Additional notes Flashcards
Vector triangles in Circular Motion
A vector triangle can be drawn with existing velocities, to determine change in velocity represented by completing the vector triangle
Textbook figure 16.9
Newton’s thought experiment
In order to get an object into orbit it must be fired at just the correct speed else it will either go out of orbit or be pulled down by gravity
Textbook figure 16.10
Maximum displacement from equilibrium position
amplitude x₀
Displacement time graph for s.h.m
Shows period (T) and amplitude (x₀)
Velocity can be determined by gradient of graph
Textbook figure 18.7
Phase difference for waves with different frequencies
Waves with different frequencies have continuously changing phase differences
Requirements for s.h.m (3)
The three requirements for s.h.m. of a mechanical system are:
- a mass that oscillates
2. a position where the mass is in equilibrium
3. a restoring force that acts to return the mass to its equilibrium position; the restoring force F is directly proportional to the displacement x of the mass from its equilibrium position and is directed towards that point
Velocity time graph for s.h.m
where displacement is zero velocity is at a maximum (could be positive or negative)
acceleration can be determined from gradient of graph
Acceleration time graph for s.h.m
acceleration is proportional to the negative displacement which is a key idea
a ∝ - x
Acceleration displacement graph for s.h.m
gradient is -ω²
Textbook figure 18.20
Gradient and amplitude relationship for s.h.m
The gradient is independent of the amplitude of the motion. This means that the frequency for the period T of the oscillator is independent of the amplitude and so a simple harmonic oscillator keeps steady time.
Key idea behind a = -ω²x
We say that the equation a = -ω²x defines simple harmonic motion-it tells us what is required if
a body is to perform s.h.m.
The equation x = x₀ sin ωt is then described as a solution to the
equation, since it tells us how the displacement of the body varies with time
Kinetic and potential energy of an oscillator
The kinetic and potential energy of an oscillator vary periodically but the total energy remains constant if the system is undamped
Textbook figure 18.22
Kinetic and potential energy graph for s.h.m
Kinetic energy is max when displacement x = 0
Potential energy is max when displacement x = ±x₀
Total energy = Ek + Ep
(total energy is the same at any point on the graph)
Textbook figure 18.23
Amplitude and driving frequency graph
Maximum amplitude is achieved when the driving frequency equals the natural frequency of oscillation
Textbook figure 18.32
Types of damping
Damping reduces the amplitude of resonant vibrations, the heavier the damping the smaller the amplitude
Textbook figure 18.34
Critical damping is just enough to ensure that a damped system returns to equilibrium without oscillating
Textbook figure 18.35
Temperature against time graph for heating water/ice at a steady rate
The regions where the temperature does not change represent where all the energy is being used to change the state of the ice/water into water/gas (breaking bonds) and no energy is being used to change the temperature, hence the temperature stays constant
During change of state:
temperature does not change, molecules are breaking free of one another and potential energy in increasing
Between change of state:
input energy raises temperature of substance, molecules move faster and kinetic energy is increasing
Note:
takes longer or more energy to go from water to gas than from ice to water
Textbook figure 19.4
Potential energy and separation graph for atoms
The electric potential energy of atoms is negative and increases as they get further apart
Textbook figure 19.5
Changing internal energy
To increase the internal energy of a gas you can heat or compress it
Likewise its internal energy can decrease if it loses heat to its surroundings or does work on its surroundings by expanding
First law of thermodynamics; Rules and positive and negative values
Positive:
(U) internal energy increases
(q) heat added to system
(w) work done on the system
Negative:
(U) internal energy decreases
(q) heat taken away from the system
(w) work done by system
At constant volume:
No work is done ∴ ∆U = q
Not allowing heat to leave or enter system:
No heat is added or lost ∴ ∆U = W
Constant temperature:
∆U constant ∴ U = 0 ∴ q + w = 0
Key idea around thermal energy transfer
Thermal energy is transferred from a region of higher temperature to a region of lower temperature
Key idea about thermodynamic temperature scale
Thermodynamic temperatures do not depend on the property of any particular substance
Resistance thermometer (thermistor and resistance wire) and thermocouple thermometer comparison
Features:
robustness
range
size
sensitivity
linearity
remote operation
Textbook table 19.2
Graphs of Boyle’s law (2)
p ∝ 1/V
Textbook figure 20.5
Relationship between volume and temperature of gas
The volume of a gas decreases as its temperature decreases
Textbook figure 20.6
Limits of Charles and Boyle’s law
At low temperatures of high pressures gasses start to deviate from these laws
Textbook figure 20.7
Basic assumptions of the kinetic theory of gases (4)
No intermolecular forces
Textbook table 20.1
Relationship between mean translational kinetic energy of an atom and thermodynamic temperature
Mean translational kinetic energy of an atom ∝ T
Monatomic and diatomic molecules
Monatomic molecules have only translational kinetic energy and diatomic molecules have both translational and rotational kinetic energy
Field lines show (2)
- Direction of gravitational force on mass placed in field
- Spacing of field lines indicate strength of gravitational field, the further apart the weaker
Types of fields (2)
Radial, field lines diverge (spread out) radially from the centre of the object
Uniform, field lines equally spaced and parallel
Terminology: field strength and potential
Field strength describes the force on a unit mass at a point
Potential describes potential energy of unit mass at a point
Johannes Kepler discovery
T² ∝ r³
The types of fields and what they act on (3)
Electric fields - acts on objects with electric charge
Magnetic fields - act on magnetic materials, magnets and moving charges (including electric currents)
Gravitational fields - act on objects with mass
Strength of a uniform field
E ∝ V
Higher the voltage, stronger the field
E ∝ 1/d
Greater the separation, weaker the field
Negative sign in strength of a uniform field between two parallel plates !equation!
E = - [V/d]
Negative sign often omitted due to interest in only magnitude, but is there to represent that V increases to the right while F acts in the opposite direction
Path of electron through uniform electric field
There is a parabolic path of a moving electron in a uniform electric field accelerating towards the positive plate
Textbook figure: 21.14
Attraction and repulsion and positive and negative charges with electric fields
If there is a positive and negative charge, then the force F is negative. This is interpreted as attraction. Positive forces, between two like charges, are repulsive. With gravitational fields there is only attraction.
Energy changes in a uniform field graph
Electrostatic potential energy changes in a uniform field
Textbook figure 22.7
Defining voltage in terms of the potential energy of a charge
V is the energy per unit positive charge at a point in an electric field
Potential changes according to an inverse law near a charged sphere graph
Textbook figure 22.10
Electric field around a positive charge graph
The dashed equipotential lines are like contour lines on a map; they are spaced at equal intervals of potential
Textbook figure 22.11
Relationship between field strength and potential gradient
electric field strength = - potential gradient
Textbook figure 23.12
Charge in a current time graph
In any circuit, the charge that flows past a point in a given time is equal to the area under a current-time graph (just as distance is equal to the area under a speed-time graph)
Markings on capacitors
Many capacitors are marked with their highest safe working voltage. If you exceed this value, charge may leak across between the plates, and the dielectric will cease to be an insulator.
Work done when charging a capacitor
When a capacitor is charges, work must be done to push additional electrons against the repulsion of the electrons that are already present
Area under graph of voltage against current
The area under the graph of voltage against current gives a quantity of energy.
The area in ‘a’ shows the energy stored in a capacitor
The area in ‘b’ shows the energy required to drive a charge through a resistor
Textbook figure 23.7
Rules for capacitors in parallel (2)
The p.d across each capacitor is the same
The total charge on the capacitors is equal to the sum of the charges
Comparing capacitors and resistors
The reciprocal formula for capacitors in series is the opposite for resistors who use the reciprocal formula for resistors in parallel
Sharing charge between capacitors
Capacitors are represented by containers of water. A wide (high capacitance) container is filled to a certain level (p.d). It is then connected to a container with a smaller capacitance, and the levels equalise. (The p.d is the same for each.) Notice that the potential energy of the water has decreased, because the height of its centre of gravity above the base level has decreased. Energy is dissipated as heat, there is friction both within the moving water and between the water and the container
Textbook figure 23.17
Charge and discharge of capacitors
The capacitor is charged by the battery when the switch is connected to terminal P.
A current is observed in the microammeter which starts off quite large and gradually decreases to zero.
When connected to terminal Q, the capacitor discharges through the resistor and a current in the opposite direction is observed.
As with the previous current it starts off large and gradually falls to zero.
Textbook figure 23.18 and 23.19
Relationships between electrical quantities and capacitance
Charge ∝ p.d
Charge is dependant on p.d
Charge is always shared between capacitors
Average power dissipated or average power tends to use the constant 1/2 when calculating.
Uses for capacitor (3)
Time delay, anti surge, anti spark.
Magnetic field introduction
(where it exists)
(making one)
A magnetic field exists wherever there is a force on a magnetic pole.
You can make a magnetic field in 2 ways:
using a permanent magnet
using the movement of electric charges, (usually by having an electric current)
Magnetic field patterns for a solenoid and a flat circular coil
Textbook figure 24.3 (a, b)
Magnetic field pattern around current carrying wire
Textbook figure 24.4
Forces between current carrying wires (parallel and antiparallel)
Textbook figure 24.22 and 24.23
Parallel currents attract one another
Antiparallel currents repel
Comparing forces in magnetic, gravitational and electric fields
All fields are:
Defined in terms of the force on a unit mass, charge or current
Decreasing strength with distance from the source of the field
Representation by field lines; direction showing direction of force
density showing relative field strength
Electric force (upwards) = Magnetic force (downwards)
Direction of conventional current and electrons
The flow of electrons opposes the direction of the flow of conventional current
Fleming’s left-hand rule for particle velocity
The force F is always at right angles to the particle’s velocity v, it’s direction can be found using Fleming’s left-hand rule
Factors affecting induced emf (straight wire and coil)
Straight wire: (BLV)
- magnitude of magnetic flux density
- length of wire in field
- speed of wire moving across magnetic field
Coil: (BAN cosx / t
- magnitude of magnetic flux density
- cross-sectional area of coil
- angle between plane of coil and magnetic field
- number of turns of wire
- rate at which coil turns in the field
Induced e.m.f for a conductor not part of a complete circuit
When a conductor is not part of a complete circuit, there cannot be a current induced by e.m.f.
Instead, negative charge will accumulate at one end of the conductor, leaving the other end positively charged, hence there is an induced e.m.f across the end of the conductor.
Textbook figure 26.10
How to induce and e.m.f
Changing magnetic flux density (B)
Changing cross-sectional area of circuit (A)
Changing angle (θ)
Origin of current in electromagnetic induction
There is a current caused by the induced e.m.f current because the electrons are pushed by the motor effect (electromagnetic induction is simply a consequence of the motor effect).
Forces and movement (solenoid, straight wire)
Textbook figure 26.22 & 26.23
Solenoids and magnetic pole induction
If a north pole is moved into a solenoid, then the solenoid itself will have a north pole at that end.
If a north pole is moved out of the solenoid, then the solenoid will have a south pole at that end.
Electromagnetic induction from generators and graphs for flux linkage and induced e.m.f against time
Textbook figure 26.25 & 26.26
Flux linkage at maximum when coil is vertical and zero when coil is horizontal
Induced e.m.f at maximum when coil is horizontal and zero when coil is vertical
Transformers
A simple transformer has a primary coil and a secondary coil, both wrapped around a soft iron core.
An alternating current is supplied to the primary coil which produces a varying magnetic flux in the soft iron core.
The secondary coil is linked by the same changing magnetic flux in the soft iron core, so an e.m.f is induced at the ends of this coil.
According to Faraday’s law, you can increase the induced e.m.f at the secondary coil by increasing the number of turns of the secondary coil, having fewer turns of the secondary coil will reduce the induced e.m.f.
Determining frequency and amplitude (peak value of voltage) on a C.R.O
Example:
If the y-gain or y-sensitivity setting is 2V/cm, then the peak voltage is 2 x (number of squares vertically at peak [cm])
If the time-base setting is 5ms/cm, then the period is 5 x (number of squares horizontally per cycle [cm])
Types of rectification
Textbook figure 27.11, 27.12 & 27.13
Smoothing
Textbook figure 27.14
Electronvolt and Joules conversion
To convert from eV to J, multiply by 1.60 x 10⁻¹⁹
To convert from J to eV, divide by 1.60 x 10⁻¹⁹
Observations of photoelectric effect
Textbook table 28.4
Emission of electrons happens as soon as electromagnetic radiation is incident on the metal
A minimum threshold frequency is needed for the emission of electrons
Increasing frequency of electromagnetic radiation increases mak Ek of electrons
Diagrams showing electron dropping to a lower energy level, emitted and absorbed
Textbook figure 28.18 a & b
(emission moving down, absorption moving up)
Wave particle duality of light
Light interacts with matter (eg. electrons) as a particle - The evidence for this is provided by the photoelectric
Light propagates through space as a wave - The evidence for this comes from the diffraction and interference of lights using slits
When electron receives energy of the same magnitude as its ground state value
Electron entirely removed from the nucleus
Basic decays
When an unstable nucleus undergoes radioactive decay the nucleus before the decay is called the parent nucleus and after the decay is called the daughter nucleus
In α decay, the nucleon number decreases by 4 and the proton number decreases by 2
In β⁻ decay, the nucleon number is unchanged and the proton number increases by 1
In β⁺ decay, the nucleon number is unchanged and the proton number decreases by 1
In gamma decay, there is no change in nucleon or proton number
For the emission of an alpha particle use the notation He and for a beta particle use the notation e.
Mass changes according to Einstein’s equation
The mass of a system increases when energy is added to it
The mass of a system decreases when energy is released from it
To calculate mass change add the mass of the decay particle to the daughter nucleus. Subtract the parent nucleus mass from this.
∆m = final mass - initial mass
Stability comparison of different nuclides
In order to compare the stability of different nuclides, we need to consider the binding energy per nucleon.
Determining binding energy per nucleon
Determine the mass defect for the nucleus
Use Einstein’s mass-energy equation to determine the binding energy of the nucleus by multiplying the mass defect by c²
Divide the binding energy of the nucleus by the number of nucleons
Fusion and fission graph of binding energy per nucleon against nucleon number
Textbook figure 29.6
Spontaneous decay
Radioactive decay is both spontaneous and random
Nuclear decay is spontaneous because:
1. the decay of a particular nucleus is not affected by the presence of other nuclei
2. the decay of nuclei cannot be affected by chemical reactions or external factors such as temperature and pressure
Nuclear decay is random because:
1. it is impossible to predict when a particular nucleus in a sample is going to decay
2. each nucleus in a sample has the same chance of decaying per unit time
Radioatice decay is the spontaneous emission of radiation from an unstable nucleus
Aims of radiographers (2)
To reduce the patient’s exposure to harmful x-rays as much as possible
To improve the contrast of the image, so that the different tissues under investigation show up clearly in the image
Types of x-rays used
Bone is a good absorber of radiation hence a hard X-ray is used
Muscle tissue is a poor absorber hence will require a longer exposure using much softer (long-wavelength, low-frequency) X-rays.
Piezoelectric effect diagrams for an applied voltage and an applied stress
Textbook figure 30.13
A-scan and B-scan
A-scan:
A pulse of ultrasound is sent into the body and the reflected “echoes” are detected and displayed on an oscilloscope or computer screen as a voltage-time graph
B-scan:
A detailed image of a cross-section through the patient is built up from many A-scans
Positron Emission Tomography uses
Investigating, diagnosing and monitoring treatment of cancers, heart disease, gastrointestinal disorders and brain function.
Unique as they observe from the inside not the outside
X-ray tube diagram
Textbook figure 30.4
electrons are accelerated, they hit a target, and when they decelerate they produce x-rays
Relating brightness of a star to luminosity (assumptions)
Can be done assuming:
1. the power from the star is uniformly radiated through space
2. there is negligible absorption of this radiated power between the star and the earth
Intensity wavelength graph for an object at a thermodynamic temperature T
For an object at a thermodynamic temperature T, the intensity wavelength curve peaks at a wavelength λₘₐₓ
The higher the temperature of a body (2), astronomy and cosmology
- The shorter the wavelength at peak (maximum) wavelength
- The greater the intensity of the electromagnetic radiation at each wavelength
Luminosity of a star is dependant on (2)
- Its surface thermodynamic temperature, T
- Its radius, r
Difference in absorption line spectrum for red-shifted vs. a stationary source
The absorption lines in the spectrum of the galaxy are all shifted to longer wavelengths - ‘red-shifted’
Adv and disadv of X-ray vs CAT scan
X-rays are quicker and cheaper
CAT scan can produce 3D image
CAT scan more harmful than individual x-ray
CAT scan can distinguish tissues with quite similar densities (attenuation coefficients)
PET scan (5) + adv. & disadv.
- Patient surrounded by ring of gamma detectors
- Tracer emits positron into body
- Positron annihilates with electron and produces 2 gamma ray photons that travel in opposite directions
- time delay between 2 photons is used to determine location of annihilation
- computer connected to detector to form image
Adv.
non-evasive
real time images
disadv.
radioactive source is used and patient is exposed to a small amount of activity
very expensive
Mean translational KE derivation
pV = NkT = 1/3Nm< c >²
1/2m < c > ² = 3/2kT
