-
Rutherford’s Gold Foil Experiment – results link to theory: basically they shot alpha particles through a gold foil
Change in wavelength due to refraction: ok so you have snells law <go look it up in the data booklet bro>. n, the refractive index, is
equal to c/v, and so
. If the n is not 1, then either the frequency has to be different or the wavelength has to be different.
The frequency is the number of waves per second. Imagine a wave going through air then water then air. The frequency and
wavelength is gonna be the same in the air on boths sides, and one changes in the water. It doesnt make any sense to destroy the
number of waves, so the frequency must be kept the same. If either the wavelength or the frequency is different, and the frequency is
not different, it deductively follows that the wavelength is different.
- Nuclear binding energy and mass deficet: Nuclear binding energy is the energy required to break apart the bands between the nucleons
of an atom. There are endothermic reactions that absorb energy and exothermic ones that give off energy. These can be fusion or
fission. Mass defect is the mass that a nucleon would have if it weren’t in the atom that it’s in. The mass defect is E/c^2, with E being the
energy that would be needed to make the mass. When going ​to​a mass defect, it releases energy of mc^2.
- Greenhouse effect and photon-gas interactions: Some of the light from the sun that is reflected by the earth’s surface goes into space,
and some of it is absorbed and re-radiated by the atmosphere. The intensity of the radiation depends on the atmospheric temperature
and the amount of radiating gas. The greenhouse effect is not actually like a greenhouse, since the atmosphere prevents radiative heat
loss rather than convective
- Albedo and black body radiation: albedo refers to the ratio of electromagnetic radiation diffusely reflected to the electromagnetic
radiation that comes in. A black body is a thing with an albedo number of zero, and is the most emissive of thermal radiation. They
absorb all the radiation that comes at them.
- Rutherford’s Gold experiment: in this experiment they demonstrated that atoms have a nucleus where all the positive charge is. They
shot alpha particles through gold, and it penetrated, which they expected. But then some of it scattered at larger than 90 degrees. This
is best explained if the positive charge of an atom is concentrated within one location. ​
These equations predicted that the number of -particles
scattered through a given angle should be proportional to the thickness of the foil and the square of the charge on the nucleus, and inversely
proportional to the velocity with which the -particles moved raised to the fourth power. In a series of experiments, ​
Geiger​and ​
Marsden​verified each
of these predictions.
- particle conservation laws: energy, momentum and angular momentum are conserved quantites. What is also conserved is mass and
charge, and also baryon number and lepton number. So in the universe there is always the same amount of these (but ofc energy and
mass can be converted into each other)
- Force for turning a car round a corner: when turning a car round a corner, you change your direction of velocity and so change your
velocity, therefore requiring a force to change that velocity. This centripetal force is provided by the static friction between the tires and
the road. Friction force is calculated by multiplying the friction coefficient with the normal force, which in the case of a car on the ground
is the force of gravity. From this one can calculate the radius from the velocity or vice versa.
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Topic
Explanation of topic
Beta minus radiation
A neutron becomes a proton and produces an electron and an antineutrino. Mass, charge and lepton number
must be conserved. The electron is there because of charge conservation, and the anti-neutrino is there because
of lepton number (electron-lepton number specifically) conservation.
Why does the neutron undergo beta-minus radiation?
How does this occur (Feynman diagram)?
Conservation of energy
in freefall motion
When a mass falls, its potential energy is converted into kinetic energy. The potential gravitational energy of the
mass is ​
mgh,​ where ​m i​s mass, ​g ​is acceleration due to gravity, and ​
h i​s the change in height due to the object
being elevated.
The assumption of ΔE p = mgΔh is that ​g​is constant throughout the change height. This is never the case
precisely, however, the change in ​g​likely will fall outside of significant digits if performed near the surface of earth
and when ​h​is relatively small, so it is a good approximation.
The kinetic energy of a mass in freefall motion (if the mass is released with v = 0) is equal to the change in
gravitational potential energy. I.e. E k = ΔE p when E k−initial = 0 .
This makes sense given the equation ​v​2 ​= u2​​+ 2a Δ s. ​The ​v​in this equation is the velocity that results from being
accelerated at ​a​for a displacement of ​s,​ given initial velocity ​u.​The ​
a​acceleration is of course ​
g​gravity, and the
s​displacement is ​h​height. Given that ​u​is zero, the equation, when rearranged, and with the aforementioned
values substituted, shows that TO BE CONTINUED
This is used in hydroelectric dams, where the energy produced by them (neglecting efficiency or friction) is equal
to the mass of the water times the height it falls times gravity.
This is also the reason why hitting the ground hurts more when you fall from a high height, since greater height
means greater potential energy, which means greater resulting kinetic energy which in turn means a greater
amount of energy for the body to dissipate in order to come to a stop when hitting the ground.
Arrays of resistors in
series and parallel
Firstly, when one member of a series is removed the whole circuit ‘fails’ (no current can flow), but it's all good
when it's just one member of a parallel circuit. The resistance decreases when adding another resistor in parallel,
whereas it increases when adding another one in series. This is why it is better to have a parallel circuit for your
lights, because that way adding a new light does not change the power a new light receives (assuming internal
resistance of voltage source is zero) (without changing the supply voltage).
Resistors can be stacked in combinations of series and parallel in order to form different resistances. This is
helpful if you only have a small selection of resistors and need to create a specific resistance for a circuit.
Relationship between
internal resistance and
the maximum current a
cell(s) can output
The internal resistance is the resistance of, or inside the, voltage source. The less resistance, the more current
the voltage source can produce, therefore minimising internal resistance maximises the maximum current.
V = ε − I r where V is the voltage measured across the cell, I is the current flowing through the (whole) circuit
when the voltage is measured, ε is the ‘actual’ or ‘real’ voltage produced by the cell and r is the resistance
inside the cell which ‘absorbs’ the measured voltage across the cell when the current increases.
The formula for this is maximum current is;
I0 =
Resistivity
ε
r
This concept is unintuitive and has unintuitive units.​Resistivity is ​
not​the resistance ( Ω ) per meter ( m ) of a
material. It is instead the resistance ( Ω ) multiplied by the surface area ( m2 ) per meter ( m ) of a material.
Why is this the case?
While this makes resistivity harder to work with in physics, it means that instead of defining different resistances
per meter for different gauge wires (with different cross-sectional areas), we can instead define a constant
property of a material that can be applied when using the material for different gauge wires.
It is extremely easy to make the mistake of thinking that resistivity is the resistance per meter of a material - do
not make this mistake!
It makes sense, since increasing length increases the distance which the charge has to travel, thereby increasing
the resistance, whereas the area increases the amount of charge that can go through at a time, thereby
decreasing resistance.
Propagation of
uncertainties
Table of calculations
Op.
Efficient propagation method
×
Sum percentage/fractional
Errors on graphs and
gradient uncertainties
÷
Sum percentage/fractional
+
Sum absolute
−
Sum absolute
√n
Divide percentage/fractional uncertainty by n
bn
Multiply percentage/fractional uncertainty by n
||
Is mathematically equivalent to √x2 root-squared which will not change uncertainty
b
Average the absolute uncertainties to gain absolute uncertainty of average. (I tested this in Excel
and it checks out)
The error bars on the graph represent the uncertainty. The gradient uncertainty can be calculated by finding the
steepest and shallowest lines of best fit that can pass through the error bars of the data, finding the difference
between these (subtracting the smaller from the larger value) and then dividing this by two.
Example 我的 physics IA
ΔP lossconst here is the gradient. The green line is the steepest line of best fit and the yellow line is the shallowest
one. It is important to note here the consideration of the uncertainty in the x-axis direction for this dataset.
Changes in an ideal gas
under isothermal
compression
In an isothermal process the temperature is constant, and there is therefore no change in temperature, whereas
in adiabatic processes there is no energy or mass transferred from or to the system. In an isothermal
compression, there is work being done on the system, which would raise its temperature, since decreasing
volume increases the temperature. However, we are not allowed to raise its temperature, and therefore heat
energy leaves the system, and this energy is equal to the work that is done in compressing the system. The
opposite is true for expansions.
Rutherford’s Gold Foil
Experiment
They shot some alpha particles through a gold foil, and the outcome was that most went through, whereas a
fraction of the alpha particles got scattered. This demonstrates that the positive charge of an atom is
concentrated within the centre, since most of the charge was unaffected in its momentum, but a small fraction
was, in a repulsive way (remembering that alpha particles are also positively charged, and positive charges repell
each other). If there are an equal number of alpha particles passing through each unit of cross sectional area,
and only a fraction experienced a significant change, it follows that only a fraction of that cross sectional area is
significantly positively charged, and therefore it is infered that the positive charge is concentrated in the centre.
With the Thomson model, they calculated the predicted change in momentum using this formula
and these values
But Thomson’s model is wrong
Albedo Number and
Black Body Radiation
Albedo Number
Albedo number is the fraction of total incoming solar radiation that is diffusely reflected. Diffuse reflection is when
the ray of light is scattered in many angles as seen below.
Usually things are higher in albedo the more white they are. I have a very high albedo number.
Black Body Radiation
A black body is a body with an albedo number of zero, meaning that it does not reflect the incident
electromagnetic radiation, but only absorbs it. It is an ideal emitter, emitting electromagnetic radiation, which can
be calculated with the formula
. There would be an ​
e​there, which is the emissivity number, but
black bodies have an ​e​of 1, since they are ideal emitters. THERE IS MORE TO PUT HERE HOLD ON
Velocity of a Plane Flying To find the resultant velocity of a plane flying through the wind, one must perform a vector addition of the velocity
in a Crosswind
of the plane without the wind and the velocity of the wind.
Also, the formula for fluid resistance (which is what the plane is traveling i.e air), is as follows:
F is the ​
drag force​,
ρ is the density of the fluid,
v i​s the speed of the object ​relative t​o the fluid,
A i​s the cross sectional area, and
C i​s the drag coefficient – a dimensionless number.
Now what we are concerned with here is when the forces are in equilibrium, resulting in a constant velocity.
Without wind, the plane still experiences friction with the air, since it is moving, and the ​
v​in the formula is given
by the velocity of the plane in this situation. In such a situation, assuming constant velocity, the force of the
engine in this situation would be equal to the force of friction in this situation. The power of the engine is thus
F​0​v​0.​ Given a headwind (or cross wind or whatever), the ​v​in the formula is going to increase, since the plane is
going to be travelling at a higher velocity relative to this backwards moving wind. Therefore, the fluid resistance
force is going to be higher, and the engine is going to be exerting a higher force to maintain constant velocity by
canceling out this fluid resistance force. Since the force is higher, and power is equal to ​
Fv,​ and the power is the
same, the ​v ​value of the aeroplane is going to be smaller. .
tl;dr its just vectors innit
Resolving Twin and
Barnpole Paradox
The Twin Paradox
There are two twins, twin A and twin B, and twin B goes on a rocket journey. He will be going very fast relative to
the earth, and the earth will be very fast relative to him. This means that, not only will time dilation of the rocket
occur in the earth’s reference frame, but also time dilation of the earth in the rocket’s reference frame. So what
happens when twin B gets back? Who will be older?
Resolution
One solution is to say that twin B accelerates and twin A does not, which would allow for an asymmetry between
them. Using a minkowski diagram would visually demonstrate how this asymmetry would play out.
This shows how, whereas twin A maintains the same inertial reference frame, twin B changes inertial reference
frames. Furthermore, since simultaneous events may not be simultaneous in other reference frames,
PHYSICS TOPIC BY TOPIC NOTES + DEFINITIONS
Topic
Important Information
1.1 - Measurement in Physics
Learning objectives
• State the fundamental units of the SI
system.
- Length - meter (m)
- Time - seconds (s)
- Amount of substance - mole (mole)
- Electric current - ampere (A)
- Temperature - kelvin (K)
- Luminous intensity - candela (cd)
- Mass - kilogram (kg)
• Be able to express numbers in scientific
notation.
- if you can’t do this you’re a spastic
• Appreciate the order of magnitude of
various quantities.
• Perform simple order-of magnitude
calculations mentally.
• Express results of calculations to the
correct number of significant figures
1.2 - Uncertainties and errors
Learning objectives
• Distinguish between random and
systematic uncertainties.
- Random uncertainty is due to a fault
in the observer and limits accuracy. It
happens when there is a spread of
values.
- Systematic is due to both the
observer and the instrumetn and is
one direction, and so limits precision
• Work with absolute, fractional and
percentage uncertainties.
• Use error bars in graphs.
• Calculate the uncertainty in a gradient or an
intercept
1.3 - Scalars and Vectors
2.1 - Motion
Learning Objectives
• Understand the difference between
distance and displacement.
- Distance is the length of the path
followed
- Displacement is the difference in
position
• Understand the difference between speed
and velocity.
- Speed is a scalar quantity. It is the
distance over time.
- Velocity is a vector quantity. It is
difference of displacement over the
difference in time. Instantaneous
velocity is when both these values are
infinitessimally small.
• Understand the concept of acceleration.
- Acceleration is difference in velocity
over difference in time
• Analyse graphs describing motion.
• Solve motion problems using the equations
for constant acceleration.
• Discuss the motion of a projectile.
Key Definitions
• Show a qualitative understanding of the eff
ects of a fluid resistance force on motion.
- see the next one
• Understand the concept of terminal speed
- when an object is travelling through a
fluid, it experiences a resistive force
from the fluid that is opposite in
direction to the direction of its
velocity. The equation for this force is
F = kv for slow things and F = kv​2 ​for
fast things.
- Terminal velocity is what happens
when for a falling object the force of
gravity and the force of fluid
resistance reach equilibrium, thus
resulting in a constant velocity. This is
calculated as v​T​= mg/k
2.2 - Force
Learning objectives
• Treat bodies as point particles.
• Construct and interpret freebody force
diagrams.
• Apply the equilibrium condition, ΣF = 0.
• Understand and apply Newton’s three laws
of motion.
• Solve problems involving solid friction
Equilibrium ​
of a point particle means that
the net force on the particle is zero
Friction
Friction acts against the motion of the object
2.3 - Work, Energy and Power
Learning objectives
• Understand the concepts of kinetic,
gravitational potential and elastic potential
energy.
- Kinetic energy:
-
-
Anything that is moving has
kinetic energy
- When work is done on an
object of mass ​m​, assuming
all the work is transferred into
the kinetic energy of the
object, the resulting kinetic
energy is equal to that work,
and this can be used to
calculate the resulting velocity.
This can be derived from the
equation ​v​2​= u​2​+ 2as.​ Just
stick ​m​in front of all of them.
Gravitational potential energy:
-
-
the ​h ​is the height which the
object falls or would fall. It
comes from the equation for
work since ​Fg​​= mg​and the
displacement is just ​h.​
Elastic potential energy:
• Understand work done as energy
transferred.
• Understand power as the rate of energy
transfer.
• Understand and apply the principle of
energy conservation.
• Calculate the efficiency in energy transfers.
2.4 - Momentum and Impulse
3.1 - Thermal Concepts
●
Use the concept of pressure
Heat​is energy that is transferred from one
●
●
●
●
Solve problems using the equation
state of an ideal gas.
Understand the assumptions behind
the kinetic model of an ideal gas
○ The molecules are point
particles, each with negligible
volume
○ The molecules obey the laws
of mechanics
○ There are no forces between
the molecules except when
the molecules collide
○ The uration of a collision is
negligible compared to the
time between collisions
○ The collisions of the
molecules with each other and
with the conttainer walls are
elastic
○ Molecules have a range of
speeds and move randomly
○ Fun Fact, real gases may be
approximated by an ideal
gas when density is low
body to another as a result of a ifference in
temperature.
Internal energy​is the total random kinetic
energy of the particles of a substance, plus
the total inter particle potentttial energy of the
particles.
Solve problems using moles, molar
masses and the Avogadro constant
Describe differences between ideal
and real gases
3.2 - Modelling a Gas
4.1 - Oscillations
●
●
●
●
4.2 - Travelling Waves
●
●
●
●
●
●
Understand the conditions under
which simple harmonic oscilattions
take place
Identify and use the concepts of
period, frequency, amplitude,
displacement and phase difference
Describe simple harmonic oscillations
graphically
Desccribe the energy transformations
taking place in oscillations
○ the total energy is conserved
Oscillation ​
is the repetitive variation,
typically in time, of some measure about a
central value or between two or more
different states.
Describe waves and wave motion
Identify wavelength, frequency and
period from graphs of displacement
against distance or time
Solve problems with wavelength,
frequency, period and wave speed
○ this one is pretty is its just v =
f*lambda, and also f = 1/T
Classify waves as transverse and
longitudinal
Describe the nature of
electromagnetic waves
Desccribe the nature of sound waves
A​
wave​is a propagating dynamic
disturbance (change from equilibrium) of one
or more quantities, sometimes as described
by a wave equation
Simple harmonic motion​is a special type
of periodic motion where the restoring force
on the moving object is directly proportional
to, and opposite of, the object's displacement
vector.
4.3 - Wave Characteristics
4.4 - Wave Behaviour
4.5 - Standing Waves
5.1 - Electric Fields
A​
standing wave​
, also known as a
stationary wave​
, is a wave which oscillates
in time but whose peak amplitude profile
does not move in space.
• Understand the concept and
properties of electric charge.
• Apply Coulomb’s law.
• Understand the concept of
electric fi eld.
• Work with electric current and
direct current (dc).
• Understand the concept of
electric potential diff erence.
An ​
electric field​is the physical field that
surrounds each electric charge and exerts
force on all other charges in the field, either
attracting or repelling them.
5.2 - Heating Effect of Electric Currents
• Understand how current in a
circuit component generates
thermal energy.
• Find current, potential difference
and power dissipated in circuit
components.
● For finding the current of a circuit, one
should use the formula ε = I(R+r), but
rearranged so as to solve for I.
● Find potential difference by
multiplying the resistance by the
current in those sections.
● power dissipated in circuit
components is just IR​2​, where I is the
current of the circuit, and R is the
resistance of that component.
• Define and understand electric
resistance.
• Describe Ohm’s law.
● Ohm’s law is that the current in a
circuit is directly proportional to the
voltage. Sometimes this does not
hold, with the resistance changing
depending on the current.
• Investigate factors that affect
resistance.
• Apply Kirchhoff ’s laws to more
complicated circuits.
5.3 - Electric Cells
5.4 - Magnetic Fields
6.1 - Circular Motion
6.2 - The Law of Gravitation
7.1 - Discrete Energy and Radiation
• Describe and explain gas spectra
in terms of energy levels.
• Solve problems with atomic
transitions.
• Describe the fundamental forces
between particles.
● Electromagnetic force
● Weak Nuclear Force
● Strong Nuclear Force
● Gravitational Force
• Describe radioactive decay,
including background radiation,
and work with radioactive decay
equations.
• Describe the properties of alpha,
beta and gamma particles
● alpha particles have two protons and
two neutrons. low penetration
● beta radiation can be positive or
negative. The negative is when a
neutron becomes a proton, and emits
an electron as well as an antineutrino.
The positive is when a proton
becomes a neutron and emits a
positron and a neutrino.
● Gamma radiation is photons. Its just
very penetraty, and it has high energy
• Understand isotopes.
7.2 - Nuclear Reactions
7.3 - The Structure of Matter
• Describe the Rutherford, Geiger
and Marsden experiment and
how it led to the discovery of
the nucleus.
• Describe matter in terms of
quarks and leptons.
• Describe the fundamental
interactions in terms of
exchange particles and Feynman
diagrams.
• Apply conservation laws to
particle reactions.
8.1 - Energy Sources
●
●
●
Solve problems with specific energy
and energy density
Distinguish between primary and
secondary energy sources and
renewable energy sources
Describe fossil fuel power stations,
nuclear power stations, wind
generators, pumped storage
hydroelecttric systems, solar power
cells and solar panels
○ Fossil Fuels
■ relatively cheap
■ high power output, ie
high energy density
■ variety of engines and
devices use them
directly and easily
■ extensive distribution
network is in place
■ will run out
■ pollute the envionment
■ contribute to
greenhouse effect by
releasing greenhouse
gases into atmosphere
○ Nuclear power
■ high power output
■ large reserves of
nuclear fuels
■ nuclear power stations
do not produce
greenhouse gases
■ radiacttive waste
products difficult to
dispose of
■ major public health
hazard should
something go wrong
■ problems associate
with uranium mining
■ possibility of producing
materials for nuclear
weapons
○ Solar power
■ free
■ inexhaustible
■ clean
■ works during the day
only
■ affected by cloudy
weather
■ low power output
■ requires large areas
■ initial costs high
○ Hydroeletric power
■ free
■ inexhaustible
■ clean
■ very dependent on
location
■ requires ddrasttic
changes to evironment
■ initial costs high
○ Wind power
■ free
■ inexhaustible
■ clean
■ depenent on local wind
conditions
■ aesthetic problems XD
■ noise problems
8.2 - Thermal Energy Transfer
●
Solve problems involving energy
transformations in the systems above
●
Understand the ways in which heat
may be transferred
Sketch and interpret black body
curves
Solve problems using the stefan
blotzmann and wien laws
Describe the greenhouse effect
○ Electromagnetic radiation
comes from the Sun to the
Earth
○ Earths surface absorbs some
of that, and so radiates some
of it
○ This then is partially radiated
back to space, and partially
absorbed by the atmosphere
and reradiated back to Earth
Apply the stefan boltzmann law to
solve energy balance problems for
the earth
●
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