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Physics Syllabus AS and A2 Modules (Atoms and particles (Strong Nuclear…
Physics Syllabus AS and A2 Modules
Thermal Physics
Specific heat Capacity
Q = mcΔθ
c=Q/mΔθ
energy supplied = mass x (specific heat capacity) x (temperature change)
-273℃ ≡ 0K
Specific Latent heat
Q=ml
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
Boyle's Law
P proportional to 1/V or PV = constant
T Constant
Charles' Law
V proportional to T or V/T = constant
P constant
T in Kelvin
Pressure Law
P proportional to T or P/T = constant
V 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
Assumptions
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.
Definitions
Isochoric
Constant Volume
Isobaric
Constant pressure
Isothermal
Constant temperature
Adiabatic
No heat added
Simple Harmonic Motion
Pendulum
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
Definition
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.
Equations
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
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
Forced vibrations happen when there is an external driving force. The frequency of this force is called the driving frequency.
Resonance
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
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
Critical damping reduces the amplitude – returns to equilibrium as quickly as possible.
Overdamping
Overdamping systems with even heavier damping are overdamped, they take longer to return to equilibrium than critically damped systems.
Fields
Gravitational fields
Radial Field
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 definitions
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.
Gravitational field
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
Gravitational potential
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.
Satellite orbits
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
Weather/spy satellites
Polar orbits
Look at one specific line over and over again
Distant orbits (geosynchronous)
Communications satellites
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
1/r relationship
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
Magnetic Fields
Electromagnetic induction
Flemings' right hand dynamo rule
Faraday's Law
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
Len's Law
The induced current flows in a direction that opposes the change that produces it.
Eddy currents
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
Thumb
Motion
First finger
Field
Middle finger
Current
Magnetic Flux density
F= BIl
F is force
B is
I is current
l is length of wire
Tesla vs Weber
Tesla
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.
Weber
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
B is
Q is charge
v is velocity
Magnetic Flux and Flux linkage
Magnetic Flux
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
Transformers
AC Current
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
Oscilloscopes
Controls
Time base
How many s or ms etc that one cm represents
Y gain/Volts per cm
The number of volts represented per cm
Images
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
Electric Fields
Capacitors
Point charges
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.
Negative
Field lines pointing inwards
Positive
Field lines pointing outwards
Uniform Field
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
pi
E0)*Q1Q2/r^2
E0 = permittivity of free space
1/4piE0 = 9x10^9
Electrical field strength (E)
Vector quantity
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
Circular motion
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
Radioactivity
Nucleus
Astronomy
Telescopes
Lenses
HR Diagrams
Stella Evolution
Cosmology
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
Isotopes
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
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
Unstable Nuclei
They emit radiation
Alpha decay
Helium Nucleus (2 protons and 2 Neutrons)
Very heavy 4mp
+2e charge
Slow moving
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
Beta Decay
Electron
Very little mass - me
-1e charge
Fast moving
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
Gamma radiation
Electromagnetic Wave
No mass
No charge
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
Conservation laws
Whenever particles interact Charge, Baryon number, Lepton number and (in strong interactions) Strangeness must be conserved
Neutrinos
Most plentiful particle in the universe
Very penetrating particle, would take a piece of lead the length of the solar system to stop one.
Zero charge
Possibly no mass or they are just very very very light
Antimatter
Every particle has a corresponding antiparticle with opposite properties
Example
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.
Electron Capture
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
5fm range
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
Quarks
All Hadrons are made of quarks
Baryons
3 quarks
Proton
uud
All baryons will eventually turn into protons so they must be the most stable baryon
Mesons
1 quark and 1 antiquark
Pi+
u and anti d
Antibaryons
3 antiquarks
Antiproton
anti uud
Properties of quarks add together to give the properties of the hadrons - can't have a partial charge or baryon number!
Quarks
Quark
Q
B
S
Up
+2/3
1/3
0
Down
-1/3
1/3
0
Strange
-1/3
-1
Anti Down
1/3
-1/3
0
Anti Up
-2/3
-1/3
0
Anti Strange
1/3
-1/3
+1
Four Forces
Force
Acts On
Range
Bosons
Particle mass
Particle lifetime
Gravity
Particles with mass
Infinite
Graviton
0
Infinite
Weak
Everything? (except bosons?)
Around 10^-18m
W+, W- and Z0
Very Heavy
Very short
Electromagnetic
Charged "Stuff"
Infinite
Photon
0
Infinite
Strong
Hadrons
Around 10^-15 m
Gluon
Heavy
Short
Equations of motion and momentum
SUVAT
u = initial velocity m/s
v = final velocity m/s
s = displacement m
a = acceleration m/s^2
Equations
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
Vectors
Scalars have only magnitude
Vectors have both magnitude and direction
Resolving vectors
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)
Projectile motion
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
1
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.
2
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
3
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
Momentum
p = mv
Momentum is the product of mass and velocity
Collisons
Elastic
Both momentum and kinetic energy are conserved.
Inelastic
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
Moments
A moment is the turning ability of a force
Moment = force × perpendicular distance from the
point to the line of action of the force
Principal
All moments anticlockwise equal all moments clockwise at equilibrium.
Three types of problem
Hinge problem
1.8x20=1.2xX
30=X
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
3x50=5A
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
Couple
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
Wave
Double slit experiment
Particle
Photoelectric effect
Similarly small particles like electrons also exhibit a wave like nature
Diffraction
This means that there is an associated wavelength with these particles - the de Broglie wavelength
lambda = h/mv
Electricity
Resistance
Resistivity
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
Filament lamp
Diode
Start Voltage of 0.7V
Resistor
Thermistor
Potential dividers
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
General
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
Super conductivity
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.
Materials
Density
p = mv
Hooke's Law
Elastic Limit
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
Springs
Parallel
Spring constant doubles
In series
Spring constant halves
Young's Modulus
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)
Waves
Diffraction
Diffraction gratings
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.
Interference
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.
Equations
c = f lambda
f = 1/T
E= hc/lambda
Definitions
Amplitude
Intensity of a wave
Wavelength
Is distance between two identical points on a wave e.g. two peaks or two troughs
Frequency
How many times a full wave passes a point in one second
Phase
Two in phase waves are moving in parallel with peaks and troughs at the same times
Can only happen in coherent waves
Speed
How fast the wave is travelling
Phase difference
The amount, in radians, that two waves are out of phase/sync with each other
Longitudinal Waves
A wave where the oscillations are parallel to the direction of energy transfer
Transverse Waves
A wave where the oscillations are perpendicular to the direction of energy transfer
Progressive waves
The movement of a disturbance from a source which transports energy to the area around the source.
Polarisation
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.
Stationary Waves
Nodes
A non-moving point on a stationary wave
Antinodes
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.
Constructive interference
Peak meets a peak or a trough meets a trough
Path difference = n lambda
Destructive interferance
Peak meets a trough and they cancel out
Path difference = 0.5 of a wave overall = (n+0.5)lambda
Refraction
Refractive index
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
Critical angle
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)
Optical fibres
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
Energy transferred
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
Power is
Errors and Accuracy
Random errors
Readings that scatter about the true value.
Reduce by taking and averaging more values.
Systematic errors
Readings that all differ from the true value by a fixed amount
Can only be removed by accounting for the source of the error
Precision
The level of agreement of different repeated measurements of the same physical property.
Accuracy
How close your value is to the actual value.
