st andrew’s academy

1

Higher Physics

Our Dynamic Universe

(2. The Universe)

St Andrew’s Academy

This booklet has notes and space for completing worked

examples on the second part of the Our Dynamic Universe

course on the Universe and covers the following key areas:

1. Gravity and mass

2. Special relativity

3. The Doppler effect

4. Redshift

5. Hubble’s law

6. Expansion of the Universe

7. Big Bang theory

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1. Gravity and mass

Learning outcomes:

Use of Newton’s Law of Universal Gravitation to solve problems involving force, masses and their separation.

F = Gm1m2

r2

Newton’s Inverse Square Law of Gravitation:

This law states that there is a force of attraction between any two objects in the

universe.

The size of the force is proportional to the product of the masses of the two objects,

and inversely proportional to the square of the distance between them.

F = Gm1m2

r2

m1 and m2 are the masses of the two objects, and r is the distance between them.

G = gravitational constant = 6.67 x 10-11 Nm2kg-2 – this value is given in

the data sheet

Example 1:

• What is the force of attraction between two pupils of average mass (60 kg) sitting 1.5

metres apart?

Value of r:

• It is important to realise that the value for r, the distance between two masses, is the

distance between the centre of the two masses.

i.e. if we consider the force between the Earth and the Moon then the value of r is the

distance from the centre of the Earth to the centre of the Moon.

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Example 2:

• Taking the radius of the Earth to be 6.4 x 106 m, find the force of attraction on a 250

kg satellite that is orbiting at a height of 36 000 km above the Earth.

(mass of Earth = 6.0 1024 kg)

This question should be broken down into two parts.

1. First of all, find the total distance, r, between the centre of the two objects.

2. Use Newton’s Universal Law

Past paper questions:

Revised higher 2012:

6

CfE Higher 2018

Revised Higher 2013 (Open-ended)

7

CfE Higher 2015:

CfE Higher 2017:

8

CfE Higher 2016:

9

Gravity & mass homework: Due date: _______________

1. The centre of the planet Jupiter is a distance of 778 x 106 km from the centre

of the Sun.

If the mass of Jupiter is 1.9 x 1027 kg and the mass of the Sun is 2.0 x 1030kg,

calculate the magnitude of the force of attraction between Jupiter and the

Sun.

2. Two pupils are sitting 1.5m apart. One pupil has a mass of 49 kg and the

other has a mass of 61 kg. Calculate the magnitude of the gravitational

attraction between the pupils.

3. A binary star is a system of two stars that orbit a common centre of mass. At

one point during the orbit, the stars are a distance of 2.56 x 106 km away

from each other (centre to centre). The force of attraction between the stars

is 2.24 x 1025 N. If the mass of one star is 3.45 x 1030 kg, calculate the mass

of the second star.

4. Calculate the gravitational force of attraction between the Earth and the Sun

using the data below: Mass of Sun = 2.00 x 1030 kg;Distance from Earth to the Sun

(centre to centre) = 1.50 x 106 km. Calculate the gravitational force of attraction

between the Earth and a geostationary satellite of mass 5000kg, if we assume that

it orbits at a height of 35,800 km above the Earth’s surface.

5. Astronomical observations tells us that Neptune has a gravitational field strength of

11.8 Nkg-1 at its surface and has a radius of 2.48 x107m. Calculate the mass of Neptune.

6.

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2. Special relativity (time dilation & length

contraction)

Learning outcomes:

Knowledge that the speed of light in a vacuum is the same for all observers.

Knowledge that measurements of space, time and distance for a moving observer are changed relative to those for a stationary observer, giving rise to time dilation and length contraction.

Use of appropriate relationships to solve problems involving time dilation, length contraction and speed.

• t’ = t .

√1 – v2

c2

• l’ = l √1 – v2

c2

Time dilation:

• Imagine a lamp which sends a pulse of light at the same time as

producing a click.

• The light is reflected from a mirror, at a known distance, D, from the

lamp.

• When it arrives back at the lamp it produces a second click.

• The total time will be: t = 2D

c

(c – speed of light)

• Now imagine that the two lamps are moving at an identical horizontal

velocity.

• To an observer moving with the lamps nothing will have changed.

• However, if there is a stationary observer watching the lamps move he will see the

pulses of light take a different path and move a longer distance, 2h.

• The time between clicks in this case will be:

• t = 2h

c

• Therefore, time will be different for two observers watching an identical system (as h

is clearly bigger than D).

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Relativity Example - CfE H 2016:

What is meant by time dilation?

• The time observed in a moving system will always be greater than that

measured in the stationary frame of reference.

• Time dilation is the difference in a time interval as measured by a stationary

observer and a moving observer.

• ie a stationary observer will record a greater time than a moving observer for the

same journey travelling at speeds close to the speed of light.

Equation for time dilation:

• t’ = t .

√1 – v2

c2

• t’ = time reference for the stationary observer

• t = time reference for the moving observer

• v = velocity of moving observer

• c = 3 x 108 ms-1

• NB: v is often given as a unit of c i.e. 0.7c

(so 0.7 x 3x108 = 2.1x108).

• In this case you can leave v = 0.7 and c = 1

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Example 1:

• A spacecraft leaves Earth and travels at a constant speed of 0.6c to its destination.

An astronaut on board records a flight time of 5 days.

• Calculate the time taken for the journey as measured by an observer on Earth.

Example 2:

• A rocket leaves a planet and travels at a constant speed of 0.8c to a destination. An

observer on the planet records a time of 20h.

• Calculate the time taken for the journey as measured by the astronaut on board.

What if we are given a speed instead of c?

• You can easily convert this into c. All you have to do is divide the speed given by the

speed of light.

• Examples:

• 2x108 ms-1 = 2x108 / 3x108 = 0.67c

• 1.2x108 ms-1 = 1.2x108 / 3x108 = 0.4c

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CfE Higher 2017:

14

CfE Higher specimen paper:

CfE Higher 2015 (open-ended):

15

Length contraction:

• A similar effect occurs with the length of a moving object. This is know as length

contraction.

• It can be defined as follows: the decrease in length of an object moving relative to an

observer.

• l’ = l √1 – v2

c2

• l’ = length for the stationary observer

• l = length for the moving observer

General rule:

• When moving at velocities close to the speed of light, for the stationary observer

(standing watching):

1. Time is longer

2. The length is shorter

• When compared to the moving observer (on board the space craft).

Example 1:

• An observer on Earth sees a spaceship travelling at 0.7c. If the rocket is measured to

be 36m in length when at rest on Earth, how long is the moving rocket ship as

measured by the observer on Earth?

Example 2:

• An observer on Earth sees a rocket zoom by at 0.95c. If the rocket is measured to be

5.5m in length, how long is the rocket ship as measured by the astronaut inside the

rocket?

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2012 Revised higher

Revised Specimen paper:

2015 CfE Higher:

17

2017 CfE Higher:

Why do we not notice time dilation when we are moving at speeds NOT close to c?

• This can be explained using the Lorentz factor.

• The Lorentz factor appears in special relativity equations for both time dilation and

length contraction.

• It has the symbol γ and can be expressed as:

• γ = 1 .

√1- (v/c)2

• Therefore we can see that if the velocity is much less than c, there will hardly be any

effect.

• For example, the max velocity of a Boeing 747 is 270 ms-1, using the Lorentz factor:

• γ = 1 .

√1- (v/c)2

• γ = 1

• And therefore has no effect

• Only velocities close to the speed of light have an effect.

• Velocities much less than the speed of light correspond to a Lorentz factor of

approximately 1.

• Therefore there is negligible change of length / time observed.

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Revised Higher 2013:

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Special relativity homework: Due date: _______________

1. The lifetime of a star is 8 billion years measured by an observer at rest with respect to the star. The star is moving away from the Earth with a speed of 0.85c. Calculate the lifetime of the star according to the observer on Earth.

2. The Twin Paradox describes how one of the twins on a space mission for a given time travelling near the speed of light, will age less than the other twin on Earth. a) Explain how this phenomena is possible. b) A spaceship travelling at 2.8 x 108ms-1

leaves Earth in May 2000 and returns in May 2016. How many years will the astronaut have aged in this time?

3. a) An aeroplane is travelling at altitude above Paisley at a speed of 240 ms-1

The pilot measures the journey as taking 50 minutes. How long did the journey take when measured by an observer in Paisley? b) A rocket is travelling at altitude above Paisley at a speed of 2.4 x108 ms-1 The astronaut on the rocket measures the journey taking 50minutes. How long did the journey take when measured by an observer in Paisley? c) Compare and contrast the answers found in a) and b).

4. A rocket passes Hadrian’s Wall as it passes over Earth.

An Astronaut in the rocket measures the time taken to travel over Hadrian’s Wall to be 6 x 10-4

s. An observer on Earth measures the time taken to travel over Hadrian’s Wall to be 8 x10-4

s. Calculate the speed of the rocket relative to the Earth.

5. A rocket of length 50m was measured at rest on Earth.

The rocket passes Earth with a constant speed of 2.1 x108 ms-1 Calculate the length of the rocket when it passes Earth and is measured by an observer that is stationary on Earth.

6. A car has a length measured of 3.2m when viewed from a spaceship travelling at

2.0 x108 ms-1 Calculate the length of the car when measured at rest on Earth.

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3. The Doppler effect

Learning outcomes:

Knowledge that the Doppler effect causes shifts in wavelengths of sound and light.

Use of an appropriate relationship to solve problems involving the observed frequency, source frequency, source speed and wave speed.

What is the Doppler effect?

• The Doppler effect is the change in frequency you notice when a source of sound

waves is moving relative to you.

• When the source moves towards you, more waves reach you per second and the

frequency is increased.

• If the source moves away from you, fewer waves reach you per second and the

frequency is decreased.

Calculating the frequency:

• When a source produces a sound of frequency fs, we can calculate the observed

frequency, fo, using a formula.

• The formula changes slightly depending on whether you move towards the source or

move away from the source.

Calculating the frequency - Moving towards the source:

• The observed frequency, fo, is higher:

• fo = fs v .

(v - vs)

• fs = frequency of source

• v = speed of sound (approximately 340 ms-1)

• vs = speed of source

• Towards = Take away

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Calculating the frequency - Moving away from the source:

• The observed frequency, fo, is lower:

• fo = fs v .

(v + vs)

• Away = Add

Example 1:

• What is the frequency heard by a person driving at 15 ms-1 toward a blowing factory

whistle (f = 800 hz) if the speed of sound in air is 340 ms-1?

Example 2:

• What frequency would he hear after passing the factory if he continues at the same

speed?


2013 Revised higher:

22

CfE Higher Specimen Paper:

2015 CfE Higher:

23

2017 CfE Higher:

24

Doppler effect homework: Due date: _______________

1. An Ambulance travelling at 12 ms-1 in a built up area emits sounds of

frequency 1000 Hz from its siren. A person standing in a bus queue hears the

siren coming towards and then passing him.

Calculate or find:

a) Frequency heard by the person when the ambulance moves towards

him.

b) Frequency heard by the person when the ambulance moves away from

him.

2. A train emits a sound of frequency 900Hz as it passes through a station. The

sound is heard by a passenger on the station platform.

a) Describe how the frequency of the sound, heard by the pupil, changes

as the train passes through the station.

b) Explain in terms of wavefronts, why this frequency change occurs. (You

may wish to use a diagram as part of your answer).

c) At one instant the pupil hears a sound of frequency 850Hz. Calculate the

speed of a train relative to the pupil on the platform at this instant.

3. A train has stopped on the track and a passenger hears a siren on another

train approaching along a parallel track. The approaching train is travelling at a constant speed of 25.0 ms-1 and the siren produces a frequency of 284Hz.

Calculate the frequency heard: a) When the train approaches the passenger. b) Once the train has passed the passenger.

4. A man standing at the roadside hears a frequency of 500Hz from a car horn driving towards him. If the car horn has a frequency of 480Hz then:

a) Calculate the speed of the approaching car.

b) If the car maintains a constant speed then calculate the frequency of the sound heard by the man as the car passes him.

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4. Redshift

Learning outcomes:

Knowledge that the light from objects moving away from us is shifted to longer wavelengths (redshift).

Knowledge that the redshift of a galaxy is the change in wavelength divided by the emitted wavelength. For slowly moving galaxies, redshift is the ratio of the recessional velocity of the galaxy to the velocity of light.

Use of appropriate relationships to solve problems involving redshift, observed wavelength, emitted wavelength, and recessional velocity.

z = λo – λr z = v

λr c

Background information:

• White light (light from galaxies and stars) is broken up into all the colours of the

rainbow

• Red Orange Yellow Green Blue Indigo Violet

Longer λ shorter λ

• All the colours have different wavelengths

What is redshift?

• Redshift (also known as Doppler shift) is how much the frequency of light from a far

away object has moved toward the red end of the spectrum.

• It is a measure of how much the ‘apparent’ wavelength of light has been increased.

• It has the symbol Z and can be calculated using the following equation:

• Z = λo – λr it can also expressed as: Z = λo - 1 NOT given in data sheet

λr λr used to calculate λr

• λo = the wavelength observed

• λr = the wavelength at rest

What is blueshift?

• When we use the equation for redshift, we can sometimes end up with a –ve value.

• This means the object is moving closer to you and is said to be blueshifted.

• It is a measure of how much the ‘apparent’ wavelength of light has been decreased.

Redshift and velocity:

• We can also work out the redshift if we know the velocity that the body is moving at

(for slow moving galaxies):

• Z = v

C

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Wavelengths:

• With a redshift, moving away, the wavelength increases. Value for Z is positive.

• With a blueshift, moving towards, the wavelength decreases. Value for Z is negative.

Example 1:

• Light from a distant galaxy is found to contain the spectral lines of hydrogen. The

light causing one of these lines has (an observed) measured wavelength of 466 nm.

When the same line is observed (at rest) from a hydrogen source on Earth it has a

wavelength of 434 nm.

(a) Calculate the Doppler shift, z, for this galaxy.

(b) Calculate the speed at which the galaxy is moving relative to the Earth.

(c) In which direction, towards or away from the Earth, is the galaxy moving?

Example 2:

• A distant star is travelling directly away from the Earth at a speed of 2·4 × 107 ms1.

(a) Calculate the value of z for this star.

(b) A hydrogen line in the spectrum of light from this star is measured to be 443 nm.

Calculate the wavelength of this line when it observed from a hydrogen source on the

Earth.

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Revised 2013:

2017 CfE Higher Qu: 5

28

CfE Specimen paper:

29


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Watch out!

• You have to be careful with the wording of some questions when deciding which

wavelength is the observed and which is at rest.

• What is this question asking for?

• It is actually asking for λo

• The 450nm is emitted from the galaxy (therefore

λr = 450nm)

• By the time it reaches the Earth will have

shifted.

Redshift homework: Due date: _______________

1. Stars or Galaxies moving away from us is known as a Red Shift. Stars or Galaxies moving towards us is known as a Blue Shift. Explain using the Doppler Effect how these names have been given in each case.

2. Explain how you can tell from the Red Shift Ratio (Z) whether stars or Galaxies are coming towards or moving away from Earth.

3. A distant star is travelling directly away from Earth at 2.1 x107 ms-1.

a) Calculate the Red Shift Ratio Z for this star. b) A hydrogen line of the spectrum of light from this star is measured to be 486nm. Calculate the wavelength of this line when it is observed from a Hydrogen source on Earth.

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4. Top Spectrum -> From a distant Star. Bottom Spectrum -> From Earth.

A Hydrogen source when viewed on Earth emits an emission line of wavelength 410nm. Observations have been made for the same line in the spectrum of light from a distant star giving a wavelength of 485nm. (Look at the thick absorption line on each spectrum!!!) a) Calculate the Red Shift Ratio Z for this star. b) Calculate the speed of the star relative to Earth.

5. The spectrum of light from most stars contains lines corresponding to helium gas.

Figure 15 (a) shows the helium spectrum from the Sun.

Figure 15 (b) shows the helium spectrum from a distant star.

a) Calculate the approximate Red Shift Ratio Z for this star. b) Calculate the approximate speed of the star relative to Earth.

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5. Hubble’s law

Learning outcomes:

Use of an appropriate relationship to solve problems involving the Hubble constant, the recessional velocity of a galaxy and its distance from us.

V = Hod

Knowledge that Hubble’s law allows us to estimate the age of the Universe. Hubble’s law:

• The astronomer Edwin Hubble noticed in the 1920s that the light from some distant galaxies was shifted towards the red end of the spectrum.

• The size of the shift was the same for all elements coming from the galaxies. • This shift was due to the galaxies moving away from Earth at speed.

The bigger the shift the faster the galaxy moves

• Hubble found that the further away a galaxy was the faster it was travelling.

• The relationship between the distance and speed of a galaxy is known as Hubble’s

Law:

v = Ho d

• Ho = Hubble’s constant = 2.3 x 10-18 s-1

Hubble’s constant:

• The value of Ho = 2.3 x 10-18 s-1 is given in data

sheet (and is the value you would use in an

exam) but can vary as more accurate

measurements are made.

• The gradient of the line in a graph of speed v

distance of galaxies provides a value for

Hubble’s constant.

• As you can see from the graph, v and d are

directly proportional

Example 1:

• What is the speed of a galaxy relative to Earth that is at an approximate distance of

4.10 × 1023 m from Earth?

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What is a light year?

• Sometimes distances can be given in light years.

• One light year is the distance travelled by light in one year.

• It can be calculated as follows using d = vt:

• 3 x 108 (speed of light) x 365 (days) x 24 (hours) x 60 (mins) x 60 (s)

• One light year = 9.46 x 1015 m


CfE Specimen paper:

Revised Higher Specimen paper:

34

Revised Higher 2012:

CfE Higher 2017:

35

Hubble’s law homework: Due date: _______________

1. Hubble’s Law is shown using the equation below. v = Ho d a) State the quantities and units in the equation. b) State any constant in the equation with its associated units. c) i) Describe the graph obtained for v against d? ii) What does this tell us about the relationship between v and d?

iii) Which quantity is worked out from the gradient of the graph of v against d?

2. A galaxy is moving away from Earth at 0.087c.

a) Convert 0.087c into ms-1.

b) Calculate the approximate distance of this galaxy from Earth in metres.

3. A distant galaxy is 20 light years away from Earth. Use Hubble’s Law to determine the velocity of the galaxy as it moves away from Earth.

4. A distant Quasar is moving away from Earth. One of the Hydrogen lines coming from the Quasar is observed to have a wavelength of 506nm from the same frame of reference. The same line is measured as having a wavelength of 486nm from a source on Earth. Calculate: a) The speed at which the Quasar is moving away from Earth. b) The distance that Quasar is from Earth in light years.

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6. Expansion of the Universe

Learning outcomes:

Knowledge that measurements of the velocities of galaxies and their distance from us lead to the theory of the expanding Universe.

Knowledge that the mass of a galaxy can be estimated by the orbital speed of stars within it.

Knowledge that evidence supporting the existence of dark matter comes from estimations of the mass of galaxies.

Knowledge that evidence supporting the existence of dark energy comes from the accelerating rate of expansion of the Universe.

The expanding Universe experiment:

Galaxy d1 - distance from Milky way

(cm)

d2 – distance from Milky way

(cm)

Time taken to travel d1 – d2 (s)

Ave. velocity (cm/s)

1

2

3

4

5

Conclusion:

• The further away the galaxy, the _________ the average velocity. • This shows that the universe is _________.

Is the Universe expanding?

• The Universe has been expanding since the Big Bang. • The objects within the Universe (ie galaxies) are not expanding – rather the space

between them is. • The expansion of the Universe is actually accelerating. • Most galaxies are moving away from each other

What evidence is there to support this?

• We can estimate how far away something is by its brightness – exploding stars in our galaxies are moving further away at an accelerated rate.

• Furthermore, light from some distance galaxies was observed to display a redshift, showing they were moving away at speed.

How can you estimate the mass of the galaxy?

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• Measurements of the velocities of galaxies and their distance from us lead to the theory of the expanding Universe.

• Gravity is the force which slows down the expansion. • The eventual fate of the Universe depends on its mass.

• The orbital speed of the Sun and other stars gives a way of determining the

mass of our galaxy. What are Dark Matter and Dark energy?

• Measurements of the mass of our galaxy and others lead to the conclusion that there is significant mass which cannot be detected — dark matter.

• Measurements of the expansion rate of the universe lead to the conclusion that it is increasing, suggesting that there is something that overcomes the force of gravity — dark energy

Past paper questions: CfE 2017

CfE 2018 Qu: 5

38

Open ended question – CfE specimen paper:

39

7. The Big Bang Theory

Learning outcomes:

Knowledge that evidence supporting the existence of dark energy comes from the accelerating rate of expansion of the Universe.

Knowledge that the temperature of stellar objects is related to the distribution of emitted radiation over a wide range of wavelengths.

Knowledge that the peak wavelength of this distribution is shorter for hotter objects than for cooler objects.

Knowledge that hotter objects emit more radiation per unit surface area per unit time than cooler objects.

Knowledge of evidence supporting the big bang theory and subsequent expansion of the Universe: cosmic microwave background radiation, the abundance of the elements hydrogen and helium, the darkness of the sky (Olbers’ paradox) and the large number of galaxies showing redshift rather than blueshift.

What happens to the colour of objects as they are heated?

• When an object is heated it does not initially glow, but radiates large amounts of energy as infrared radiation. We can feel this if we place our hand near, but not touching, a hot object.

• As an object becomes hotter it starts to glow a dull red, followed by bright red, then orange, yellow and finally white (white hot). At extremely high temperatures it becomes a bright blue-white colour.

Light and temperature

• We can see that the temperature of an object affects the light it gives off. • This means that the temperature of an object is linked to both the frequency and

wavelength of the light it emits. • A graph of intensity versus wavelength has a characteristic shape and can be shown

in a “Planck distribution.” Planck distribution

• Is also known as a black-body spectrum and has three main features:

1. The basic shape is more or less the same 2. As the temperature of the object increases,

the peak intensity wavelength decreases (so frequency increases)

3. As the temperature of the object increases, the intensity and energy increases

• Summarised as follows: • T ↑ λ ↓ therefore f ↑ intensity ↑ energy ↑

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Past paper questions: 2014 Revised higher:

2017 CfE Higher:

41

What is the Big Bang Theory?

• The universe started as a very hot and dense singularity and then rapidly expanded.

What evidence is there for the Big Bang?

1. The expanding universe:

The Universe is expanding at an accelerated rate.

Some galaxies are redshifted showing that they are moving away from us.

2. Cosmic Microwave Background Radiation:

This radiation can be detected on Earth coming from all directions in space.

This radiation is constant throughout the universe.

This radiation provides a constant temperature throughout the universe

(approximately 3K).

3. Abundance of light elements:

The lighter elements (Hydrogen and Helium) would have formed first,

therefore they would be found in bigger quantities.

Observations of the known Universe confirms this.


2014 Revised higher

42


Open-ended question - 2014 Revised Higher

43


44

Expansion of the Universe and Big Bang Theory homework

Due date: _______________

1. a) What is meant by the term ‘Dark Energy’? b) What is meant by the term ‘Dark Matter’?

c) Does ‘Dark Energy’ or ‘Dark Matter’ make up a bigger percentage of the universe?

2. a) State three pieces of evidence for the ‘Big Bang Theory’. b) Give a brief description of each of these four pieces of evidence.

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Unit 1 Our Dynamic Universe Revision Questions

46

Equations of Motion

47

Momentum and impulse

48

Gravity and mass

49

Special relativity

A spacecraft is travelling at a constant speed of 2.75 x 108 ms-1 relative to a planet. A

technician on the spacecraft measures the length of the spacecraft as 125 m. What length

does the observer on the planet measure the spacecraft to be? 3

Doppler

A jet aircraft engine emits a sound of frequency 1.4 kHz. If the jet is travelling towards the

observer at 240 ms-1 calculate the frequency of the sound detected by a stationary observer.

3

Redshift and Hubble’s Law

50

Expansion of the Universe

1

Big bang

1

Open ended – Big Bang

51

Our Dynamic Universe revision Past Paper questions

Year Questions

Multi-Ch Section B

CfE 2019 8, 9, 10 4, 5, 6

CfE 2018 1,2,3,4,5,6,7 1,2(NOT(a)(ii),3,4,5

CfE 2017 1,2,3,4,5,6,7 1,2,3,4,5

CfE 2016 1,2,3,4,5,6,7 1,2,3,4,5,6

CfE 2015 1,2,3,4,5,6,7,8 1,2,3,4,5,

CfE Spec 1,2,3,4,5,6 1, 2(a), 3,4,5,6

Rev. 2015 1,2,3,4,5,6,7 21,22,23,24,25

Rev. 2014 1,2,3,4,5,6,7 21, 22, 23(a), 24

Rev. 2013 1,2,4,5,6,7,8,9 21, 22, 23, 24, 25

Rev. 2012 1,2,3,4,5,6,7,8 21, 22, 24, 25, 33

Rev. Spec 1,2,3,5,6,7,8,9,10 21, 22, 23, 24, 25

2015 2, 3, 4 21, 22, 23

2014 2, 3, 4 22, 23

2013 2, 4 21, 22(a)+(b), 23

2012 2, 3, 4 22

2011 2, 3, 4 21, 22

2010 1, 2, 3, 21(b), 22, 23

2009 2, 3, 4, 5 21, 22(b)

2008 2, 3, 4, 5, 6 21 (a)+(b), 22

2007 2, 4, 5, 6 22

2006 2, 3, 5 21, 22

2005 2, 3, 4, 5 22

2004 1, 2, 3, 4, 5, 6 22(a)

2003 2, 3, 4, 5 21, 22

2002 1, 2, 3, 4 21(a)+(c), 23

2001 2, 3, 4, 5 21, 23 (a)

2000 3, 4 21, 22(a)+(b)

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