AS Physics
Mechanics
Forces and Momentum
Moments
Work, Energy and Power
Motion
SUVAT Equations
s = vt - 1/2 at^2
v = u + at
s = 1/2 (v + u) t
v^2 = u^2 + 2as
y-time Graphs
Displacement-time
Flat line: Stationary
Straight diagonal line: Constant speed
Positive slope: Moving forward
Negative slope: Moving backwards
Steeping curve: Acceleration
Flattening curve: Deceleration
Velocity-time
Flat line: Constant speed
Positive slope: Acceleration
Negative slope: Deceleration
Area underneath: Displacement
Acceleration-time
Flat line above x axis: Constant acceleration
Flat line on x axis: Constant speed
Flat line below x axis: Constant acceleration in the opposite direction
Area underneath: Speed
Scalars and Vectors
Scalar: Only has a magnitude
Vector: Has a magnitude and direction
Speed
Mass
Distance
Weight
Displacement
Velocity
Resolving Vectors
Pythagoras Theorem, Sine Rule or Cosine Rule: Find the magnitude from components
SOHCAHTOA: Find the direction (as an angle)
Projectile Motion
Acceleration is ALWAYS 9.81
Vertical and Horizontal Components of motion are independent to each other
Maximum Height
Use vertical component
Refer to v^2 = u^2 + 2as
Time of Flight
Use vertical component
Refer to 2 x (v = u + at)
Horizontal Distance
Use horizontal component
Refer to s = vt
Drawing Free Body Diagrams
Must involve both horizontal and vertical forces
Draw arrows to a length representing the size of the force
Waves
Transverse and Longitudinal Waves
Interference and Stationary Waves
Refraction, Reflection and Polarisation
Waves, Electrons and Photons
The Photoelectric Effect and Atomic Spectra
Key definitions
Wavefront
Coherence
Path difference
Superposition
Interference
Phase
The stage a point is at on a complete wave cycle
The vector sum of two meeting waves' displacements
Waves that have the same frequency and phase difference
A line that represents points where a wave is in phase
Difference in distance of two waves from where they meet
Is either constructive or destructive as a result of superposition
Standing waves
Formed by two coherent waves
Waves superpose whilst travelling in opposite directions
Constructive interference happens - antinodes form
Destructive interference happens - nodes form
Path and phase difference
Path difference
Phase difference
Below x axis: Moving in the opposite direction
No need to draw horizontal and vertical components
Newton's 1st and 2nd Laws
1st Law
Object remains at rest or constant velocity unless acted on by a RESULTANT force
Interference differences
Destructive: pi or (n + 1/2)λ
Constructive: 2pi or nλ
No resultant force if opposite forces are equal to each other
2nd Law
Two ways to describe
Resultant force is directly proportional to acceleration
When a resultant force acts on an object, it accelerates at the force's direction
F = ma
Applying both laws to scenarios
Moving objects can have a resultant force acting due to:
With increasing acceleration, the driving force increases, but so do drag forces
A driving / thrust force produced by them
Their own weight (if they are falling)
Friction and drag forces
Those forces will equal each other to the point of no resultant force
A maximum terminal velocity would be reached
Gravity
W = mg
g = 9.81 on Earth
g = W / m
Freefall - an object falls only due to its weight, so acceleration is always g
Newton's 3rd Law
When two bodies collide with each other, they exert equal and opposite forces
Conditions
Exactly two objects involved
Same type of force
Same magnitude
Same line of direction
Examples
A foot exerts a force on the ground. The ground exerts the same force on the foot for it to step forward
Momentum as a quantity
p = mv
Units are kg ms^-1
A vector quantity
Conservation of momentum
In a closed system, the sum of momentums before an event/collision = sum of momentums after it
Closed system - no external forces or external energy transfer
Applying N3
Understand that two objects exert equal and opposite forces on each other
One object gains momentum, the other loses it
Magnitudes of forces before and after
Before: F
After: -F
Acceleration is equal for objects of equal mass
One object accelerates from 0 to v
The other object decelerates from v to 0
Moment = Fx
F for force
x for PERPENDICULAR distance
Units are Nm
Centre of gravity
Conservation of momentum
For a system to be in equilibrium, about a pivot, clockwise moments = anticlockwise moments
The point where all of an object's weight is said to act on
An object is stable if the centre of gravity lies above its base
Wider base - more stable
Thinner base - less stable
Work done
Energy transferred in applying force by a distance
Force must be in same direction of motion
If not in same direction, use sin0 or cos0
W = Fd
Types of energy stores
Kinetic
Gravitational Potential
Energy stored in a moving object
Changes with velocity / acceleration
KE = 1/2 mv^2
Energy stored when in a gravitational field
Changes with height
Acceleration --> Increases
Deceleration --> Decreases
Higher --> Increases
Lower --> Decreases
On ground = 0
GPE = mgh
Conservation of energy
Energy cannot be created or destroyed, only transferred
There is a link between KE and GPE - one can be transferred to the other
Objects in freefall
Moving pendulum
Drag forces may have effects on the total energy in the system
Power
Rate of energy transfer
P = W / t
P = Fv
Efficiency
Can relate to energy or power transfer
Ratio of useful output to total input
Useful Output / Total Input
Electricity
Current, Voltage, Resistance and Power
Current
The rate of flow of charge
I = Q / t
Q for charge (C)
t for time (s)
Made up of charge carriers, e.g. electrons
Measured in amperes (A)
Two types
Conventional: + to -
Electron: - to +
Voltage / Potential Difference
The work done per unit charge
V = W / Q
W for work done (J)
Q for charge (C)
Resistance
Opposes current
Ohm's law
V = IR
Measured in ohms (Ω)
Current is directly proportional to p.d. for a CONSTANT TEMPERATURE
Obeyed by a fixed resistor
Kirschoff's Laws
1st Law
2nd Law
Sum of currents entering junction = Sum of currents leaving junction
Charge is being conserved
Series and Parallel
Q(t) = Q(1) + Q(2)...
For series: Same at every point
For parallel: Total split between branches
I(t) = I(1) + I(2)...
I(t) = I(1) = I(2)...
Sum of e.m.f.s in a closed loop = Sum of p.d.s in that closed loop
Energy is being conserved
Closed loop represents series circuit
Series and Parallel
For series: e.m.f. is split across components
E = V(1) + V(2)...
For parallel: p.d. for each closed loop is equal to e.m.f.
E = V(1) = V(2)...
In series
In parallel
R(t) = R(1) + R(2)...
V(t) = V(1) + V(2), so IR(t) = IR(1) + IR(2), but current is constant
1/R(t) = 1/R(1) + 1/R(2)...
I(t) = I(1) + I(2), so V/R(t) = V/R(1) + V/R(2), but p.d. is constant
Power
P = IV
As V = IR, P = I^2R
As I = V/R, P = V^2 / R
Exponential increase if voltage or current increases (e.g. 4x if I or V doubles)
As P = W/t, then W = IVt
IV graphs
Ohmic conductors
Filament bulbs
Thermistors
Diodes
Straight line - resistance is constant and Ohm's law is followed
Decreasing gradient - temperature increases with current, so will resistance, hence current increases much slower over time
Current is zero on one side, but very high on the other
Increasing gradient - temperature increases with current, but resistance falls, so current increases at a faster rate
Diodes let current flow in ONE DIRECTION ONLY
Forward bias - of low resistance, current can flow
Reverse bias - of very high resistance, no current can flow
Resistance, Resistivity and Potential Dividers
Resistivity
R = pl / A
R is directly proportional to p (resistivity) & l (length of wire)
R is inversely proportional to A (cross sectional area of wire)
How well a material opposes current
Resistance exists as electrons in current collide with ions of a wire
Ions reduce the flow of charge
Kinetic energy of electrons is transferred as heat, rate of flow decreases
The Current Equation
I = nAqv
v for drift velocity
I for current
n for charge carrier density
A for cross sectional area
q for charge
Drift velocity - mean velocity of charge carriers, e.g. free electrons
Relationships
Charge carrier density - number of charge carriers per unit volume
v is inversely proportional to n, A & q
v is directly proportional to I
Resistivities of different materials
Insulators have high resistivity - very little or no charge carriers
Conductors have low resistivity - lots of charge carriers including free electrons
Semiconductors have varying resistivity - normally have low number of delocalised electrons, but number increases with temperature / intensity
Since V = IR, for a constant current V must also increase with length
Potential Divider Circuits
Circuits that vary a component's output voltage as a fraction of the input voltage
Resistance can vary to adjust the voltage ratio of R1 and R2
Vout = (Vin * R2) / (R1 + R2)
For two different resistors:
Larger R: Greater share of Vin
Smaller R: Smaller share of Vin
Effects of semiconductors
Their voltage increases with resistance, so a resistor's voltage is of a lower share then
Their voltage decreases with resistance, so a resistor's voltage is of a higher share then
Potentiometers and variable resistors are responsible for this variance
Potentiometers
Variable resistors
Can be set from 0V-Vin
V is measured even w/o current
Cannot set to 0V with other components around
Needs current for V to be measured
EMF and Semiconductors
EMF
The work done per unit charge by a power supply
Charges gain electrical energy as power supply transfers converted chemical energy to them
Internal Resistance
Resistance of a power supply
Causes energy from charges to dissipate as heat energy
Voltage is lost from the EMF as a result - known as lost volts
Terminal P.d.
The p.d. across a cell's terminals or load resistor, taking into account of internal resistance and lost volts
Instead of charges gaining electrical energy, they transfer it to / do work on other components
Resistance and temperature
For metallic conductors and filament lamps
Electrons collide with vibrating ions
Kinetic energy is transferred as thermal energy by the electrons
Temperature increases, so vibrations and their amplitude increase
The rate of collisions between electrons and ions increase
Because the flow of current is resisted and overall current decreases, obviously resistance increases
For thermistors
When temperature increases, electrons gain more energy to be emitted from shells in ions
The no. of charge carriers increases, so current increases, which reduces resistance
Resistance and Light Intensity
For LDRs
When light intensity increases, more light energy is provided for electrons to be emitted from ions
The no. of charge carriers increases, so current increases, which reduces resistance
Difference in distance travelled by two waves from where they meet to their sources
Measured in the angle between them (° or rad)
Difference of stages two points are at on a wave cycle
Measured in multiples of wavelength
Photoelectric effect
When EM radiation is absorbed by an electron on a metal surface, that electron is emitted
hf = hc/λ = Φ + ½mv^2
EM radiation travels as quanta of energy or particles known as photons
The energy of a photon
Φ for work function
½mv^2 for max. kinetic energy
Minimum energy requirement for emitting electrons
Remaining energy transferred after work function releases electrons
f for threshold frequency
Minimum frequency requirement for emitting electrons
Particle vs Wave Nature of Light
Particle Nature
Wave Nature
Increasing intensity increases rate of electron emission
One electron absorbs one photon (energy), and is emitted spontaneously
Energy increases with frequency given that it is above the threshold
Any frequency will cause electron emission
Increasing intensity increases energy
Energy absorbed by electrons gradually increases
c for speed of light
h for Planck's constant
The electronvolt (eV)
A energy unit expressing very small quantities
1 eV = 1.6 x 10^-19 J
Energy Levels and Line Spectra
Excitation - electrons gain energy to move up energy levels of an element
De-excitation - electrons move down energy levels and emit photons of discrete frequency
Electrons must absorb discrete energy to move up energy levels
Energy requirement equals to the energy level difference
Absorption can be due to temperature, absorbing photons, collisions with other atoms / ionisation
Stationary waves on a string
v = √(T / μ)
T for string tension
μ for mass per unit length
At fundamental frequency (shown in image), λ = 2L, L being length of string
Lenses
Definitions
Focal point: Where rays of light intersect / are brought to a focus at
Focal length: Distance between centre of lens and focal point
Types of lenses
Concave / Diverging lens
Convex / Converging lens
Parallel rays appear to be brought / diverge from focal point
Parallel rays are brought / converge to focal point
Power of lens
The ability for a lens to refract light
Ray diagrams
P = 1/f
P is inversely proportional to f
P for Power in (D)
f for focal length
If multiple lenses are used in series (compound lens), total power is the sum of individual powers
With regards to distance: 1/f = 1/u + 1/v
u for object distance from lens
v for image distance from lens
Materials
Density, Upthrust and Viscous Drag
Density
The mass per unit volume of an object
p = m / v
Units are kg m^-3
Upthrust
An upwards force on an object submerged in a fluid
Equal to weight of fluid displaced
Volume of object = Volume of displaced fluid
Weight of object ≠ Weight of displaced fluid
Can be expressed as pVg
p for fluid density
V for object volume
An object stops falling when upthrust (and viscous drag) equals its weight
Viscous Drag
Frictional force opposing object motion in a fluid
Expressed by Stoke's law: F = 6πηrv
Where:
r for radius
v for velocity
Role of drag in terminal velocity
Falling: W = U + D
Drag is in direction of upthrust
Rising: W = U - D
Drag is in direction of weight
Can be expressed by:
η for viscosity coefficient (how well the fluid resists flowing)
Only applicable for:
Small, spherical objects
Low velocity motion
Laminar flow
Laminar vs Turbulent Flow
Relation to temperature
For a gas - increases with it
For a liquid - decreases with it
Laminar flow has layers with same direction and no mixing
Turbulent flow has layers with constantly changing direction and mixing
Stretching Materials
Hooke's Law
Force applied on an object is directly proportional to its extension below its limit of proportionality
F = kΔx
F for force applied
Δx for extension
k for spring constant (Nm^-1) - measure of stiffness
Force-extension graphs
C: Yield point
Elastic deformation
B: Elastic limit
Plastic deformation
A: Limit of proportionality
Point where Hooke's law stops being obeyed
Point before elastic deformation stops being seen
Point where material shows increasing extension for little to no force applied
Before B
After B
Material returns to original shape from deformation once force is removed
Material retains deformed shape once force is removed
Elastic strain energy
Area under a force extension graph
Written in 2 forms
1/2 FΔx
1/2 kΔx^2
Work done on an object and stored by it in order to stretch it
Diffraction
The idea that a wave spreads out when in contact with an obstruction such as a slit / obstacle
Increases as the slit width narrows to the wavelength
More than wavelength - no more diffraction
Huygens Principle
Points of a wavefront are sources of wavelets
Wavelets can interfere with each other constructively and destructively
Diffraction Gratings
When a monochromatic light beam passes through a grating, light and dark fringes form due to diffraction
dsin0 = nλ
d for spacing between slits (m)
1/ No. of slits per (m)
0 for angle from central maxima
n for order of maxima
λ for wavelength
Young Modulus
A measure of stiffness - ratio of stress to strain
Stress - force applied per unit area in Pa
Stress = Force / Area
Strain - extension per unit length (no dimensions)
Strain = Extrension / Length
Young Modulus = Stress / Strain in Pa
Stress strain graphs
No different from force-extension graphs
Breaking / Fracture stress - point where material breaks due to complete separation of atoms
Young modulus found from gradient of linear elastic region-
Magnification
Image height / Object height
Lens distance to image / Lens distance to object
Real vs Virtual Images
Real images
Virtual images
Form on a screen
Created by intersecting rays from diverging or converging
Cannot be formed on a screen
Created by diverging rays
Diverging: Object is at any distance
Converging: Object is less than focal length away
Inverted
Upright
Polarisation
Oscillations are confined to one plane, which includes direction of energy transfer
Light can be partially polarised if reflected from a non-metallic surface
Transverse waves are polarised as oscillations are in more than one direction, unlike longitudinal waves
s = ut + 1/2 at^2
Electric and Magnetic Fields
Electric Fields
Defining an electric field
A region that a charged particle feels a force in
Charges can create their own electric fields that exert forces on other charges
Force is felt regardless if it is moving or not
Electric Field Strength
General
Due to point charge
Electric Field Strength = Force / Charge
Force per unit charge acting on a positive charge
Direction
Towards a positive charge
Away from a negative charge
Colomb's Law
The electrostatic force between two charges is:
Proportional to product of charges
Inversely proportional to square of separation
F = kQ1Q2 / r^2
Force is:
Negative due to opposite charges / attraction
Positive due to same charges / repulsion
Field Strength = kQ / r^2
Field produced is radial
Electric Potential
Work done per unit charge to move a positive charge from infinity to a point in an electric field
Potential gradient - rate of change in potential with respect to direction of displacement
If potential gradient changes more rapidly with displacement, field strength is stronger
Decreases the further you are from a positive charge
Increases the further you are from a negative charge
If potential gradient changes more gradually with displacement, field strength is weaker
Due to parallel plates
Field strength = V / d
Field produced is uniform
Electric Potential Energy
Work done to move a positive test charge:
Away from a negative charge
Near to a positive charge
Equation: V = kQ/r
For positive charge, V is positive and increases as r decreases
For negative charge, V is negative and decreases as r decreases
More work is done to overcome repulsion
Less work is needed since the attractive force becomes stronger