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Examiner’s tips At A2 you will go further and deeper into the study of physics – you will build on the work done at AS. As at AS, the work at A2 is also divided into units and modules. Each unit corresponds to one of your examination papers. These tips have been written to help you in your studies and have been divided into the modules that fit in each unit. At A2 you will study: Unit G484: The Newtonian world 1 Newton’s laws and momentum 2 Circular motion and oscillations 3 Thermal physics. Unit G485: Fields, particles and frontiers of physics 4 Electric and magnetic fields 5 Capacitors and exponential decay 6 Nuclear physics 7 Medical imaging 8 Modelling the universe. To help you in your revision, the key words for each of the modules listed above have been divided into smaller topics. This will enable you to look carefully at one small section at a time. Use these tips to guide you – they will help you to know what to look for. These tips are not intended as a comprehensive set of revision notes – they can form a skeleton for your revision but you should refer to your textbook and the Revision flashcards and Content checklist to complete your notes. Ideally, these tips are intended as a summary of key areas where students commonly make mistakes or to highlight certain subjects which are essential to understanding. Something to bear in mind when preparing for your unit examinations: the questions on the exam papers will be fairly evenly spread across each unit. For instance, for the paper on Unit G484 (60 marks) you can expect to have to answer five or six questions – perhaps two from each module. Similarly, for the paper on Unit G485 (100 marks) you can expect to have to answer 10 questions – probably two or three from each module (N.B. only one question for the module on capacitors as it is fairly short). This means you have to revise all the modules covered in the different units – you cannot leave anything out! General guidance The first two rules of doing well in any examination are: read the question fully; and answer the question that is asked, not the one that you hoped for. © Pearson Education Ltd 2009 This document may have been altered from the original 1 These might seem silly statements but every year examiners see answers that, although containing correct physics, gain few marks because they do not answer what is required by the actual question. Another common mistake is for candidates to incorrectly transfer a number in the question, such as writing down 36 instead of 30. Diagrams and sketch graphs can earn marks – often more easily and quickly than written explanations – but they will only earn marks if they are carefully drawn. Examiners are not paid to guess what candidates have drawn! If asked to draw or sketch a graph always ensure you use a sensible scale and label both axes with both quantities and units. If plotting a graph use a pencil and draw small crosses or dots for the points. Diagrams must always be neat, clear and fully labelled. Using bullet points in written explanations can sometimes help you concentrate on the actual answer. Remember, scientific words have specific meanings and these meanings may differ to those used in everyday language, so take great care when using words such as force, energy and power – they are not the same thing so do not mix them up! Learn definitions so that you can write them down quickly and exactly – make a definition list or book for each section. Calculations in A2 physics A considerable number of marks in any A2 physics paper are given over to calculations. Get into the habit of tackling all calculations in the same way: write down the relevant equation; change the subject of the equation into the one that is being asked for in the question; put the correct figures from the question into the calculation, checking as you do so that you have written down the correct powers of ten – a common mistake here is to forget that a mm2 is 10–6 m2; work out the answer; and make sure you have the correct unit. Your answer to a calculation should always be given to the same number of significant figures as the figures in the question. Remember, when carrying out calculations it is vital that you explain what you have done as well as the symbols you have used. © Pearson Education Ltd 2009 This document may have been altered from the original 2 Examiners often comment on the errors made by candidates when using calculators. For example: Make sure you do not get the answer 18 to the calculation 12 / 2 x 3. When entering values such as 103 in your calculations remember this is actually 1x103 and you should enter “1 Exp 3” instead of the common mistake of entering “10 Exp 3” which results in 10000 instead of the required 1000. If you are not sure about either of these calculations then try them out on your calculator now! If you make mistakes, set yourself a list of simple calculations to do and practise before you go into the examination room. You should always check each line of your answer as you do it. Then make sure your answer makes sense – questions are not set in which the wavelength of light turns out to be 500 m or the charge on an electron to be 1.6 x 10–16. Making simple mistakes in your arithmetic can bring you down by as much as two grades, so take care! At A2, exponential equations are used in three different modules: discharge of a capacitor through a resistor; radioactive decay; and the absorption of X-rays by matter. All these calculations are very similar. You must learn how to use your calculator correctly when working out such mathematical problems. Another important type of calculation that you’ll come across during your A2 studies is that involving rate of change. Examples include: force which is rate of change of momentum; induced e.m.f. which is rate of change of flux linkage; and current which is rate of flow of charge. In all of these examples you have to remember to divide by time taken. When sitting the examination, you will be provided with a list of equations – acquaint yourself with such equations before sitting the exam. Make sure you know what each symbol stands for: V can be volume or voltage; E can be energy or electric field strength; W can be work done, energy transferred or energy stored; and A can be amplitude, area or activity. You must know and understand what the symbols or letters represent in any equation you use! © Pearson Education Ltd 2009 This document may have been altered from the original 3 Unit G484: The Newtonian world Module 1 – Newton’s laws and momentum Key words Newton’s laws of motion: linear momentum (p); force; impulse Collisions: principle of conservation of momentum; elastic collision; and inelastic collision You must learn how to use each of Newton’s laws when working out calculations. Basically: The first law states that a body continues travelling in a straight line at constant velocity unless a force acts on it. The second law states that if a force acts, then the force is equal to the rate of change of momentum and acts in the direction of the force. The third law states that if body A exerts a force on body B then body B will exert an equal and opposite force on body A. For example, for gases being forced out of the back of a rocket you may have to calculate the change in momentum per second of the gas backwards, and this will be equal to the force on the rocket forwards. In this instance, it is probably the second and third laws that are the most likely to occur. For the second law you will need to know how to calculate linear momentum and be aware that momentum is a vector. You should be able to show how the equation F = ma comes directly from the second law when the mass remains constant. You need to be able to define impulse of a force and know the equation impulse = change in momentum – these data are not given on the formula list given to you during the examination. You must also recognise that the area under a force against time graph is equal to the impulse. You need to know the principle of conservation of momentum and how to apply it to solve problems when two bodies collide in a straight line. You must remember when working out such calculations that momentum is a vector and therefore direction matters. It’s a good idea to draw two simple diagrams representing the bodies immediately before and after the collision – show the masses, velocity and directions of the bodies on these diagrams. This way you’ll use all the figures given to you in the question and have them readily available in your answer. © Pearson Education Ltd 2009 This document may have been altered from the original 4 Remember that in any collision, momentum is always conserved but there is usually a change in kinetic energy. You must know the difference between a perfectly elastic collision and an inelastic collision. Module 2 – Circular motion and oscillations Key words Circular motion: radian; centripetal acceleration; centripetal force Gravitational fields: gravitational field strength; Newton’s law of gravitation; time period; Kepler’s third law; geostationary orbit SHM: displacement; amplitude; period; frequency; angular frequency; phase difference; simple harmonic motion (SHM); damping; forced vibration; and resonance It is essential that you can explain why a force perpendicular to the velocity is needed to keep a body moving in a circular path. It goes like this: a body in a circular path is constantly changing direction therefore constantly changing velocity therefore has an acceleration and so needs a force (Newton’s 2nd law) now show the change in velocity is towards the centre of circle and therefore force is towards the centre. Make sure you can use the equations: v = 2πr/T; a = v2/r; and F = m v2/r. You need to be able to: describe that a mass creates a gravitational field around it define gravitational field strength as the force per unit mass show how the equation g = -GM/ r2 comes from Newton’s law of gravitation. You should be able to use gravitational field lines to represent a gravitational field when drawing diagrams. Try to be neat and clear in your diagrams and remember, these field lines never cut each other. You should understand that satellites in circular orbits around the Earth or planets moving around the Sun have a gravitational force acting on them. When using diagrams, this force must point directly from the centre of one of the bodies to the centre of the other. This force provides the centripetal force needed for the object to move in a circular path. So by using: v = 2πr/T and F = m v2/r = -GMm/r 2 © Pearson Education Ltd 2009 This document may have been altered from the original 5 you should be able to show T2 = (4π2/GM)r3. Following on, you may be asked to calculate the height of a geostationary satellite, i.e. T = 24 hr. Remember to change time into seconds and that r is the distance (in metres) to the centre of the Earth not the height above the Earth. The equation is also an explanation of Kepler’s third law (T2 α r3) which can be used to calculate time periods or planetary distances from the sun using: (T1/T 2) 2 = ( r1/r 2) 3 You need to be able to describe some simple examples of free oscillations such as a simple pendulum or a child on a swing (not being pushed!). You must be able to use these examples to describe and explain the interchange between kinetic energy and potential energy during simple harmonic motion (SHM). You must be able to state that: SHM occurs when the motion of a body is such that its acceleration is directly proportional to its displacement from a fixed point and the acceleration is always directed towards that fixed point. Note the definition does not refer to oscillations (up and down or side to side) – it is one of the worst-remembered definitions! From this definition comes the SHM equation: a = -(2πf)2x where a is the instantaneous acceleration, f the frequency and x the displacement. You then need to be able to use the equations: x = Acos(2πft) or x = Asin(2πft) and vmax =(2πf)A (you will not need to prove these equations). You also need to be able to describe and use sketch graphs to help explain: how, during SHM, displacement, velocity and acceleration change with time – remember these are sine or cosine graphs how, during SHM, acceleration changes with displacement – a straight line with negative slope going through the origin. (It is useful to remember that for a body moving with SHM at zero displacement it has no acceleration but maximum velocity, and at maximum displacement it has maximum acceleration and zero velocity.) how the amplitude of a forced vibration varies with frequency near to the natural frequency of the system – you must be able to give practical examples of forced oscillations and resonance the effects of damping on an oscillating system and how the forced oscillation graph above changes with damping. © Pearson Education Ltd 2009 This document may have been altered from the original 6 Make sure you know the relevant graphs and can draw them carefully and accurately. Be able to give examples of where resonance is useful (e.g. cooking food using microwaves) and where resonance should be avoided (e.g. in suspension bridges). Module 3 – Thermal physics Key words Solid, liquid and gas: kinetic model of matter; Brownian motion; pressure; internal energy Temperature: thermal energy; absolute scale of temperature; absolute zero; kelvins; degrees Celsius Thermal properties of material: specific heat capacity; latent heat of fusion; latent heat of evaporation; melting; boiling; evaporation Ideal gases: Boyle’s law; kinetic theory of gases; mole; Avogadro constant; and translational kinetic energy of atoms Using a simple kinetic model for matter you need to be able to briefly describe each of the following: solids, liquids and gases in terms of spacing, ordering, motion and forces between atoms or molecules how pressure exerted by a gas is due to collisions between its molecules and the container – o every collision with the sides of the container causes a change in the direction of a molecule o this means a change in velocity o which in turn denotes a change in momentum and a force o and because of the millions of molecules, a force acting across the whole surface o this results in the production of pressure on the sides of the vessel. how internal energy is the sum of the random distribution of kinetic and potential energies of the molecules of a system how a rise in temperature of a body leads to an increase in its internal energy how a change of state leads to a change in internal energy but not a change in temperature melting, boiling and evaporation © Pearson Education Ltd 2009 This document may have been altered from the original 7 how an experiment that demonstrates Brownian motion provides evidence for the random motion of molecules. Always remember heat and temperature are different things: heat is a form of energy temperature is a measure of how hot the object is and it is measured in kelvins or degrees Celsius. Heat will always flow from high to low temperatures. You need to be able to explain that: thermal energy, which you have previously referred to as heat, is transferred from regions of higher temperature to regions of lower temperature – i.e. heat flows from a hot body to a colder body if two objects have the same temperature then they are in thermal equilibrium – i.e. no heat flows between them when the two objects are in contact. You need to be able to: describe how there is an absolute scale of temperature that does not depend upon the property of any substance describe that the absolute zero of temperatures is the temperature at which a substance has minimum internal energy convert from kelvins to degrees Celsius. Regarding thermal properties of materials you must be able to: define the meaning of specific heat capacity (SHC) describe an electrical experiment for measuring SHC use the equation E = mcΔθ describe what is meant by latent heat of fusion and latent heat of evaporation. Remember when writing about melting or boiling that although there is no change in temperature, there is a change in internal energy – this is because of the need to break bonds of attraction between molecules. Always remember that when carrying out calculations concerned with gases – e.g. Boyle’s law or the gas equation – then the temperature is measured in kelvins. You must be able to state the assumptions of the kinetic theory of gases and from these know: what a mole is and the value for the Avogadro constant how to use the equations pV = NkT and pV = nRT, remembering N is the number of atoms and n is the number of moles that the mean translational kinetic energy of an atom of an ideal gas is directly proportional to the absolute temperature of the gas © Pearson Education Ltd 2009 This document may have been altered from the original 8 how to use E = 3kT/2 to find the translational kinetic energy of atoms. Unit G485: Fields, particles, and frontiers of physics Module 1 – Electric and magnetic fields Key words Electric fields: electric field strength; Coulomb’s law Magnetic fields: patterns; Fleming’s left-hand rule; magnetic flux density; the tesla; the mass spectrometer Electromagnetism: magnetic flux; weber; magnetic flux linkage; Faraday’s law of electromagnetic induction; Lenz’s law; ac generator; and transformers When revising electric fields, remember that the definitions and equations are very similar to those for gravitational fields – apart from substituting charge for mass. However, one main difference is that: for gravitational fields – the forces between masses are always attractive for electric fields – the forces can be either attractive or repulsive depending on the sign of the charges. You therefore need to know that electric fields are created by electric charges and that electric field strength (E) is the force acting per unit of positive charge. The importance of it being the positive charge is that this defines the direction of the force on a charge and that electric lines of force always go from the positive to the negative. You must: know Coulomb’s law leads to the equation F = Qq/4πεor2 be able to use both this equation and E = Q/4πεor2 for a point charge. Remember the field between two parallel plates is uniform and E = V/d. know the effect on a charged particle when it is moving: o parallel to a uniform electric field – similar to throwing a stone vertically from the Earth’s surface o perpendicular to a uniform electric field – similar to throwing a stone horizontally from a cliff top. You need to be able to draw the magnetic field patterns for: a long straight current-carrying wire © Pearson Education Ltd 2009 This document may have been altered from the original 9 a long straight solenoid. Remember magnetic fields are defined in a different way to gravitational and electric fields. They are defined in terms of the force on a currentcarrying conductor and so you need to be able to state and use Fleming’s left-hand rule for the force on a current-carrying conductor placed at right angles to a magnetic field. This leads to the following equations: F = BIL F = BILsinθ From these you must learn the definitions for magnetic flux density (B) and the tesla. Remember a beam of charged particles is the same as an electric current. So: If the beam is at right angles to a uniform magnetic field then there will be a magnetic force at right angles to the motion. This causes a centripetal acceleration and so the particles will move in a circular path. You must know: the force on a charged particle moving at right angles to a magnetic field is F = BQv that there is no force if the particle is moving parallel to the field. You must then be able to analyse the motion of charged particles when placed simultaneously in electric and magnetic fields. Normally: this is for a charged particle travelling straight through undeviated so the effect of the magnetic force cancels out the electric force therefore FB = BQv = FE = Ve/d. Remember this is used in the first part of a mass spectrometer to get a beam of ions all travelling at the same velocity. These ions are then subjected to a magnetic field which makes them travel in a circular path, the radius of which depends on the ions’ mass. When revising electromagnetism you need to be able to define: magnetic flux the weber magnetic flux linkage Faraday’s law of electromagnetic induction Lenz’s law. You must then be able to use the equations: φ = BAcosθ induced e.m.f. = -rate of change of magnetic flux linkage © Pearson Education Ltd 2009 This document may have been altered from the original 10 Module 2 – Capacitors and exponential decay Key words: capacitance; farad; energy stored; time constant; and exponential decay equation You must learn the definitions for: capacitance the farad. You need to know how to: use the equation Q = VC solve circuit problems involving capacitors in series and parallel. Remember that: The equation for capacitors in series is similar to the one for resistors in parallel. The equation for capacitors in parallel is similar to that for resistors in series. One fact that is often forgotten is that: The area under a p.d. against charge graph is equal to the energy stored by a capacitor. You also need to be able to use the two equations for energy stored in a charged capacitor. This capacity to store energy often leads onto questions that require you to describe some uses of capacitors, for example: in flash photography lasers used in nuclear fusion backup supplies in computers. Ensure you can write a few sentences on each of these examples. When a capacitor discharges through a resistor it does so exponentially. Also, you need to be able to: sketch graphs showing the variation with time of p.d., charge and current and how these graphs will change if the resistance is increased or decreased know how to use the exponential equation define the time constant and its equation explain how exponential decays have constant-ratio properties. © Pearson Education Ltd 2009 This document may have been altered from the original 11 Module 3 – Nuclear physics Key words Nuclear atom: alpha-particle scattering; nuclear atom; proton number; nucleon number; strong nuclear force; nuclides; isotopes Fundamental particles: quarks and antiquarks including up, down, topness, bottomness, charm and strangeness; hadrons; baryon number; weak interaction; neutrinos; antineutrino; positron; leptons Radioactive decay: alpha decay; beta decay; gamma decay; activity; decay constant; half-life; decay equations Nuclear fission and nuclear fusion: mass-energy equation; binding energy; binding energy per nucleon; and chain reaction You need to be able to: describe, in detail, the alpha-particle scattering experiment and how the results provided evidence for the existence, charge and small size of the nucleus draw a diagram of the apparatus used explain why the beam had to be very narrow, the gold foil so thin, the need for a vacuum and how the alpha-particles were detected draw a neat diagram to show scattering taking place near to the nucleus and at a distance from the nucleus. It is a good idea to know: the relative sizes of the atom and the nucleus – i.e. just how much bigger the atom is to the nucleus learn a value, to the nearest power of ten (in metres), for the diameters and volumes of both an atom and a nucleus. You should be able to use the standard notation, to represent a nuclide and know how this notation can be used to show nuclear reactions – e.g. in alpha and beta decay or in fission and fusion. Remember, the total for both the number of protons and the number of nucleons always remains constant on both sides of the equation. Remember, when showing the need for a very short-ranged strong nuclear force of attraction you use: Coulomb’s law to determine the force of repulsion between two protons in a nucleus © Pearson Education Ltd 2009 This document may have been altered from the original 12 Newton’s law of gravitation to determine the force of attraction between two protons in a nucleus. Since these forces are not equal – the force of repulsion being much greater than the force of attraction – you therefore need the strong nuclear force of attraction. You need to be able to describe a simple quark model of hadrons in terms of: up quarks and antiquarks down quarks and antiquarks strange quarks and antiquarks by knowing their: charge baryon number strangeness. It’s a good idea to draw a table showing the properties of quarks and antiquarks and then show how these can be combined into various hadrons such as protons and neutrons – remember that because protons and neutrons contain quarks they are not fundamental particles. You also need to know that the quark model can be extended to include the properties of: charm topness bottomness. Make a list of all the quantities that are conserved in nuclear decay and use it to describe the two types of β decay in terms of: a simple quark model the weak interaction between quarks. This will also help explain why: neutrinos and antineutrinos must be produced during β+ and βdecay, respectively a β+ particle is a positron whilst a β- particle is an electron electrons, neutrinos and their antiparticles are members of a group known as leptons. You must be able to describe: how radioactivity is the spontaneous and random decay of unstable nuclei the nature, penetration and range of α-particles, β-particles, and γrays – draw a table to show charge, mass, what it is, what stops it and how far it travels in air for each of these types of radiation. © Pearson Education Ltd 2009 This document may have been altered from the original 13 You need to be able to define: activity the decay constant half-life. You also need to know that: The randomness of radioactive decay leads to the fact that the rate of decay (activity) is proportional to the number of nuclei present – i.e. A = -λN. This leads on to: the exponential decay equations for radioactivity and how they are similar to the decay of charge on a capacitor in a C-R circuit. You do not need to be able to prove these equations but you do need to be able to use them! [It may be worthwhile acquainting yourself with how to do exponentials on your calculator in order to do this type of calculation.] Radioactive dating will also require you to be able to use: the exponential equations the equation λt1/2 = 0.693. When revising for nuclear fission and fusion you must learn to apply Einstein’s mass-energy equation to determine: binding energy binding energy per nucleon the energy released in nuclear reactions. You must be able to interpret the binding energy per nucleon against nucleon number graph, in particular, you need to understand the importance of the maximum binding energy per nucleon and why fusion is more likely to occur before this point and fission after it. For nuclear fission you need to be able to describe: how nuclear fission can be induced a nuclear chain reaction the role of fuel rods, control rods and moderator in a fission reactor peaceful and destructive uses of nuclear fission the environmental effects of nuclear waste. For nuclear fusion you need to be able to describe: the conditions in the core of stars that make fusion possible. © Pearson Education Ltd 2009 This document may have been altered from the original 14 Module 4 – Medical imaging Key words X-rays: photoelectric effect; Compton effect; pair production; intensity; attenuation; image intensifier; contrast media; CAT scan Diagnostic techniques: medical tracers; gamma camera; PET; MRI; magnetic resonance; precession; Larmor frequency; relaxation time; non-invasive techniques; ultrasound; piezoelectric effect Ultrasound transducers: A-scan; B-scan; acoustic impedance; and reflected intensity. It is essential you know how to: define intensity use the exponential equation to show how intensity of a collimated beam of X-rays varies with the thickness of the medium through which it is travelling – known as attenuation explain how X-rays are produced and the three ways in which they interact with matter. When describing how X-rays are used in imaging internal body structures, you should be able to write a couple of sentences on each of the following: the use of image intensifiers the use of contrast material the use of a barium meal when imaging soft tissue such as the intestines. You also need to be able to describe: the operation of a CAT scanner the advantages of a CAT scan over an X-ray image. For medical diagnostic methods you should be able to: describe the use of medical tracers such as technetium-99m describe the main components of a gamma camera describe the principles of positron emission tomography (PET) outline the principles of magnetic resonance with reference to: o the precession of nuclei o the Larmor frequency o resonance o relaxation times. describe the main components of an MRI scanner: o how an MRI scan can be used to obtain diagnostic information about internal organs o the advantages and disadvantages of MRI. © Pearson Education Ltd 2009 This document may have been altered from the original 15 describe the need for non-invasive techniques explain what is meant by the Doppler effect and how it can be used in determining the speed of blood. It may be useful to learn around five facts for each of these points and be able to write them down in a logical manner – but don’t forget, you need to answer the actual question asked, i.e. not just stating all the facts you know! When revising ultrasound you need to be able to: describe the properties of ultrasound describe the piezoelectric effect explain how ultrasound transducers emit and receive highfrequency sound describe the principles of ultrasound scanning – including the difference between A-scan and B-scan calculate acoustic impedance and the fraction of reflected intensity using the necessary equations describe the importance of impedance matching explain why gel is required when taking an ultrasound scan. Module 5 – Modelling the universe Key words Structure of the universe: stars; galaxies; radiation; solar system; star formation; astronomical unit; parsec; light year; Olbers’ paradox; Hubble’s law; Hubble’s constant; redshift; cosmological principle; microwave background radiation Evolution of the universe: standard model of the universe; big bang; open universe; flat universe; closed universe; and critical density When referring to the universe the distances measured are, not surprisingly, extremely large! You must know the: definitions for distances measured in AU, pc, ly approximate values, in metres, of the parsec and the light-year Olbers’ paradox and why it suggests that the model of an infinite static universe is incorrect. It is important that you can: state and explain Hubble’s law © Pearson Education Ltd 2009 This document may have been altered from the original 16 describe and interpret the redshift observations use the equation Δλ/λ = v/c convert the conventional units for the Hubble constant into SI units state the cosmological principle describe and explain the significance of the 3K microwave background radiation. With regard to the evolution of the universe you need to be able to: explain that the standard model implies a finite age for the universe calculate the age of the universe using the equation age = 1/H0 describe the evolution of the universe from 10–43 s after the big bang to the present. You need to be able to: define critical density and know its equation ρO = 3HO2/8πG explain how the ultimate fate of the universe depends on its density and how this will determine whether the universe will become: o open o flat o or closed. Current thinking is that the density of the universe is close to – and possibly exactly equal to – the critical density needed for a flat cosmology. © Pearson Education Ltd 2009 This document may have been altered from the original 17