Additional notes

Question 1

Vector triangles in Circular Motion

Answer 1

A vector triangle can be drawn with existing velocities, to determine change in velocity represented by completing the vector triangle

Textbook figure 16.9

Question 2

Newton’s thought experiment

Answer 2

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

Question 3

Maximum displacement from equilibrium position

Answer 3

amplitude x₀

Question 4

Displacement time graph for s.h.m

Answer 4

Shows period (T) and amplitude (x₀)

Velocity can be determined by gradient of graph

Textbook figure 18.7

Question 5

Phase difference for waves with different frequencies

Answer 5

Waves with different frequencies have continuously changing phase differences

Question 6

Requirements for s.h.m (3)

Answer 6

The three requirements for s.h.m. of a mechanical system are:

1. 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

Question 7

Velocity time graph for s.h.m

Answer 7

where displacement is zero velocity is at a maximum (could be positive or negative)

acceleration can be determined from gradient of graph

Question 8

Acceleration time graph for s.h.m

Answer 8

acceleration is proportional to the negative displacement which is a key idea

a ∝ - x

Question 9

Acceleration displacement graph for s.h.m

Answer 9

gradient is -ω²

Textbook figure 18.20

Question 10

Gradient and amplitude relationship for s.h.m

Answer 10

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.

Question 11

Key idea behind a = -ω²x

Answer 11

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

Question 12

Kinetic and potential energy of an oscillator

Answer 12

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

Question 13

Kinetic and potential energy graph for s.h.m

Answer 13

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

Question 14

Amplitude and driving frequency graph

Answer 14

Maximum amplitude is achieved when the driving frequency equals the natural frequency of oscillation

Textbook figure 18.32

Question 15

Types of damping

Answer 15

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

Question 16

Temperature against time graph for heating water/ice at a steady rate

Answer 16

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

Question 17

Potential energy and separation graph for atoms

Answer 17

The electric potential energy of atoms is negative and increases as they get further apart

Textbook figure 19.5

Question 18

Changing internal energy

Answer 18

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

Question 19

First law of thermodynamics; Rules and positive and negative values

Answer 19

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

Question 20

Key idea around thermal energy transfer

Answer 20

Thermal energy is transferred from a region of higher temperature to a region of lower temperature

Question 21

Key idea about thermodynamic temperature scale

Answer 21

Thermodynamic temperatures do not depend on the property of any particular substance

Question 22

Resistance thermometer (thermistor and resistance wire) and thermocouple thermometer comparison

Answer 22

Features:
robustness
range
size
sensitivity
linearity
remote operation

Textbook table 19.2

Question 23

Graphs of Boyle’s law (2)

Answer 23

p ∝ 1/V

Textbook figure 20.5

Question 24

Relationship between volume and temperature of gas

Answer 24

The volume of a gas decreases as its temperature decreases

Textbook figure 20.6

Question 25

Limits of Charles and Boyle's law

Answer 25

At low temperatures of high pressures gasses start to deviate from these laws Textbook figure 20.7

Question 26

Basic assumptions of the kinetic theory of gases (4)

Answer 26

No intermolecular forces Textbook table 20.1

Question 27

Relationship between mean translational kinetic energy of an atom and thermodynamic temperature

Answer 27

Mean translational kinetic energy of an atom ∝ T

Question 28

Monatomic and diatomic molecules

Answer 28

Monatomic molecules have only translational kinetic energy and diatomic molecules have both translational and rotational kinetic energy

Question 29

Field lines show (2)

Answer 29

1. Direction of gravitational force on mass placed in field 2. Spacing of field lines indicate strength of gravitational field, the further apart the weaker

Question 30

Types of fields (2)

Answer 30

Radial, field lines diverge (spread out) radially from the centre of the object Uniform, field lines equally spaced and parallel

Question 31

Terminology: field strength and potential

Answer 31

Field strength describes the force on a unit mass at a point Potential describes potential energy of unit mass at a point

Question 32

Johannes Kepler discovery

Answer 32

T² ∝ r³

Question 33

The types of fields and what they act on (3)

Answer 33

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

Question 34

Strength of a uniform field

Answer 34

E ∝ V Higher the voltage, stronger the field E ∝ 1/d Greater the separation, weaker the field

Question 35

Negative sign in strength of a uniform field between two parallel plates !equation!

Answer 35

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

Question 36

Path of electron through uniform electric field

Answer 36

There is a parabolic path of a moving electron in a uniform electric field accelerating towards the positive plate Textbook figure: 21.14

Question 37

Attraction and repulsion and positive and negative charges with electric fields

Answer 37

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.

Question 38

Energy changes in a uniform field graph

Answer 38

Electrostatic potential energy changes in a uniform field Textbook figure 22.7

Question 39

Defining voltage in terms of the potential energy of a charge

Answer 39

V is the energy per unit positive charge at a point in an electric field

Question 40

Potential changes according to an inverse law near a charged sphere graph

Answer 40

Textbook figure 22.10

Question 41

Electric field around a positive charge graph

Answer 41

The dashed equipotential lines are like contour lines on a map; they are spaced at equal intervals of potential Textbook figure 22.11

Question 42

Relationship between field strength and potential gradient

Answer 42

electric field strength = - potential gradient Textbook figure 23.12

Question 43

Charge in a current time graph

Answer 43

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)

Question 44

Markings on capacitors

Answer 44

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.

Question 45

Work done when charging a capacitor

Answer 45

When a capacitor is charges, work must be done to push additional electrons against the repulsion of the electrons that are already present

Question 46

Area under graph of voltage against current

Answer 46

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

Question 47

Rules for capacitors in parallel (2)

Answer 47

The p.d across each capacitor is the same The total charge on the capacitors is equal to the sum of the charges

Question 48

Comparing capacitors and resistors

Answer 48

The reciprocal formula for capacitors in series is the opposite for resistors who use the reciprocal formula for resistors in parallel

Question 49

Sharing charge between capacitors

Answer 49

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

Question 50

Charge and discharge of capacitors

Answer 50

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

Question 51

Relationships between electrical quantities and capacitance

Answer 51

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.

Question 52

Uses for capacitor (3)

Answer 52

Time delay, anti surge, anti spark.

Question 53

Magnetic field introduction (where it exists) (making one)

Answer 53

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)

Question 54

Magnetic field patterns for a solenoid and a flat circular coil

Answer 54

Textbook figure 24.3 (a, b)

Question 55

Magnetic field pattern around current carrying wire

Answer 55

Textbook figure 24.4

Question 56

Forces between current carrying wires (parallel and antiparallel)

Answer 56

Textbook figure 24.22 and 24.23 Parallel currents attract one another Antiparallel currents repel

Question 57

Comparing forces in magnetic, gravitational and electric fields

Answer 57

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)

Question 58

Direction of conventional current and electrons

Answer 58

The flow of electrons opposes the direction of the flow of conventional current

Question 59

Fleming's left-hand rule for particle velocity

Answer 59

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

Question 60

Factors affecting induced emf (straight wire and coil)

Answer 60

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

Question 61

Induced e.m.f for a conductor not part of a complete circuit

Answer 61

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

Question 62

How to induce and e.m.f

Answer 62

Changing magnetic flux density (B) Changing cross-sectional area of circuit (A) Changing angle (θ)

Question 63

Origin of current in electromagnetic induction

Answer 63

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).

Question 64

Forces and movement (solenoid, straight wire)

Answer 64

Textbook figure 26.22 & 26.23

Question 65

Solenoids and magnetic pole induction

Answer 65

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.

Question 66

Electromagnetic induction from generators and graphs for flux linkage and induced e.m.f against time

Answer 66

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

Question 67

Transformers

Answer 67

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.

Question 68

Determining frequency and amplitude (peak value of voltage) on a C.R.O

Answer 68

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])

Question 69

Types of rectification

Answer 69

Textbook figure 27.11, 27.12 & 27.13

Question 70

Smoothing

Answer 70

Textbook figure 27.14

Question 71

Electronvolt and Joules conversion

Answer 71

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

Question 72

Observations of photoelectric effect

Answer 72

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

Question 73

Diagrams showing electron dropping to a lower energy level, emitted and absorbed

Answer 73

Textbook figure 28.18 a & b (emission moving down, absorption moving up)

Question 74

Wave particle duality of light

Answer 74

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

Question 75

When electron receives energy of the same magnitude as its ground state value

Answer 75

Electron entirely removed from the nucleus

Question 76

Basic decays

Answer 76

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.

Question 77

Mass changes according to Einstein's equation

Answer 77

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

Question 78

Stability comparison of different nuclides

Answer 78

In order to compare the stability of different nuclides, we need to consider the binding energy per nucleon.

Question 79

Determining binding energy per nucleon

Answer 79

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

Question 80

Fusion and fission graph of binding energy per nucleon against nucleon number

Answer 80

Textbook figure 29.6

Question 81

Spontaneous decay

Answer 81

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 ## Footnote Radioatice decay is the spontaneous emission of radiation from an unstable nucleus

Question 82

Aims of radiographers (2)

Answer 82

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

Question 83

Types of x-rays used

Answer 83

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.

Question 84

Piezoelectric effect diagrams for an applied voltage and an applied stress

Answer 84

Textbook figure 30.13

Question 85

A-scan and B-scan

Answer 85

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

Question 86

Positron Emission Tomography uses

Answer 86

Investigating, diagnosing and monitoring treatment of cancers, heart disease, gastrointestinal disorders and brain function. Unique as they observe from the inside not the outside

Question 87

X-ray tube diagram

Answer 87

Textbook figure 30.4 electrons are accelerated, they hit a target, and when they decelerate they produce x-rays

Question 88

Relating brightness of a star to luminosity (assumptions)

Answer 88

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

Question 89

Intensity wavelength graph for an object at a thermodynamic temperature T

Answer 89

For an object at a thermodynamic temperature T, the intensity wavelength curve peaks at a wavelength λₘₐₓ

Question 90

The higher the temperature of a body (2), astronomy and cosmology

Answer 90

1. The shorter the wavelength at peak (maximum) wavelength 2. The greater the intensity of the electromagnetic radiation at each wavelength

Question 91

Luminosity of a star is dependant on (2)

Answer 91

1. Its surface thermodynamic temperature, T 2. Its radius, r

Question 92

Difference in absorption line spectrum for red-shifted vs. a stationary source

Answer 92

The absorption lines in the spectrum of the galaxy are all shifted to longer wavelengths - 'red-shifted'

Question 93

Adv and disadv of X-ray vs CAT scan

Answer 93

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)

Question 94

PET scan (5) + adv. & disadv.

Answer 94

1. Patient surrounded by ring of gamma detectors 2. Tracer emits positron into body 3. Positron annihilates with electron and produces 2 gamma ray photons that travel in opposite directions 4. time delay between 2 photons is used to determine location of annihilation 5. 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

Question 95

Mean translational KE derivation

Answer 95

pV = NkT = 1/3Nm< c >² 1/2m < c > ² = 3/2kT