and AC) must cancel out in accordance with the principal of moments.
Graph is x proportional to y.
If y α x then the graph of y against x is a straight line passing through the origin.
Changes to emf
In normal use, the emf of a battery doesn't change. However, changing the current affects the lost volts and the terminal pd. Increasing the current increases the lost volts (more r), which lowers the terminal pd.
Combining resistors in series
In series, the total resistance is equal to the sum of the individual resistances. Adding more resistors in series causes the pd to remain the same and the current to decrease (because the resistance increases). R_T=R_1+R_2+R_3... This is proved as the total V is the sum of the pds across each resistor: VT = V1 + V2... and this can therefore be written as IRT = IR1 + IR2..., and given the current through each resistor must be the same, this therefore gives R_T=R_1+R_2...
Wave model prediction: High frequency light should work just as well
Increasing the frequency increases the energy of the emitted electrons, but not the number of them. --- Higher frequency photons have more energy, so electrons gain, more energy and so move faster.
Number density in insulators
Insulators - The outer electrons are involved in forming the bonds which hold the atoms together and are not available for conduction.
Wave model prediction: Greater intensity should mean greater energy.
Intensity of light has no effect on the energy of the emitted electrons, only the number of them. --- Intensity does not alter the energy of photons, only the numbers released.
Internal Resistance Diagram
Internal resistance is like a resistor in the battery, it can't be directly measured, but it is present. If a large current is needed, then a power source with a low internal resistance is required, for example in car batteries.
Internal Resistance
Internal resistance is like a resistor in the battery, it can't be directly measured, but it is present. If a large current is needed, then a power source with a low internal resistance is required, for example in car batteries. It occurs because work has to be done by the charges as they move through the power source. As a result, some energy is 'lost' when there is a current in the power source. This lost energy is known as 'lost volts'.
Energy (J) made up of base units
Kgm2s-2
Force (N) made up of base units
Kgms-2
LDR
LDRs vary their resistance dependant on light, used in automatic street lamps and in brightness sensors for phones and laptops. LDRs are also made from semiconductors. They have a very high resistance in the dark, and as light shines onto the material, the number of charge carriers increases dramatically, leading to a rapid decrease in resistance.
Systematic/Random errors
Left: Zero/systematic error - when the meter reads higher/lower than it should. Right: Random errors - when scatter is caused by random errors in measurement.
Single slit diffraction
Light is diffracted when passed through a single slit, producing bright and dark bands on a screen. The central band is bright, with alternate bright and dark bands either side. The central band is also double the width of the slits either side.
Longitudinal Wave
Longitudinal Waves - The particles in these vibrate and oscillate in the same direction as the movement of the wave through compression and decompression. Sound is a longitudinal wave.
Path Difference
Path Difference - This is the same as phase difference but taken off a snapshot graph, it is the difference in the distance travelled by two coherent waves at a particular point. It is measured in metres or fractions of the wavelength (λ).
Phase Difference
Phase Difference - This compares the relative positions of two or more particles in the same waves or the relative points in the cycle of two or more different waves. It's the fraction of a cycle between the oscillations of two particles. It is measured in degrees or radians, such that a whole wave is 360° (2π) and half a wave's difference is 180° (π).
Evidence for particles
Photoelectric effect
Planck's constant and LEDs
Planck's constant can be determined using LEDs. LEDs have a threshold voltage at which they begin to turn on. By setting up a simple circuit with a safety resistor (as to not overload the LED), we can use a potentiometer to vary the voltage through the LED, and use a voltmeter to measure this. Using a black tube, we can hold this over the LED and look through it and then vary the pd to the precise point that it begins to turn on. You can do this for several different LEDs of known wavelength to get a set of values for λ and V. We can then plot the voltage against 1/λ. Since W=Ve and E=hc/λ, they are both equal to energy so can be set equal to find Ve=hc/λ, and since c and e are constants, V=hc/e×1/λ, therefore the gradient of the graph will be equal to hc/e. Using the constants of c and e, we can therefore find an approximation for the value of h.
Plastic materials
Plastic acts in a similar way to rubber (polymeric) when force is applied. When the force is released, it maintains its extension, even when the force is released, only moving back slightly. This is plastic deformation, as it does not return back to its original shape.
Polarisation
Polarisation means that particles in a transverse wave all oscillate in the same plane (normal transverse waves oscillate in all planes). A polaroid at 90° to the plane of polarisation will stop all light, as polarised light that is then polarised into another plane will not pass through, as there is no light travelling in the plane that the polaroid is at. Longitudinal waves can't be polarised as their particles vibrate in the same direction as the wave travels. Therefore, they cannot be polarised to all vibrate in the same plane as they already do.
Potential difference
Potential difference is the measure of the energy provided to the charge carriers. It can be defined as the amount of work done per unit charge. It is how much energy is needed to push the charge a certain distance.
Pressure equation
Pressure (Nm-2) = Force (N) /Area (m2). p=F/A
Resistivity
R=ρL/A, R = resistance (Ω), A = Cross sectional area (m2), L = Length, ρ = Resistivity (Ωm). Resistivity is an intrinsic property of a material that allows you to calculate the resistance, so all copper wires will have the same resistivity, that of the metal copper. Resistance is the disruption of the flow of charge whereas resistivity is the amount of resistance caused by a material. The resistivity of a material varies with temperature, so as the material heats up, its resistivity increases. Values of resistivity can vary greatly from 10-8 Ωm to 1016 Ωm.
Resistance
Resistance is a characteristic of all materials. Some materials (e.g. air) have a high resistance. Other materials (e.g. gold) have a very small resistance. Electrical resistance is similar to friction, in that it is a resistance to movement. Electrons drift slowly through a conductor when a voltage is put across the ends. The metal's atoms interfere with the motion of the electrons, causing resistance. The higher the temperature, the faster the metal atoms vibrate, and the more likely they are to impede electron flow, hence increasing resistance.
Scalar/Vector quantities
Scalar quantity - a physical quantity with no direction, only a magnitude. Vector quantity - a physical quantity with a specified direction and magnitude.
Number density in semi-conductors
Semiconductors - The process is similar to metals but the number density of charge carriers is much smaller. The drift velocity is therefore much faster, in m/s.
Cells with high/low internal resistance
Some cells are deliberately built to have a high internal resistance in order to limit current, their allows high-voltage power supplies for classrooms to remains safe and not electrocute people. Very low internal resistances are used for rechargeable batteries like car batteries and phones and laptops, allowing them to be charged with high currents without overheating or wasting energy.
Standing waves on a string
Standing waves on a string have a node at both ends.
Stress
Stress occurs inside a solid and is dependent on the force applied and the cross-sectional area of the material. As the area the force is applied to increases, the stress decreases. Therefore, stress ∝1/area, and since stress∝force, then stress=force/area, shown as σ=F/A. Stress is therefore measured in Nm-2 or Pa.
What affects air resistance
Surface area in direction of motion, Viscosity of air/fluid, Speed of object
Deriving c=fλ
T=1/f ; Since v=s/t and in the time for one cycle, a wave travels one wavelength, then v=λ/T ; T=1/f so v=λ/(1/f)=fλ ; ∴v=fλ and so, for EM waves where v = c, c=fλ
Centre of gravity
The centre of gravity of an object is the point where the weight of the body can be considered to act. In a uniform body of uniform density, this will be in the centre.
Ohm's Law
The current in an ohmic conductor is proportional to the voltage across it, provided that the temperature and other physical conditions are kept constant. V α I so k = V/I, V = kI, R = V/I
Wavelength definition
The distance between identical points in a wave train
Displacement definition
The distance from the equilibrium position (dotted line)
Elastic energy
The elastic energy stored in a string is E_E=1/2 Fx^2. This is because the area under a linear Force/Extension graph is E_E=1/2 Fx, and so substituting in F=kx gives E_E=1/2 Fx^2.
Conventional current vs electron flow
The electric charges flowing are usually negatively charged electrons. Therefore, they flow from negative to positive. However, conventional current flows from positive to negative
Emf relation to terminal pd
The emf<terminal pd "where " I≠0. If the current is very low, then ε≈V, which is why high-resistance voltmeters connected across a cell give a reading close to the emf.
Emf definition
The energy transferred from one type of energy to electrical energy per unit charge.
Drag
The frictional force experienced by an object as it travels through a fluid
Impulse
The impulse on an object is the force applies x the time it takes to act. It is the area under a force time graph.
Intensity
The intensity of a wave measures the energy incident per square metre of a surface per second (in "J" "m" ^(-2) "s" ^(-1) ",which is W" "m" ^(-2). If waves spread out from a source, then the area over which they spread is a sphere. Therefore, "intensity"= "power" /(4πr^2 ), so "intensity"∝ "1" /〖"(distance)" 〗^2 . "Intensity"= "power" /area.
Electron gun
The metal plate is heated up by a large PD. This causes the electrons to gain kinetic energy and so escape from the surface. These electrons are then free to move, and a nearby anode is connected to the metal plate (which becomes the cathode). The electrons therefore move towards the anode, which they hit. A small hole in the anode creates a beam of electrons that have come from the cathode, hence this is known as a cathode ray tube.
Torque
The moment provided by a couple is equal to the product of one of the forces and the perpendicular distance between them. The moment of a couple is also called torque. A moment can be supplied by a single force and may result in a non-zero resultant force on the object, whereas torque implies that only the turning effect is being considered.
Number density
The number density of a material is the number of charge carriers per unit volume and is a factor in determining how well a material conducts electricity.
Path difference in superposition.
The path difference is the distance from a point to each source in wavelengths. So, the path difference of M on the diagram is 2 from s2 and 3 from s1, so it has a path difference of |2-3| = 1. P on the diagram has a path difference of 2.5 as it is 4 wavelengths from s1 but only 1.5 from s1 as it is a minimum, so it has a phase difference of .5. For constructive interference, the phase difference will always be nλ (where n is an integer), whereas for destructive interference it will be (n+0.5)λ.
Principal of superposition
The principle of superposition - When two or more waves of the same type exist at the same place, the resultant wave will be found by adding the displacements of each individual wave.
Moment
The product of the force and the perpendicular distance at which the force acts.
Newton's 2nd law
The rate of change of momentum of an object is directly proportional to Net force is the rate of change of momentum, thus F=ΔP/Δt, where p = momentum. Therefore, F=(mv-mu)/t. F=ma is a special case of this law, replacing (mv-mu)/t for m((v-u)/t)=ma. It is a special case as it only applies when the mass remains constant throughout the collision.
Stopping potential
The stopping potential is where the energy (KE) that the electrons are released with is equal to the energy required to get them across.
Principle of moments
The sum of the clockwise moments will always equal the sum of the anticlockwise moments for an object in equilibrium about any axis.
Kirchhoff's First Law
The sum of the currents into a junction is equal to the sum of the currents leaving the junction - this is conservation of charge. The way the current splits depends on the resistance and PD in the branches.
Distance
The total length of the path taken.
Ultimate tensile strength
The ultimate tensile strength is a measure of the strength of a material. If depends on: what it is made of, the thickness at its thinnest point, the amount of load placed upon it
Wave model prediction: Low frequency light should still work
There is a minimum frequency observed, below which no electrons are released, no matter the intensity. --- Photons of low frequency light have less energy than the work potential, so don't have enough to release an electron.
Total internal reflection
There will always be some reflection of the wave. However, total internal reflection (i.e. none passes through) occurs when the wave is travelling into a less optically dense material (lower value of n) and the angle of incidence is greater than the critical angle. If this happens, then all the light incident on the boundary is reflected back into the incident material, and the angle of incidence is equal to the angle of reflection.
Result of Kirchhoff's Second Law
Therefore, the pds in a series circuit will add up to the emf across the battery. The same applies with multiple sources of emf, these are just added to get a total emf, and if these have opposing polarities, then you need to take one away from the other. In a parallel circuit, each parallel branch can be thought of as a separate circuit, so the voltage across that branch equals the total emf.
IV graph: diode
These are also non-ohmic as they don't obey Ohm's law. There don't have a constant resistance. They also change depending on their polarity. At point A on the graph, the resistance is very high, infinite for practical purposes. The diode therefore doesn't light up or conduct. At B, the pd increases and the resistance gradually starts to drop. This is the threshold or activation pd, the point at which there is a rapid decrease in resistance allowing a current to flow, the diode to conduct and therefore light up. The resistance then drops very sharply, and from C it has very little resistance.
Potential Divider Circuits
This can be done by using two resistors in series. A circuit can then be connected in parallel with one of these resistors. Therefore, the pd supplied to this circuit can be varied by changing the resistances of R1 and R2. The pd across each of the resistors will be in proportion to its resistance so that V_1/V_2 =R_1/R. The supply voltage is known as Vin and the voltage to the rest of the circuit (in parallel with the resistor) is known as Vout. The pd supplied to the rest of the circuit can either be worked out using V=IR, or using the potential divider formula V_out=R_2/(R_1+R_2 )×V_in where R2 is the resistor over which the rest of the circuit is connected.
Percentage Error from repeated values
This can be worked out from repeated readings by doing % "uncertainty = ( 1/2×"range" )/"average" ×100%
Young modulus
This is a measure of how difficult it is to change the shape of a material. Young Modulus=ΔStress/ΔStrain, so E=σ/ε. Given that σ=F/A and ε=x/l, you can use this to find that E=FL/ax, which is measured in Pascals (Pa) or Nm-1.
Absolute Uncertainty
This is just the range of possible values. It is |Best value - Worst Value|, giving you the range, or the absolute uncertainty in that measurement.
Strain
This is the ratio between the extension of a material and its original length. It is normally just given as a number, but can be given as a percentage. Strain=Extension/(Original Length), shown as ε=x/l. Strain will always be between 0 and 1, and it has no units.
Best and Worst Values
This is the uncertainty in a measurement, given using the ± sign. This is defined as equal to the smallest unit of measuring in most cases (unless given otherwise). Therefore, on a meter ruler incremented in mm, the error would be ±1mm. On a graph, a 'worst line' can be drawn to find the error in the graph. This line is drawn from the bottom of the range bar on the first point to the top of the range bar on the last point, providing this also passes through all the other range bars. The min and max values can then be worked out from the uncertainty by simply adding or taking it.
Total internal reflection in fibre optic cables
This is used in fibre optical cables, where the light comes in at a very shallow angle to allow it to be bigger than the critical angle and to stop the wave becoming spread out, it keeps it together. The coating has a slightly lower value of n (e.g. 1.46 compared to 1.48), and so the light will be totally internally reflected within the cable, allowing a high-speed fibre optic cable.
Time period definition
Time taken for one complete wave to pass a point
Combining absolute uncertainties
To + or, add the absolute uncertainties. E.g.: 1.56 ± 0.02m + 4.53 ± 0.05m = 6.09 ± 0.07m
Combining % errors
To X or ÷, add % errors, so to find the % error in R, since R = V/I, you can add the errors, so % error in R = 10% + 2% = 12% R= 2.0/0.50=4.0Ω±12% R=4.0Ω±0.48Ω To raise to the power of n, multiply the percentage uncertainty by n: e.g. If length of cube = 5.7 ± 0.2 cm, then % uncertainty = 3.51%. 3.51% X 3 = 10.5%. Therefore, the volume of the cube = 190 ± 10.5 cm3.
Transverse Wave
Transverse Waves - The particles in these vibrate and oscillate perpendicular to the movement of the wave. Light is an example of a transverse waves.
EM waves
Travel at the speed of light, therefore c=fλ. Are transverse waves. Can therefore be plane polarised. Remember wavelength = speed of light/frequency.
Mathematical Vector addition
Use trigonometry to work out the length and angle of the remaining side.
Graphical Vector Addition
Vectors are drawn tip to tail, the end of one vector is added to the start of the next one, as in the dashed lines on the diagram. For graphical vector addition, keep the protractor the same way round at all points. Measure the angle relative to the initial axis (the one to which the protractor is aligned) as is done in bearings. The resultant vector can be measured using the scale and the angle found relative to the initial axis to find the bearing. The diagram shown is 3 ms-1 at 45° then 5 ms-1 at 135°, giving a resultant vector of 5.9 ms-1 at 103° (the actual answer is 5.83 ms-1 at 104°).
Superposition explanation.
Waves that are in phase will form constructive interference, adding to each other to create a wave with an amplitude equal to the sum of the original waves' amplitudes. Waves that are in antiphase (phase difference of ℼ) will form destructive interference and will cancel each other out. The peaks of an interference pattern are called maxima, and the troughs where they cancel out are called minima.
Use of wave and particle models
We use the particle model when light interacts with matter. We use the wave model when the wavelength of the light is similar to the dimensions of the object with which it interacts, or similar to the width of the gap.
Forces in a lift
When a lift is accelerating upwards, there is an increased force on the occupant. When it is decelerating upwards, there is a decreased force on the occupant.
Partial reflection
When a ray of light is incident on the boundary between media of different optical density, most of the light is transmitted, and it changes speed, this is refraction. Some of the light may reflect though, this is partial reflection.
Refractive index
When a wave refracts, its speed is decreased, its frequency stays the same and its wavelength is decreased, in accordance with v=fλ. The refractive index of a substance is defined using n, where n ≥ 1. sin〖θ_1 〗/sin〖θ_2 〗 =v_1/v_2 =n_2/n_1 . Therefore, the ratio of the sins of the angles of incidence, θ1, and refraction, θ2, is equivalent to the ratio of the velocities in the two media, and equivalent to 1/ the refractive index, n. Remember, n_1 sin〖θ_1 〗=n_2 sin〖θ_2 〗. Air has a refractive index of 1. Airndiamond is the refractive index from air to diamond. This is similar to ndiamond, which is from a vacuum to diamond. 1n_2=n_1/n_2 .
Principle of moments
When an object is in equilibrium the sum of the anticlockwise moments about a turning point must be equal to the sum of the clockwise moments about any axis.
Superconductors
When some materials are cooled to nearly 0K, their resistivity drops as expected, but they suddenly fall to absolutely zero. This is known as superconductivity, and any components made of it have zero resistance at 0K, so huge amounts of charge can pass through without it even getting warm. These are used in the LHC at CERN to carry up to 20 000A.
Plastic deformation
When the force is removed, a string that has undergone plastic deformation will still follow Hooke's law when stretched again, but just with a different force constant.
Springs in series and parallel
Where n=number of springs in series/parallel and k=force constant. k_s=k/n in series. k_p=kn in parallel.
How to find the centre of mass
With a card, you can pin the object in one corner so it is suspended by this pin. Use a plumb line to find vertical. Draw a line down this vertical. Repeat for at least two more corners of the object. Where these 3 (or more) lines intersect is the centre of gravity.
W=VQ
Work Done (J) = Potential Difference (V) x Charge (C). The speed of an electron accelerated through a PD of V can be calculated through the formula Ve= 1/2 mv^2, where e = 1.6x10-19 and m = 9.11x1031.
Young double slit experiment
Young put sunlight through a very narrow slit to create consistent light, which is required to produce an interference pattern. He then put this through a double slit to produce an interference pattern. The two black triangles in the diagram can be shown to be similar, and for small angles sinθ≈tanθ. ∴ λ/a=x/D, or λ=ax/D
Remember to comment on... (when describing a motion graph)
constant acceleration and deceleration, and same with velocity. Also remember to comment when velocity/acceleration increasing at a constant rate
Stress strain graphs explanation
https://www.youtube.com/watch?v=gGXHdgsFA9s
Momentum made up of base units
kgms-1
De Broglie Equation
λ=h/mv This is used when a particle is behaving like a wave to calculate the wavelength of the wave of electrons from their mass and velocity (momentum).
