Physics Syllabus AS and A2 Modules (Atoms and particles (Strong Nuclear…
Physics Syllabus AS and A2 Modules
Specific heat Capacity
Q = mcΔθ
energy supplied = mass x (specific heat capacity) x (temperature change)
-273℃ ≡ 0K
Specific Latent heat
Energy = mass * specific latent heat
Every material has two latent heat values, specific latent heat of fusion – melting or specific latent heat of vaporisation – boiling.
Latent heat of vaporisation is greater than the latent heat of fusion because you have to move the particles much further apart which requires more energy.
One of the assumptions made of gases is that there are no forces of attraction between gases, i.e. they just have kinetic energy and no potential energy.
The Gas Laws
P proportional to 1/V or PV = constant
V proportional to T or V/T = constant
T in Kelvin
P proportional to T or P/T = constant
T in Kelvin
P or V against T should give a straight line, if you extrapolate it back to 0, when T is in degrees C, P or V should be 0 at -273.15C
Ideal Gas Law
Combines all three gas laws
PV = nRT
Pressure x Volume = Number of moles x Universal molar gas constant (8.31) x Temperature in K
Kinetic energy equation
PV = 1/3 N m c2 ( c2 bar)
N = number of atoms/molecules in the gas
m = mass of a single gas atom/molecule (kg)
c2 = the mean square root of a single gas atom/molecule (m2/s2)
Average kinetic energy of one gas particle ½mc2 (c2 bar)
1/2mc2 = 3RT/2Na = 3kT/2
K = Boltzmann's Constant
k = R/Na
REALLY IMPORTANT AS PROVES THAT AVERAGE KINETIC ENERGY OF A GAS PARTICLE DEPENDS ON TEMPERATURE IN KELVIN
All gas molecules identical
Gas contains a large number of molecules
Molecules have negligible volume compared to the volume of the container
Molecules are constantly moving randomly
You can use Newton's laws and they apply
Collisions between molecules and walls of the containers are perfectly elastic
Molecules move in straight lines between collisions
Any force that acts during the collision acts for a much less time than the forces between the collisions.
No heat added
Simple Harmonic Motion
T = 2 pi squrt(l/g)
g is acceleration due to gravity
Mass on a spring
T = 2 pi squrt(m/k)
k = spring constant
The object has an acceleration which is proportional to it's displacement from equilibrium. The acceleration is always directed towards the equilibrium wherever the object is.
a = -ϖ2x (ϖ2 = a positive constant) ϖ = 2pi/T = 2pi f
v = + or – ϖsqurt(A2-x2) A = amplitude of oscillation i.e. when x is max
therefore vmax = + or – ϖA at equilibrium
x = A cos(ϖt) t = time since oscillation started – when timer started at maximum displacement
x = A sin(ϖt) t = time since oscillation started – when timer started at equilibrium
Free and Forces Vibrations
Free vibrations involve no transfer of energy to or from the surroundings. If you stretch the mass on a spring, it oscillates at it's resonance frequency
Forced vibrations happen when there is an external driving force. The frequency of this force is called the driving frequency.
Resonance – when the driving frequency approaches the natural frequency the system gains more and more energy from the driving force and so vibrates with a rapidly increasing amplitude. When this happens the system is resonating.
Damping forces are forces that transfer the energy from the system to the surroundings, some systems are deliberately damped to stop them oscillating or to minimise the effect of resonance.
Critical damping reduces the amplitude – returns to equilibrium as quickly as possible.
Overdamping systems with even heavier damping are overdamped, they take longer to return to equilibrium than critically damped systems.
Radial field – field acts inward towards the centre of the Earth – lines converge towards centre of the Earth, lines diverge as you get further from the Earth.
Gravitational potential energy
Work done by an external force in bringing the mass from infinity to its location without change in kinetic energy
Newton's law of universal gravitation
The force of attraction between two point masses is directly proportional to the product of the masses and inversely proportional to the square of the distance between them
Force is proportional to product of the masses and inversely proportional to the square of their separation.
Is a region in space in which another mass in that region experiences an attractive force caused by the first body.
Gravitational field strength
Is the gravitational force per square unit mass placed at the point inside the field
Work done per unit mass by an external force in bringing the mass from infinity to its location without change in kinetic energy
F = Gm1m2 / r2
r is the distance between the centre of the masses
G = gravitational constant = 6.67x10-11 Nkg-2m2
g = GME/rE2
Inverse square relationship, the further you get away from the Earth the weaker the gravitational field.
Graph is a graph of exponential decay.
PE = mgΔh
so since g changes we can't use this equation any more if we are making Δh large.
Centripetal force F = mv2/r = GmME/r2
So v = sqrt(GME/r)
i.e. each orbit requires a certain v to match that r, smaller r greater v
In a low orbit r = rE
T = 2 x pi x rE/ v
Low orbits where r ≈ rE
Look at one specific line over and over again
Distant orbits (geosynchronous)
T = 24 Hours
signals going to same place all the time
Satellites in one relative place to the Earth
Expensive to get out to these places
Time lag due to distance between satellites and you.
Gravitational potential energy (V)
Gravitational potential is equal to the work done in moving a mass of 1kg from ∞ to a particular point in the gravitational field.
Unit = Jkg-1
V = -(GME)/r
r = distance from centre of earth
V on earth's surface is -63 x106 Jkg-1 = -63 MJkg-1
At ∞, V = 0
∆PE = ∆Vm (in real life mass of spaceships etc changes due to burning fuels but in physics questions it doesn't matter)
Gravitational potential lets us work out the increase in gravitational potential if we move something into space it replaces ∆PE = mg∆h (g not constant)
How to get V change
Subtract (=∆V = difference in potential) Jkg-1
Multiply by the mass that you have moved. J
Get VO (potential at orbit)
Get VE (potential at surface)
i.e. ∆GPE = ∆V*m
Gradient of curve = ∆V/∆r = GM/r
gravitational field strength at that point
Flemings' right hand dynamo rule
When there is a change in magnetic flux linkage, the EMF induced in the circuit is directly proportional to the rate of change of magnetic flux in the circuit or coil.
E = N Φ/dt
The induced current flows in a direction that opposes the change that produces it.
Eddy currents are currents induced in a conductor when flux linkage changes
These result in power being lost from the system as heat
Flemings' left hand motor rule
Magnetic Flux density
F is force
I is current
l is length of wire
Tesla vs Weber
Magnetic flux density when a force of 1 Newton acts on a current carrying conductor of 1 Amp and length 1 metre placed perpendicular to the magnetic field.
Magnetic flux that produces 1 volt when flux in a circuit of 1 turn is reduced to zero at a uniform rate in 1 second
Force on charged particles moving in a magnetic field
F = BQv
F is force
Q is charge
v is velocity
Magnetic Flux and Flux linkage
Φ = BA
Φ = BAcos theta if field is at an angle
Magnetic flux is the product of area and magnetic flux density passing through the area.
Flux linkage (lambda)
Magnetic flux linkage is the product of magnetic flux passing through each turn and the number of turns in the coil
lambda = N Φ
N is number of coils
Maxwell's right hand screw rule
If current is flowing downwards the magnetic field around the wire will be a circle going clockwise
Alternating current is current that changes with time
Mains supply is AC current as it is very easily generated, by using steam to turn a coil in a magnetic field.
A transformer changes an alternating p.d. to a different peak value using electromagnetic induction.
Power is mainly conserved in transformers due to them having a 95% efficiency
But there still is some inefficiency
The continuously changing flux causes currents called eddy currents, which cause the core to heat up and energy to be lost.
Reduce by having a laminated core
Resistance in coils
Low resistance copper wires are used
Step up transformer
More turns on the secondary coil than on the primary coil
Increase the voltage to decrease the current to decrease the energy lost through the transfer cables.
Step down transformer
More turns on the primary coil than the secondary coil
Decrease the voltage to increase the current to make it safer and more useable in the home.
VI before * inefficiency value of transformer = VI after
How many s or ms etc that one cm represents
Y gain/Volts per cm
The number of volts represented per cm
This is a DC current of 3V, 3cm up from 0 and Y gain is 1, but the time base is off.
Connected to ground with timebase off.
Connected to ground with timebase on
3V from AC power supply time base set to 2ms per cm
Peak voltage is displacement from peak to zero
Can do Vrms = V0/sqrt(2) to get rms voltage
Time period is the time it takes for one wave to pass a point, no of cm of the wave * timebase.
Can do 1/T = f to get frequency
Peak to peak voltage is the voltage measured from one peak to the other peak in a straight line down.
3V AC power supply, time base off
DC Supply, 3V timebase on
Minimal point producing a charge
Electric field is a radial field
When drawn, direction of field lines are always the path that a positive charge would follow.
Field lines pointing inwards
Field lines pointing outwards
e.g. Two metal plates, one positive and one negative, in between plates field lines travel in a straight line from positive to negative, (except at edges where field lines curve a little)
Field is uniform between plates
Field lines are parallel
Coulomb's law of electrical charges
Force between two point charges
F = (1/4
E0 = permittivity of free space
1/4piE0 = 9x10^9
Electrical field strength (E)
Unit NC^-1 or Vm^-1
For a point charge
E = F/Q
Ex due to Q1 = 1/4piE0 * Q1/r^2
For a uniform field
E = V/d
V = pd between two points
d = distance between plates
Electrical potential (V)
"The work done in moving 1C of positive charge from infinity to a particular point in a field"
V = 1/4piE0 * Q/r
Scalar value and can be negative
Effect of Q on V
Positive Q value
1C of positive charge at infinity would be repelled from the positive charge and hence there would be work done to move the charge closer to the charge
V is positive
Negative Q value
1C of positive charge at infinity would be attracted to Q and would be pulled in as positive and negative attract and thus the field would do the work.
Negative V value
ω = θ/t
Angular speed = angle (rad) / time
v = arc length / t
linear speed = length / time
ω = v/r
angular speed = linear speed / radius of circle
f = 1/T
frequency = 1 / time period
ω = 2 pi / T
angular speed = 2 pi / time period
ω = 2 pi x f
angular = 2 pi x frequency
Atoms and particles
Atoms are made of protons, neutrons and electrons
Protons and neutrons are found in the nucleus
Electrons are found in the electron shells outside of the nucleus
Proton number (Z) = number of protons
Nucleon number (A) = number of protons and neutrons in the nucleus
An isotope is an atom with the same number of protons and electrons but a different number of neutrons, thus it behaves in the same way as another isotope of the same element as they have the same electronic configuration.
CMR = charge/nucleus mass
electron mass is negligible
e = 1.6x10^-19
mp = 1.67x10^-27
Charge on an ion = charge / mass of nucleus
Charge of atom = 0 as there is no overall charge
Charge of nucleus = proton number x e / Nucleon number x mp
They emit radiation
Helium Nucleus (2 protons and 2 Neutrons)
Very heavy 4mp
High ionizing power
Low penetrating power, cannot penetrate through a piece of paper or skin.
Occurs in large unstable nuclei of more than 60 protons
Very little mass - me
Medium ionizing power
Medium penetrating power, can penetrate papers but not light metals
Neutron becomes a proton and expels a electron and an antineutrino from the nucleus
Occurs in neutron heavy/neutron rich nuclei
Moves at the speed of light (3x10^8 m/s)
Low ionizing power
High penetrating power - can only be stopped by layers of lead and concrete
Whenever particles interact Charge, Baryon number, Lepton number and (in strong interactions) Strangeness must be conserved
Most plentiful particle in the universe
Very penetrating particle, would take a piece of lead the length of the solar system to stop one.
Possibly no mass or they are just very very very light
Every particle has a corresponding antiparticle with opposite properties
Proton and antiproton
Baryon numbers of 1 and -1
Charges of 1 and -1
When an antiparticle and a particle meet they annihilate each other and produce the energy from which they were made.
When there is a lot of energy pair production will occur where energy becomes a particle and its antiparticle.
This is where a proton in the nucleus pulls in a proton and becomes a neutron and emits a neutrino.
Strong Nuclear Force
Stronger than electrostatic repulsion
Only works on protons and neutrons
attracts above 5fm
repels below 5fm
Why do heavy atoms have way more neutrons than protons?
Because small atoms are smaller than 5fm so the strong force cancels out the electrostatic repulsion but in bigger atoms the neutrons are needed to provide the SNF but not suffer from any electrostatic repulsion
All Hadrons are made of quarks
All baryons will eventually turn into protons so they must be the most stable baryon
1 quark and 1 antiquark
u and anti d
Properties of quarks add together to give the properties of the hadrons - can't have a partial charge or baryon number!
Particles with mass
Everything? (except bosons?)
W+, W- and Z0
Around 10^-15 m
Equations of motion and momentum
u = initial velocity m/s
v = final velocity m/s
s = displacement m
a = acceleration m/s^2
s = (u+v)/2 x t
s = ut + 1/2 at^2
v^2 = u^2 + 2as
v = u + at
t = time s
Velocity Time Graphs
Acceleration = gradient at that point
Area under the curve is total distance travelled
Displacement is total area between the positive curve and the x - axis - total area between the negative curve and the x - axis
Distance Time graphs
Velocity = gradient
Distance = total positive distance travelled + total negative distance travelled
Displacement = total positive distance travelled - total negative distance travelled
Scalars have only magnitude
Vectors have both magnitude and direction
If you have Fy in the y direction and Fx in the x direction then Ftotal is Sqrt(Fy^2+Fx^2) and the angle from the x axis is tan^-1(Fy/Fx)
Motion in horizontal and vertical
directions are independent.
Calculate time to get to ground using S = how high up it is U=0 V = end velocity A = 9.81 T= time to reach ground
This will then help you in the horizontal direction as S = horizontal distance travelled U = initial velocity V = end velocity A = acceleration T = time calculated before
Newton's Laws of motion
No resultant force = no acceleration
So if there is no resultant force the velocity of the object will not change whether the velocity be 0 or 10000000000ms-1
A body continues in a state of rest or uniform motion unless an external resultant force acts upon it.
Resultant force = acceleration
So if there is a resultant force the velocity of an object will change
The rate of change of momentum is proportional to the resultant force acting upon the body
Every action has an equal and opposite reaction
So if I push a wall it pushes me back
For every action there is an equal and opposite reaction
p = mv
Momentum is the product of mass and velocity
Both momentum and kinetic energy are conserved.
Only momentum is conserved.
Force = rate of change of momentum
Impulse is the change of momentum
The principal of linear momentum
The total linear momentum in a closed system remains the same unless a non-zero external force acts upon the system
A moment is the turning ability of a force
Moment = force × perpendicular distance from the
point to the line of action of the force
All moments anticlockwise equal all moments clockwise at equilibrium.
Three types of problem
Moments clockwise = moments anticlockwise
sin40 x 30 =19.28N
Given that the block has a weight of 20N By taking moments about the hinge calculate the tension in the string,
T = 19N
Two pivot problem
Calculate the up force from A and hence find the force from B
30N = A
To calculate force from A take moments about B
Moments clockwise = moments anticlockwise
50-30 = 20N = B
Single pivot problem
Calculate Force F, given that the system is at equilibrium
Take moments around O
Moments clockwise = moments anticlockwise.
20x1.5+ 100x1.2 = 50x2.5 + 3.7F
150 = 125 + 3.7F
25 = 3.7 F
F = 6.8N
A pair of equal and opposite coplanar forces
Moment of a couple
Force × perpendicular distance
between the lines of action of the forces
Light, The Photoelectric effect, energy levels and electricity
Wave Particle Duality
Electromagnetic energy is emitted and absorbed in discrete quanta of energy
Light behaves both like a wave and like a particle
Double slit experiment
Similarly small particles like electrons also exhibit a wave like nature
This means that there is an associated wavelength with these particles - the de Broglie wavelength
lambda = h/mv
𝜌 = RA/L
𝜌 = resistivity of the material
R = Resistance of the material
A = cross sectional area of the material
L = length of the material
Resistivity is a fair measure of resistance as resistance varies with length and cross sectional area of a wire
Resistors in series
Add together the resistance of the resistors in series to get the total resistance
e.g. Two 4 Ohm resistors in series total resistance equals 4+4 = 8 ohms
Resistors in parallel
1/Rt = 1/R1 + 1/R2 + 1/R3........
Rt = (1/R1 + 1/R2....)^-1
e.g. two resistors of 4ohms 1/4 + 1/4 = 1/2 (1/2)^-1 = 2 ohm resistance
Graphs that you need to know about
Start Voltage of 0.7V
A potential divider is a simple circuit that uses resistance to supply a variable potential difference.
They work because of the fact that voltage is divided up to all components in series
EMF and Internal Resistance
ε = E/Q
ε = EMF
E = Energy
Q = charte
EMF is the energy provided by a cell or battery per coulomb of charge passing through it
Batteries all have an internal resistance which can lead to "lost volts" in the batteries where some of the voltage is divided up to this interna; resistance
ε = I(R+r)
ε = current * total resistance
ε = V + Ir
If you plot a graph of Voltage against current, intercept is EMF and gradient is -r
Electric current as the rate of flow of charge; potential
difference as work done per unit charge
I = ∆ Q/∆ t ,
Current is the rate of flow of charge
V = W/Q
R = V/I
Energy and Power equations
P = IV = I^2R = V^2/R
E = IVt
In some metals and alloys when the material is cooled to a critical temperature the resistance of the material falls to ZERO
The Photoelectric effect
This is the phenomenon when electrons are emitted when light of sufficient frequency is incident on the surface of a metal
Stopping potential is the minimum p.d. required to stop any photoelectrons
Work function is the minimum energy of a photon required to cause a photoelectron to be released
Threshold frequency is the minimum frequency of a photon required to cause an electron to be released
Work function = h*threshold frequency
Electron line spectrums
When an electron decreases in energy levels a photon of the energy of the gap between the levels is emitted.
Each element has a unique line spectrum due to the differences in electron configuration of that element.
p = mv
Whee the spring has been over stretched and will no longer go back to its original shape.
Limit of proportionality
This is the part of the graph where it stops being straight - where the force stops being proportional to extension
F = k∆L
Spring constant doubles
Spring constant halves
YM = tensile stress/tensile strain
YM = FL/EA
F = force (N)
L = length of material (m)
E = Extension (m)
A = cross sectional area (m^2)
d sin theta = n lambda
d = distance between slits on the diffraction grating
sin theta = sin of the angle from n=0 of the light
n = order of maxima
lambda = wavelength of light
White light through a diffraction grating compared to monochromatic light.
The spreading of waves around an obstacle or through an aperture.
Young's Double slit experiment
w = lambda D/s
w = fringe spacing
lambda = wavelength
D = distance between slits
s = distance between slits and the screen.
Double slit diffraction of monochromatic light
Double slit diffraction of white light
The superposition of multiple waves that result in a combined pattern.
c = f lambda
f = 1/T
Intensity of a wave
Is distance between two identical points on a wave e.g. two peaks or two troughs
How many times a full wave passes a point in one second
Two in phase waves are moving in parallel with peaks and troughs at the same times
Can only happen in coherent waves
How fast the wave is travelling
The amount, in radians, that two waves are out of phase/sync with each other
A wave where the oscillations are parallel to the direction of energy transfer
A wave where the oscillations are perpendicular to the direction of energy transfer
The movement of a disturbance from a source which transports energy to the area around the source.
A polarising lense will only allow waves in one direction to get through
Only for transverse waves
Two polarising lenses will block out all light when place with one rotated 90 degrees to the other.
A non-moving point on a stationary wave
A point of maximum movement on a stationary wave.
First harmonic equation
𝑓 = 1/2𝑙*sqrt(T/μ)
f = frequency
l = length of the string
T = Tension in the string (N)
μ = mass (kg) / length of teh string (m)
The formation of stationary waves by two waves of the same
frequency travelling in opposite directions
These are formed when two coherent waves, superpose and create nodes and antinodes where the displacement is 0 or double the original amplitude of the waves respectively.
Peak meets a peak or a trough meets a trough
Path difference = n lambda
Peak meets a trough and they cancel out
Path difference = 0.5 of a wave overall = (n+0.5)lambda
This is a ratio of the lights speed in the material vs speed in a vaccume
n = c/cs
Refractive index is always greater than 1
Laws of refraction
𝑛1 sin 𝜃1 = 𝑛2 sin 𝜃2
sin 𝜃c = 𝑛2/𝑛1
for 𝑛1 > 𝑛2
Total internal reflection
Occurs when a ray is travelling from a less optically dense medium and the angle of incidence is greater than that of the critical angle
Critical angle = sin-1(n2/n1)
Tube of high refractive index glass surrounded by a lower refractive index cladding to try to make the light reflect back into the fibre
The tube is so thin that the light always hits the fibre at an angle bigger than the critical angle
Work, energy and Power
W = Fscos theta
Rate of doing work = Rate of energy transfer
P = (∆ W/∆ t)= Fv
efficiency = useful output power/input power
Energy is always conserved
∆Ep = mg∆h
Ek = 1/2mv^2
Work done is the product of the force and displacement in the direction of the force
Errors and Accuracy
Readings that scatter about the true value.
Reduce by taking and averaging more values.
Readings that all differ from the true value by a fixed amount
Can only be removed by accounting for the source of the error
The level of agreement of different repeated measurements of the same physical property.
How close your value is to the actual value.