Topic 7: Measurement and Uncertainties
7.1 Graphical Analysis
Logarithmic functions
7.1.1 Transform equations involving power laws and exponeritials into the generic straight line forms y = mx ± c and plot the corresponding log-log and semi-log graphs from the data.
The use of log-linear and log-log graph paper is not required.
7.1.2 Analyse log-log and semi-log graphs to determine the equation relating two variables.
Students should be able to determine the parameters of the original equation from the slope and the intercept.
7.2 Uncertainties
Uncertainties in calculated results
7.2.1 State uncertainties as absolute, fractional and percentage uncertainties.
7.2.2 Determine the uncertainties in results calculated from quantities with uncertainties.
A simple approximate method rather than root mean square calculations is sufficient to determine maximum uncertainties. For functions such as addition and subtraction, absolute uncertainties can be added. For multiplication, division and powers, percentage uncertainties can be added. For other functions (eg trigonometrical functions) the mean, highest and lowest possible answers can be calculated to obtain the uncertainty range. If one uncertainty is much larger than others, the approximate uncertainty in the calculated result can be taken as due to that quantity alone.
Uncertainties in graphs
7.2.3 Determine the uncertainties in the slope and intercepts of a straight-line graph.
Students should be able to draw lines of minimum and maximum fit to the data points, plus error bars.
Topic 8: Mechanics
8.1 Projectile Motion
8.1.1 State the independence of the vertical and horizontal components of notion for a projectile in a uniform field.
8.1.2 Describe the trajectory of projectile motion as parabolic in the absence of friction.
Proof of the parabolic nature of the trajectory is not required.
8.1.3 Solve problems on projectile motion.
Problems may involve projectiles launched horizontally or at any angle above or below horizontal. Applying conservation of energy may provide a simpler solution to some problems than using projectile motion kinematics equations.
8.2 Gravitation
Gravitational force and field
8.2.1 State Newton's law of universal gravitation.
Students should be aware that the masses in the force law are point masses not extended masses, but that the interaction between two spherical masses is the same as if the mass were concentrated at the centres of the spheres.
8.2.2 Define gravitational field strength.
Students should recognize the vector nature of gravitational fields.
8.2.3 Derive an expression for the gravitational field as a function of distance from a point mass.
This includes the field outside a spherical mass. See 8.2.1.
8.2.4 Derive an expression for gravitational field at the surface of a planet.
Students should also understand how the gravitational field strength and the acceleration due to gravity at the surface are related.
8.2.5 Solve problems involving gravitational forces and fields.
Vector addition is required to find the gravitational field strength due to more than one mass.
Gravitational energy and potential
8.2.6 Define gravitational potential energy and gravitational potential.
Students should understand that the work done in moving a mass between two points in a gravitational field is independent of the path taken and that gravitational potential energy is taken to be zero at infinity.
8.2.7 State the expression for gravitational potential due to a point mass.
8.2.8 Explain the concept of escape speed.
8.2.9 Derive an expression for the escape speed of an object from the surface of a planet.
8.2.10 Solve problems involving gravitational potential energy and gravitational potential.
These should include problems on escape speed.
8.3 Orbital Motion
Note: Although orbital motion can be circular, elliptical or parabolic, this section only deals with circular orbits. This section is not fundamentally new physics, but an application which synthesizes ideas from gravitation, circular motion, dynamics and energy.
8.3.1 State that gravitation provides the centripetal force for circular orbital motion.
8.3.2 State Kepler's third law: the law of periods.
8.3.3 Derive Kepler's third law.
This derivation is for the case of circular orbits and assumes Newton's law of universal gravitation.
8.3.4 Derive expressions for the kinetic, potential and total energy of an orbiting satellite.
8.3.5 Draw graphs showing the variation of the kinetic energy, gravitational potential energy and total energy with orbital radius of a satellite.
8.3.6 Discuss the concept of weightlessness in both orbital motion and in free fall.
8.3.7 Solve problems involving orbital motion.
8.4 Friction
8.4.1 Describe the nature and properties of frictional forces.
Students should identify the factors affecting friction.
8.4.2 Distinguish between static and dynamic (sliding) friction.
8.4.3 Define coefficient of friction.
Both static and dynamic coefficients are required.
8.4.4 Solve static and dynamic problems involving friction.
8.5 Statics
Static equilibrium
8.5.1 Define torque (moment of a force).
The vector nature of torque need not be addressed but students should include the sense (eg clockwise or counterclockwise) of a torque.
8.5.2 State the conditions for translational and rotational equilibrium.
8.5.3 Describe the concept of centre of gravity.
Students are not required to calculate the centre of gravity of objects. However. they should be aware that the weight of an object may be taken as concentrated at the centre of gravity for determination of gravitational torques.
8.5.4 Solve problems for extended objects in equilibrium.
Topic 9: Thermal Physics
9.1 Thermodynamic Systems and Concepts
Note: Although there are many thermodynamic systems, in this sub-topic discussion will be restricted to a fixed mass of an ideal gas.
9.1.1 Explain what is meant by thermodynamic system.
Students should recognize the distinction between a system and its surroundings.
9.1.2 Describe the concepts heat, work and internal energy.
The descriptions should include the expansion and compression of an ideal gas as an example.
9.1.3 Deduce an expression for the work involved in a volume change of a gas at constant pressure.
9.2 Processes
The first law of thermodynamics
9.2.1 State the first law of thermodynamics
9.2.2 State that the first law of thermodynamics is a statement of the principle of energy conservation.
9.2.3 Describe the isochoric (isovolumetric), isobaric, isothermal and adiabatic processes.
In each process the heat transferred, the work done and internal energy change should be addressed. The ideal gas equation of state should be applied to all processes except the adiabatic. Students should realize that a rapid compression or expansion of a gas is approximately adiabatic.
9.2.4 Draw and annotate thermodynamic processes and cycles on p-V diagrams.
9.2.5 Calculate the work done in a thermodynamic cycle from a p-V diagram.
9.2.6 Solve problems involving state changes of a gas.
Heat engines and heat pumps
9.2.7 Outline the concept of the heat engine and the heat pump.
9.2.8 Draw and annotate schematic diagrams of a heat engine and a heat pump.
Energy transfer paths should be shown.
9.2.9 Define the term thermal efficiency of a heat engine.
9.2.10 Draw and annotate the Carnot cycle on a p-V diagram.
Students should be aware that the Carnot cycle produces the maxirnum possible theoretical efficiency of a heat engine operating between two heat reservoirs.
9.2.11 State Carnot's theorem.
9.2.12 State an expression for the efficiency of a Carnot engine in terms of the temperatures of the two reservoirs.
Discuss the possibility of changing the thermal efficiency by altering the reservoir temperatures.
9.2.13 Solve problems involving heat engines and heat pumps
9.3 Second Law of Thermodynamics and Entropy
9.3.1 State that heat can be completely converted to work in a single process, but that continuous conversion of heat into work requires a cyclical process and the rejection of some heat.
9.3.2 State the Kelvin-Planck formulation of the second law of thermodynamics.
It is sufficient for students to acknowledge the impossibility of constructing a heat engine operating in a cycle that does not transfer energy to a cold reservoir. Teachers might like to show that if this were possible then it would imply that energy can be transferred spontaneously from a cold to a hot reservoir. This leads to the Clausius statement of the second law.
9.3.3 Analyse situations in terms of whether they are consistent with the first and/or second law.
9.3.4 State that entropy is a system property that expresses the degree of disorder in the system.
9.3.5 State the second law in terms of entropy changes.
A statement that the overall entropy of the universe is increasing will suffice.
9.3.6 Discuss examples of natural processes in terms of entropy changes.
Students should understand that although local entropy can decrease, any process will increase the total entropy of the system and surroundings.
9.3.7 Discuss the idea of energy degradation in terms of the second law.
Topic 10: Wave Phenomena
10.1 Doppler Effect
10.1.1 Describe and explain the Doppler effect.
Students should recognize that in general the velocities of source and or detector are specified with respect to the medium. They should know however that light in a vacuum is unique and, in this case, it is the relative velocity of source and detector that is relevant.
10.1.2 Construct wave front diagrams for moving-detector and moving-source situations.
10.1.3 Derive the equations for the Doppler effect for sound in the cases of a moving detector and a moving source.
10.1.4 Solve problems on the Doppler effect for sound.
Problems may include both a moving source and a moving detector but not both simultaneously.
10.2 Beats
10.2.1 Explain the formation of beats.
Students should be able to sketch the resultant waveform from the superposition of two component waves.
10.2.2 Derive the beat frequency formula.
10.2.3 Solve problems involving beats.
10.3 Two-source Interference of Waves
10.3.1 Explain, by means of the principle of superposition, the interference pattern produced by waves from two coherent point sources.
Water, light and sound waves should be considered.
10.3.2 State the conditions necessary to observe interference between two light sources.
10.3.3 Outline Young's double slit experiment for light and draw the intensity distribution of the observed fringe pattern.
Restrict this to the situation where the slit width is small compared to the slit separation so that diffraction effects on the pattern are not considered.
10.3.4 Derive expressions for the locations of the maxima and minima of the double slit fringe pattern.
These include the angular form sinØ = ný/d and the form s = ý D/d for locations on a screen at distance D, involving the small angle approximation.
10.3.5 Solve problems involving two-source interference.
Topic 11: Wave Phenomena
11.1 Electrostatic Potential
Electric potential due to a point charge
11.1.1 Define electric potential.
Students should understand the scalar nature of potential and that the potential at infinity is taken as zero.
11.1.2 Determine the electric potential due to various charge configurations.
This includes single point charge, collections of point charges and the potential outside a charged sphere. Students will not be expected to derive the equation
V = q/4Æ0/r
11.1.3 State and apply the formula relating electric field strength to potential gradient.
It is sufficient that students know that E = -ðV./ðx.
11.1.4 Describe the similarities and differences between gravitational fields and electrical fields.
Equipotentials
11.1.5 Describe and sketch patterns of equipotential surfaces.
This should include patterns due to isolated point charges. charged conducting spheres, two point charges and parallel conducting plates.
11.1.6 Explain the relation of equipotential surfaces to electric field lines.
11 .2 Electromagnetic Induction
Induced electromotive force (e.m.f.)
11.2.1 Describe the production of an induced e.m.f. by relative motion between a conductor and a magnetic field (motionally induced e.m.f.).
11.2.2 Derive the formula for the e.m.f induced in a straight conductor moving in a magnetic field.
11.2.3 Define magnetic flux and flux linkage.
11.2.4 Describe the production of an induced e.m.f. that is produced by a time-changing magnetic flux.
11.2.5 State Faraday's law.
11.2.6 Explain how a motionally induced e.m.f. can be equated to a rate of change of magnetic flux.
Students should be able to show that the induced e.m.f., Blv, is equal to ðØ/ðt.
11.2.7 State Lenz's law
11.2.8 Solve electromagnetic induction problems.
11.3 Alternating Current
11.3.1 Describe the e.m.f. induced in a coil rotating within a uniform magnetic field
Students should understand. without deriving, that the induced e.m.f. is sinusoidal if the rotation is uniform.
11.3.2 Explain the operation of a basic alternating current (ac) generator.
11.3.3 Define the concepts of root mean square voltage and root mean square current.
11.3.4 Solve ac circuit problems for ohmic resistors.
11.3.5 Describe the components and characteristics of an ideal transformer and explain its operation.
A qualitative explanation is sufficient.
11.3.6 Explain the use of high voltage step-up and step-down transformers in the transmission of electric power.
11.3.7 Solve problems on the operation of ideal transformers and power transmission.
Topic 12: Quantum Physics and Nuclear Physics
12.1 Quantum Physics
The quantum nature of radiation
12.1.1 Describe the photoelectric effect and Einstein's explanation of this effect.
Students should be familiar with the concept of the photon and should be able to explain why the wave model of light is unable to explain the photoelectric effect.
12.1.2 Outline an experiment to test the Einstein model.
Millikan's experiment involving the application of a stopping potential would be a suitable example.
12.1.3 Solve problems involving the photoelectric effect.
The wave nature of matter
12.1.4 Describe de Broglie's hypothesis and the concept of matter waves.
Students should also be aware of wave-particle duality (the dual nature of both radiation and matter).
12.1.5 Outline an experiment to test the de Broglie hypothesis.
12.1.6 Solve problems involving matter waves.
For example, students should be able to calculate the wavelength of moving electrons.
Atomic spectra and atomic energy states
12.1.7 Outline how atomic spectra can be observed.
12.1.8 Explain how atomic spectra provide evidence for the quantization of energy in atoms.
An explanation in terms of energy differences between allowed electron energy states is sufficient.
12.1.9 Outline the Bohr model of the hydrogen atom.
No mathematical details are required. Refer to the fact that the model enabled the discrete wavelengths of the hydrogen spectrum to be predicted.
12.1.10 State the limitations of the Bohr model.
12.1.11 Outline the Schrodinger model of the hydrogen atom.
The model assumes that electrons in the atom can be described by wave functions. These have to fit boundary conditions in three dimensions in the atom, giving rise to both radial and angular allowed modes with discrete energy states (analogous to the discrete allowed frequencies of standing waves). The electron has an undefined position. but the square of the amplitude of the wave function gives the probability of finding it at a point.
12.1.12 Calculate spectral wavelengths from energy level differences and vice versa.
X-rays
12.1.13 Outline the experimental set up for the production of X-rays
12.1.14 Draw and annotate a typical X-ray spectrum.
Students should be able to identify the continuous and characteristic features of the spectrum and the minimum wavelength limit.
12.1.15 Explain the origins of the features of a typical X-ray spectrum.
12.2 Nuclear Physics
The nucleus
12.2.1 Explain how the radii of nuclei can be determined by charged particle scattering experiments.
Use of energy conservation for determining closest-approach distances for Coulomb scattering experiments is sufficient.
12.2.2 Describe how the masses of nuclei can be determined using a mass spectrometer.
Students should be able to draw a schematic diagram of the mass spectrometer but the experimental details are not required. Students should appreciate that nuclear mass values provided evidence for the existence of isotopes.
12.2.3 Describe one piece of evidence for the existence of nuclear energy levels.
For example, alpha particles produced by the decay of a nuclide have discrete energies; gamma ray spectra are discrete. Students should appreciate that the nucleus, like the atom, is a quantum system with allowed states and discrete energy levels.
Radioactive decay
12.2.4 Describe both ß+ and ß- decay, including the existence of the neutrino and the antineutrino.
Students should know that ß energy spectra are continuous and that the neutrino was postulated to account for the missing energy and momentum.
12.2.5 State the radioactive decay law as an exponential function and define the decay constant.
12.2.6 Derive the relationship between the decay constant and half-life.
12.2.7 Solve problems using the radioactive decay law.
12.2.8 Outline methods for measuring the half-life of an isotope.
Students should know the principles of measurement for both long and short half-lives.
12.3 Particle Physics
Note: This section is intended to be a brief factual introduction to particle physics.
12.3.1 Outline the concept of antiparticles and give examples.
12.3.2 Outline the concepts of particle production and annihilation and apply the conservation laws to these processes.
Students should know that particles can be produced in high-energy interactions in particle accelerators. Details of accelerators are not required. Students should appreciate that these processes are instances of the conversion of energy to rest mass and vice versa (in accordance with Einstein's mass-energy relation), and are subject to various conservation laws:
mass-energy, momentum, electric charge. lepton number and baryon number.
12.3.3 List and outline the four fundamental interactions.
Students should also be aware that the electromagnetic force and weak nuclear force are instances of a single electro weak force with two types of exchange particles.
12.3.4 List the three classes of fundamental particle.
It is sufficient to know that the classes are leptons, quarks and exchange bosons (force mediators), and that there are six types of quarks and leptons. plus their antiparticles, grouped in three generations. Students should know that isolated quarks have not been detected.
12.3.5 State that there are three classes of observed particle.
It is sufficient to know that the classes are leptons, hadrons and exchange bosons. Hadrons are divided into mesons and baryons.
12.3.6 Outline the structure of nucleons in terms of quarks.
Students should be able to relate nucleon properties to composition, e.g. describe protons as "up,up,down".
12.3.7 Outline the concept of an interaction as mediated by exchange of particles.
Students should be able to associate the four interactions with their respective exchange properties and should also be aware of the colour force between quarks and the associated gluons.
The material that follow are reproduced with the permission of the International
Baccalaureate Organization.