HSC Physics Simultaneity

One of the most difficult and misunderstood concepts in the space section of the current NSW HSC Physics syllabus is simultaneity. Listed below are some tutorial points on this concept. Two sentences from Einstein's own popular exposition on relativity, Relativity, the Special and General Theory, Methuen, 1920, are given italics.

  1. A frame of reference is a measurement system (coordinate system) where time and position values of an event can be determined. A railway platform is a frame of reference. A moving train is a frame of reference. A person on the platform makes measurements in the platform reference frame. A passenger on the train makes measurements in the reference frame of the train.
  2. Two events are simultaneous in a reference frame if each has the same time coordinate in this reference frame.
  3. Every reference body (coordinate system) has its own particular time; unless we are told the reference body to which the statement of time refers, there is no meaning in a statement of the time of an event.
  4. Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity).
  5. Suppose that two simultaneous events (such as lightning strikes) occur at the different points x1 and x2 in the reference frame of the platform. The times at which these events occur in the reference frame of the train are not the same as those in the reference frame of the platform. The time interval between these events in the platform reference frame is zero. The time interval between these events in the reference frame of the train is -v/c2(1-v2/c2)-1/2(x2-x1). This expression shows that the time interval between two events depends on the location of the events and the relative speed of the reference frames. The factor c is the speed of light in a vacuum, this being the same in all inertial (non accelerating) frames of reference.

HSC Physics Back EMF

During the next 4 weeks I will list the most misunderstood concept in each of the four sections of the current NSW HSC Physics syllabus. Back emf is the most misunderstood concept in the motors and generators section. Here are some tutorial points on back emf.

  1. Look at a demonstration motor and a generator. Draw diagrams of these labelling the parts.
  2. When the magnetic flux through a coil changes an emf is induced in the coil.
  3. Imagine a coil of wire (solenoid) carrying a constant current. As the current flows through the windings it makes a magnetic field that passes through the coil. If the current is turned off it does not drop to zero immediately. For a short time the current keeps flowing at a value that exponentially falls towards zero. During this time interval an emf is induced in the coil due to the changing magnetic flux through it causing the current to "keep going" for a short time, opposing the change that is happening. Sketch graphs showing (A) the current flowing in the coil versus time, (B) the potential difference across the coil versus time.
  4. As the coil of a motor rotates in a magnetic field the changing magnetic flux through it induces an emf in the coil in accordance with Lenz's law. This emf tends to make an induced current in the opposite direction to the current supplied to the coil and is called a back emf.
  5. When a motor is first turned on the current in the coils is large as there is no back emf. As the coils gain speed the back emf increases and the current in the coil decreases.

IB Physics Revision 2017

The IB Physics examination papers are on October 31 and November 1. From now until this date I will list questions to help students revise for their Physics examination. This list will be updated over the next six weeks.

Students can increase their marks significantly during this period if they are positive, organised and have a plan. What is required is a balanced approach to study with adequate nutrition, sleep, exercise and recreation.

  1. Powers of Ten The radius of a proton is 0.88 fm. What is the density of a proton in kg/m3? (A) 10-6, (B) 102, (C) 1010, (D) 1018, (E) 1026
  2. Uncertainty Analysis The measured uncertainty in the length of a pendulum is 2%, the uncertainty in its mass is 3% and the uncertaity in the acceleration due to gravity is 4%. What is the percentage uncertainty in its period of oscillation? (A) 1% (B) 2%, (C) 3%, (D) 4%, (E) 5%
  3. Dimensions Surface tension is force per unit length. What are the dimensions of surface tension? (A)ML-2 (B)MT-2 (C)ML-2T-2 (D)L-1T-2 (E) ML-1T-2
  4. Relative Velocity At noon a ship S is 10 km west of a tanker T. The velocity of S relative to the Earth is constant at 12 km/h N30°E and the constant velocity of T relative to the Earth is 4.0 km/h S60°W. What is the distance between the vessels at 3pm on the same day? (A)3.2 km (B) 21 km (C) 41 km (D) 48 km (E) 58 km
  5. Change in Velocity A particle moves at a constant speed v around a circular path. What is the magnitude of its change in velocity after it turns through an angle 2𝜽? (A) vcos𝜽 (B) vsin𝜽 (c)2vcos𝜽 (D) 2vsin𝜽 (E)vsin2𝜽
  6. Constant Acceleration A stone is thrown vertically upwards from the edge of a building and strikes the ground after a time t1. When the stone is thrown vertically downwards from the same point at the same initial speed it hits the ground after a time t2. The time to fall if the stone was released from rest is (A) t1+t2 (B) t1-t2 (C) (t1t2)1/2 (D) (2t1t2)1/2 (E) (0.5t1t2)1/2
  7. Resultant Force A marble dropped from a height h above soft sand penetrates a distance d into the sand before comng to rest. If the marble is dropped from a height 2h the distance that it travels in the sand before coming to rest is (A) d (B) 2d1/2 (C) (2d)1/2 (D) 21/2d (E) 2d
  8. Stretching a Spring An unstretched spring of force constant k has one end tied to a vertical wall and a mass m at its other end. A constant horizontal stretching force F is applied to the mass. The extension of the spring in the horizontal direction when the mass comes to rest is (A) F/2k (B) F/k (C) 2F/k (D) 3F/k (E) 4F/k
  9. Explosion A mass M is initially at rest. It breaks up into two equal pieces having a total kinetic energy E. What is the magnitude of the relative velocity of the two pieces after explosion? (A)(2E/m)1/2 (B) (4E/m)1/2 (C) (8E/m)1/2 (D) (2m/E)1/2 (E) (4m/E)1/2
  10. Ideal Gas Boltzmann's constant is equal to (A) R/NA (B) RNA (C) NA/R (D) R+NA (E) R/NA2
  11. Ideal Gas Particles A cylinder contains a volume V of helium gas at a temperature T. A second cylinder contains a volume 2V of argon gas at a temperature T. (A) the average speed of a helium atom is the same as that of an argon atom, (B) the average speed of a helium atom is less than that of an argon atom, (C) the average speed of a helium atom is greater than that of an argon atom, (D) each container contains the same number of particles, (E) the pressure exerted by each gas is the same
  12. Change of State A copper block is heated in a Bunsen flame. The copper block is then placed on a large block of ice at 0°C in which it becomes half buried. What was the initial temperature of the copper block? (A) 5°C (B) 22°C (C) 42°C (D) 62°C (E) 82°C
  13. Specific Heat Capacity One kilogram of copper and the same mass of water are heated using the same Bunsen burner. (A) the rate of temperature increase of both objects is the same, (B) the rate of temperature increase of water is greater than that of copper, (C) the rate of temperature increase of copper is greater than that of water, (D) the rate of internal energy increase is the same for each object, (E) the rate of internal energy increase for water is greater than that of copper.
  14. Electric Current Two copper wires, P and Q, at the same temperature have the same battery of zero internal resistance connected across each of them. The length of P is twice that of Q. The drift speed of the electrons in P is (A) the same as that in Q, (B) greater than that in Q, (C) less than that in Q (D) is zero (E) depends on the diameter of the wire.
  15. Resistance Four equal resistors R form the sides of a square. Another resistor R is placed across a diagonal of the square. What is the total resistance between the other two corners of the square? (A)R/4 (B) R/2 (C) R (D) 2R (E) 4R
  16. Electric Field Strength Point charges of +4Q and -Q are placed a distance d apart in a vacuum. The resultant electric field is zero at a distance (A)2d to the left of -Q (B) d to the left of -Q (C) d to the right of -Q (D) 1.5d to the right of -Q (E) 2d to the right of -Q
  17. Electrical Power A battery of emf 12V and constant internal resistance is connected to a 6Ω resistor. The power of the 6Ω resistor is greatest when the internal resistance is (A) 0Ω (B) 3Ω (C) 6Ω (D) 9Ω (E) 12Ω
  18. Multiple Point Source Interference Monochromatic, coherent light is produced by two point sources. The intensity of the maxima produced on a screen is I. The experiment is repeated using 4 point sources with the same source spacing. The intensity of the principal maxima on the screen is (A) I, (B) 2I, (C) 4I, (D) 8I (E) 16I
  19. Secondary Maxima The number of secondary maxima between the principal maxima in the interference pattern produced by 4 coherent, monochromatic point sources of light is (A) 0, (B) 1, (C) 2, (D) 3, (E) 4
  20. Interference Pattern Compared to the interference pattern produced by 2 coherent, monochromatic point sources the intereference pattern produced by 8 sources of the same spacing (A) has brighter principal maxima that are closer together, (B) has brighter principal maxima that are farther apart, (C) has brighter principal maxima that are the same distance apart, (D) has principal maxima of the same intensity that are the same distance apart, (E) has principal maxima of the same intensity that are the closer together.
  21. Single Rectangular Slit Diffraction Monochromatic light passes through a single narrow slit. The intensity pattern is observed on a screen at a large distance from the single slit. Why does the intensity not stay at zero after the central maximum?

HSC Physics Revision 2017

The HSC Physics examination is on October 30. From now until this date I will list questions to help students revise for their Physics examination. This list will be updated during the next two months.

Students can increase their marks significantly during this period if they are positive, organised and have a plan. Remember that the HSC Physics examination is not "difficult Physics". What is required is a steady approach to study with adequate nutrition, sleep, exercise and recreation. 

  1. Accelerating Reference Frame A train moving in a straight line on horizontal ground is accelerating to the east. A ball is released from rest (relative to the floor of the train) from a height of 2.0 m. Sketch the path of the ball in the reference frame of the (i) train, if the train is moving to the east (ii) Earth, if the train is moving to the east (iii) train, if the train is moving to the west, and (iv) Earth, if the train is moving to the west.
  2. AC Motor An AC generator is reversed so that AC is now fed into the coil through the brushes that rub against the slip rings. Does the coil spin?
  3. Photocells and Solar Cells Describe the differences between a photocell and a solar cell.
  4. Cloud Chamber Describe how a cloud chamber detects the presence of radiation. Which radiation produces the (i) thickest tracks? (ii) thinnest tracks? (iii) straightest tracks? (iv) Can gamma rays be directly observed in a cloud chamber?
  5. Earth Satellite A satellite is in orbit above the Earth's equator. Determine the altitude of the satellite if it (i) appears stationary above the equator, (ii) appears to pass overhead (as seen by a person on the equator) from west to east every 8 hours, (iii) appears to pass overhead from east to west every 8 hours.
  6. Magnetic Field of Two Currents Two long straight parallel wires at a distance d apart carry currents of I and 4I in opposite directions. Where is the resultant magnetic field strength zero?
  7. Heinrich Hertz Describe how Hertz discovered the photoelectric effect.
  8. Strong Nuclear Force Sketch graphs showing the force between two nucleons and the potential energy of two nucleons as a function of their distance apart.
  9. Artificial Gravity A space station far away from any planet or star has the shape of a torus of outer radius 500 m. It rotates about an axis through its centre and perpendicular to its plane at constant rate of 10 rev/min. An astronaut of mass 80 kg is standing on the inside of the outer surface of the space station (i) describe the force/s acting on the astronaut, (ii) determine the weight of the astronaut (iii) an apple is released from rest inside the spacestation at a distance of 1 m from the outer wall. Describe the subsequent motion of the apple.
  10. EMF and Back EMF What is the difference between an induced EMF (as in a generator) and a back EMF (as in a motor)?
  11. CRO Describe how an electron beam produces a two dimensional image on the screen of a cathode ray oscilloscope.
  12. Electron in the Hydrogen Atom According to quantum physics, how do we describe the electron in the hydrogen atom?
  13. Maximum Range A basketball is thrown at a speed U an angle 𝜽 to the horizontal from of a height h above the ground. Show that the angle that gives the maximum range on the ground is given by csc2𝜽max = 2(1+gh/U2).
  14. Magnetic Force Two electrons are moving at the same velocity v relative to the laboratory side by side in parallel paths a distance d apart in the laboratory reference frame. Determine the magnitude of the resultant force between the electrons in the (a) reference frame of the electrons, (b) laboratory reference frame.
  15. Planck and Einstein Outline the political views of Max Planck and Albert Einstein. How did this affect their scientific work?
  16. Enrico Fermi Assess the contribution of Enrico Fermi to Physics.
  17. High Speed Electron An electron is accelerated from rest through a potential difference of 100,000 V using a particle accelerator. Find the final speed of the electron.
  18. Loudspeaker Describe how a loudspeaker uses the motor effect to produce sound waves.
  19. Blackbody Radiation Curve Explain why the blackbody radiation curve has a peak at a certain wavelength. Does a photon of this wavelength have the greatest energy?
  20. Linear Accelerator Describe how a linear accelerator produces a high speed particle.
  21. Projectile Practical A marble is projected horizontally at a known constant speed from a spring gun at various heights above the floor and the horizontal range is measured in each case. (i) Plot this data so that a straight line graph is produced, (ii) how can the graph be used to determine g?
  22. Step-Up Transformer A step-up transformer is used to increase the voltage of an AC supply with respect to the ground. Explain how this reduces reduces the heat loss along the transmission line from the power station.
  23. Phonons A student in an answer to a question on the BCS theory mentions a "phonon". Outline what a phonon is.
  24. Forces of Nature Outline the force that holds together, giving the carrier particle in each case (i) the nucleons in an alpha particle, (ii) the quark combination that produces a proton
  25. Michelson and Morley Describe the result of the Michelson and Morley experiment.
  26. Torque and Work Describe the difference between torque and the work done by a force.
  27. n-type Semiconductor Is an n-type semiconductor negatively charged?
  28. Binding Energy The mass of the two protons, two neutrons and two electrons is greater than their combined mass when they form a helium atom. Describe why this is so.
  29. Gravitational Potential Energy When is the gravitational potential energy of two masses least? When they are close together or far apart? Explain.
  30. Cathode Rays Describe Thomson's experiment to measure the charge to mass ratio of cathode rays.
  31. Bragg Diffraction Using a labelled diagram, explain using wave concepts how constructive interference occurs when x-rays strike a solid object.
  32. Line Spectrum Explain how the presence of a line spectrum indicates the existence of energy levels in the hydrogen atom.
  33. Orbital Decay In an answer a student states that the speed of an orbiting satelite decreases when it is subjected to air drag. Is this correct?
  34. Back EMF Does the back emf eventually stop the coils of a DC motor from spinning? Explain.
  35. Electromagnetic Waves Describe how Heinrich Hertz experimentally produced radio waves and identified these as belonging to the same group as light waves.
  36. Moderator A neutron given off in a fission reaction has a kinetic energy of 6.0x10-13 J. This is reduced to 6.0x10-21 J by causing the neutron to make a series of collisions with carbon nuclei in the moderator. The fractional loss of kinetic energy of a neutron at each collision is 0.14. Find the number of collisions involved in this process. [122]
  37. Polar Orbit A satellite is placed in an orbit that passes over points near the north and south poles of the Earth. Does this satellite possess more energy than a similar satellite in orbit at the same altitude above the equator?
  38. Power Which combination has the higher power? A large resistance R connected to a battery or a smaller resistance r?
  39. Carbon Carbon has 4 electrons in its outer shell. (a) is the outer shell the same as the valence band? (b) is its valence band full? (b) is carbon a semiconductor?
  40. Electron Wavelength Compared to an electron in the ground state, the wavelength of an electron in the first excited state of the hydrogen atom is (A) 1/4, (B) 1/2, (c) the same, (D) twice as large (E) 4 times as large
  41. Acceleration A student doing a physics problem calculates the acceleration of an electron as 2.0x1014 ms-2. Is this possible?
  42. DC Motor A DC motor has a split-ring commutator and the coils are in a radial magnetic field. An open switch is in the circuit. The switch is now closed. Sketch graphs showing (A) the current flowing in the coils in terms of time (B) the torque exerted by the magnetic field on the coil in terms of time.
  43. Band Structure A conductor and a semiconductor are at room temperature. Choose the correct statement.(A) the conduction band of the conductor is empty (B) the conduction band of the semiconductor is empty (C) the conduction band of a semiconductor is partially filled (D) the conduction band of a conductor is full (E) the valence band of a semiconductor is full
  44. Neutron A neutron (A) is not affected by a magnetic field (B) has no spin about its axis (C) has a magnetic moment causing it to align itself with a magnetic field (D) has zero magnetic moment since it has zero charge (E) is made of a proton and an electron.
  45. Orbit A satellite of total mass m moves at a constant speed v in a circular orbit around a planet. It suddenly fires a projectile of mass 0.5m at a speed of 0.5v in the opposite direction to its initial velocity. After it launches the projectile the satellite (A) continues in the same orbit with the same speed, (B) moves to a higher orbit (C) escapes from the planet, (D) moves to a lower orbit, (E) continues in the same orbit with a shorter period
  46. Soft Iron Core The role of the iron core in a transformer is to (A) reduce the eddy currents, (B) connect together the primary and secondary coils, (C) increase the magnetic flux passing through the coils, (D) carry all of the magnetic field of the primary coil through the secondary coil, (E) change the voltage of the primary coil.
  47. Type 1 and 2 Superconductors Superconducting magnets use (A) type 1 superconductors since B=0 inside them, (B) type 1 superconductors since B≠0 inside them, (C) type 2 superconductors since B≠0 up to a certain value, (D) type 2 superconductors since B=0 inside them, (E) both type 1 and type 2 superconductors.
  48. Bohr's Postulate In 1913 Niels Bohr proposed that mvr = n h/(2𝜋), where n is the principal quantum number, m is the mass of the electron, v is the speed of the electron and r is the radius of the stationary state. (A) the original Bohr theory is still used to explain the hydrogen atom, (B) Bohr's equation gives the magnitude of the electron angular momentum that agrees accurately with modern experiments, (C) Bohr's equation was replaced since quantum mechanics predicts that for each value of n there are n possible values of the orbital angular momentum, (D) the electron is now considered to have non-zero orbital angular momentum in its ground state, (E) the electron is now considered to have zero orbital angular momentum for every value of n.
  49. Projectile1 A ball is thrown at 49m/s at 60° to the horizontal. Neglecting air resistance, the times after projection when the velocity vector makes an angle of 30° with the horizontal are (A)2.16s, 6.50s (B) 2.33s, 6.33s (C) 2.89s, 5.77s (D) 3.66s, 5s (E) 4.00s, 4.66s.
  50. Projectile2 A ball is thrown at 49m/s at 60° to the horizontal. Neglecting air resistance, the times after projection when the speed of the ball is 35m/s are (A) 0.48s, 8.18s (B) 1.10s, 7.56s (C) 1.78s, 6.88s (D) 2.56s, 6.10s (E) 4.00s, 4.66s.
  51. Air Resistance The drag force acting due to air resistance on a projectile is proportional to the square of the speed of the projectile. A projectile is thrown vertically upwards at 49m/s. The maximum height reached is 60m. The projectile is now thrown at the same speed at an angle to the vertical. The maximum possible range of the projectile on the horizontal is (A) 30m (B) 60m (C) 94m (D) 120m (E) 180m
  52. Speed A projectile is thrown at 49m/s at 60° to the horizontal in the absence of air resistance. The gradient of the distance travelled-time graph for the projectile has a maximum value of (A) 98m/s, (B) 75m/s, (C) 49m/s, (D) 42m/s, (E) 24.5m/s.
  53. Average Speed Two identical projectiles, P and Q, are thrown on level ground at the same speed. P is thrown at 30° to the horizontal and Q is thrown at 60° to the horizontal. Neglecting air resistance, (A) the range of P is greater than Q, (B) the average speed of each projectile is the same during their flight, (C) the average speed of P is greater than the average speed of Q, (D) the average speed of P is less than the average speed of Q, (E) the average velocity of each object is the same during the flight.

HSC Quanta to Quarks

The HSC Physics topic Quanta to Quarks includes the concept of the wave nature of an electron.

  1. When we draw an electron as a wave what does the height of the wave represent?
  2. Is the electron mass spread out along the wavelength?
  3. In quantum mechanics an electron is described by a wave function. Is this the same as the de Broglie matter wave?
  4. What is the physical interpretation of the wave function?
  5. According to quantum mechanics what actually is the electron in the hydrogen atom? Is it a particle moving in an orbit?

Curl of a Vector

In electromagnetism and fluid dynamics we often determine the curl of a vector quantity. This is a mathematical operation that follows set rules and is used to determine a field vector. What does curl mean physically?

In electromagnetism when rationalised SI units are used, the curl of the electric field vector (E) is equal to minus the partial time derivative of the magnetic induction vector (B) and the curl of the magnetic field vector (H) is equal to the sum of the current density (J) and the partial time derivative of the electric displacement vector (D). These relationships are known as the Faraday-Maxwell law and the Ampere-Maxwell law respectively.  In fluid mechanics the curl of the fluid velocity vector (u) is equal to the vorticity (W).

The curl operation is a mathematical way of determining whether the work done (also called the circulation) in moving around a small circle centred at the field point is zero. If the work done is zero the field is said to be conservative or irrotational, meaning that a small paddle wheel placed at that point in the field would not spin if the field was the velocity field of a fluid, hence the name of the operation curl. Some textbooks call the curl operation rot, the significance coming from the rotation of the test paddle wheel. The mathematical rule connecting curl with work done is known as Stokes' theorem, one of the very important theorems of vector analysis along with those of Gauss and Green.

The curl operation is a very important part of the language of electromagnetism. The curl operator is part of the mathematical language that we use to show that time varying electric and magnetic fields propagate through space at the speed of light.

Trial Physics Revision 2017

In most schools in NSW the trial HSC examinations occur in three weeks. Class assessment tasks have finished so we can now concentrate on studying. How can you best prepare for these examinations? First, you must have a study timetable, just like a daily school timetable where you have 60 minutes for each subject. Stick to the schedule. Have a 10 minute break between study sessions. Secondly, in your study sessions work through past examination questions by writing down answers on lined paper. Set out your work in an organised fashion so that this habit becomes automatic in examinations. Remember that perfect practice makes perfect. Here are some Physics revision questions:

  1. Reliability An experiment is performed to measure the acceleration due to gravity. Outline how we can make the result reliable.
  2. Ceramic Insulators Outline the function of the ceramic insulators on electricity transmission lines.
  3. Silicon and Germanium Describe the advantages of silicon over germanium in semiconductor devices.
  4. Zeeman Effect Describe the Zeeman effect. How is it explained?
  5. Orbital Speed The orbital speed of a satellite moving in a circular path of radius r is v. Find the orbital speed of a satellite moving about the same planet in a circle of radius 2r.
  6. DC Motor A simple DC motor has one rectangular coil of wire placed in a uniform magnetic field. Explain, using a diagram, why the magnetic force on each side of the coil is constant as it spins but the torque acting on the coil is not.
  7. Superconductors Superconducting magnets are used to produce very strong magnetic fields in particle accelerators. Explain how this is possible if the magnetic field inside a superconductor is zero.
  8. Matter Waves A student states that an electron is described as a particle moving along a standing wave. Explain why this is incorrect.
  9. Relativity A spacecraft travels at a constant velocity v between two planets that are a distance d apart. Determine the time taken for the journey according to (a) the reference frame of the planets (b) the reference frame of the spacecraft.
  10. Split-Ring Commutator A split-ring commutator is connected to the output terminals of a single coil generator that is spinning at a constant rate. Draw graphs showing for one rotation of the coil (i) the current in a particular side of the coil (ii) the magnetic force on this side of the coil (iii) the current in a particular brush (iv) the electrical power in the coil (v) the mechanical power suplied to the coil
  11. Resistance A copper wire is maintainted at a temperature of 2K. Describe how an electric current flows through the conductor.
  12. Uncertainty Principle An observation is made of the position of an electron. How does this affect the momentum of the electron?
  13. Rocket Motion A rocket starts from rest and accelerates vertically upwards due to the expulsion of exhaust gases at a constant speed relative to the rocket. The mass of the rocket decreases at a constant rate. Draw graphs showing for the same time interval the rockets (i) acceleration (ii) velocity (iii) distance travelled (iv) momentum.
  14. AC An alternating current of peak value I flows in a conductor of resistance R. Show that the heat energy released during one cycle of the AC is one-half of that of a constant current I.
  15. Cathode Rays A glass tube contains air. A high voltage is applied between two electrodes in the tube. Describe the appearance of the discharge in the tube as the pressure in the tube is reduced.

Electric Current

What happens when a current flows through a conductor? In HSC Physics students learn that the resistance of a conductor is due to the collisions of the conduction electrons with the atoms in the conductor. These collisions transfer energy from the electrons to an increase in the vibrational energy of the atoms causing an increase in temperature of the conductor. What would be an estimate of the drift speed of conduction electrons through a metal;  1 mm/s, 1 m/s, 1000 m/s or 1,000,000 m/s? The answer is 1 mm/s. When a light globe is switched on an electric field is sent along the connecting wire at a speed of about one-third of the speed of light and this field pushes electrons at the far end of the wire through first, so the globe appears to glow immediately. Quantum mechanics also teaches us that electrons behave as waves. The electron waves are scattered by the irregularly spaced atoms in the conductor which are displaced from a regular pattern due to their thermal vibration.

Why is Gravitational Potential Energy Negative?

Student's learn in HSC and IB Physics classes that the gravitational potential energy of two attracting masses is negative. Why is this? Let us consult the popular Physics textbooks to see what their authors say.

Resnick, Halliday and Walker Fundamentals of Physics (10th edition, page 365)...we choose a reference configuration with U equal to zero when the separation distance between the masses is infinite. The gravitational potential energy decreases when the separation decreases. Since U=0 for r=infinity, the potential energy is negative for any finite separation and becomes progressively more negative as the particles move closer together..

Serway and Jewett Physics for Scientists and Engineers (8th edition, page 386)...the potential energy is negative because the force is attractive and we have chosen the potential energy as zero when the particle separation is infinite. Because the force between the particles is attractive, an external agent must do positive work to increase the separation between the particles. The work done by the external agent produces an increase in potential energy as the two particles are separated.

Knight Physics for Scientists and Engineers (4th edition, page 366)...All a negative potential energy means is that the potential energy of the two masses at separation r is less than their potential energy at infinite separation.

Tipler and Mosca Physics for Scientists and Engineers (6th edition, page 374)....this means that U approaches zero as r approaches infinity. At first this may seem like a strange choice because for finite values of r all values of U are negative. This just means, however, that the potential energy is at a maximum when Earth and particle are at infinite separation.

Sears, Zemansky, Young, Freedman University Physics (14th edition, page 429)...in defining U we have chosen U to be zero when the body is infinitely far from the Earth. As the body moves towards the Earth, gravitational potential energy decreases and becomes negative.

Ohanian and Markert Physics for Engineers and Scientists (3rd edition, page 289)...the potential energy is always negative and its magnitude is inversely proportional to r. If the distance r is small, the potential energy is low (the potential energy is much below zero); if the distance r is large, the potential energy is higher (the potential energy is still negative but not so much below zero). Thus the potential energy increases with distance; it increases from a large negative value to a smaller negative value or to zero. Such an increase of potential energy with distance is characteristic of an attractive force. For instance, if we want to lift a communications satellite from a low initial orbit (just above the Earth's atmosphere) into a high final orbit (such as a geostationary orbit) we must do work on this satellite (by means of a rocket engine). The work we do while lifting the satellite increases the gravitational potential energy from a large negative value (much below zero) to a smaller negative value (not so much below zero).


Studying Physics and Mathematics

With the trial examination period for 2017 quickly approaching it is important to talk about the best way to study Physics and Mathematics. The answer is to do questions. Questions may be from past exam papers or summary books. At this stage in schools new work should have been completed with a path of revision left towards the HSC. Write detailed answers to your questions. In Physics use the words clearly and make sure you answer the question that is asked. In Mathematics do not jump too many steps at once in your working as this is a very common source of error. Most importantly do not attempt at this stage to summarise or write out the text-book. This just takes up time and does not engage your brain to promote thinking and understanding.

Period of Trigonometric Functions

A very common question in HSC Maths papers is to find the period of a given trig function. Some students regret putting the period of tan(x) as 2𝛑 in last year's HSC 2Unit paper! Here is a quick tutorial set on determining the period of trigonometric functions. Answers are given below.

  1. sin(x)
  2. 2cos(x)
  3. tan(x)
  4. csc(x)
  5. sec(x)
  6. cot(x)
  7. 3sin(2x)
  8. tan(2x)
  9. cos(x/2)
  10. sin(𝜋x+3)
  11. 2cos(x/3+π)
  12. cos(x)+sin(x)
  13. cos(2x)+sin(2x)
  14. cos(x/2)+sin(x/2)
  15. sin(x)+sin(2x)
  16. sin(x)+sin(2x)+sin(3x)

[2𝛑, 2𝜋, 𝜋, 2𝜋, 2𝜋, 𝜋, 𝜋, 𝜋/2, 4𝜋, 2, 6𝜋, 2𝜋, 𝜋, 4𝜋, 2𝜋, 2𝜋]

Ideal Gases

Question 11 in IB Physics November 2016 Paper 1 was a question on determining the gradient of the V-T graph for an ideal gas. Only 11% of candidates answered this question correctly and this statistic is the lowest in SL papers in the last 4 years. Why was this question so difficult? The correct alternative, C, has the same form as the most chosen alternative, B . Alternative B contains the gas constant R whereas alternative C contains the Boltzmann constant k, which is correct; 66% of candidates sitting for the paper confused the constants by selecting alternative B. This could have been avoided by using the formulae on page 6 of the Data Booklet. Make use of the Data Booklet in Physics examinations.

Cathode Rays

Here are some points about the nature of cathode rays for HSC Physics.

  1. Cathode rays (now called electrons) are small negatively charged particles leaving the cathode and attracted to the anode in a discharge tube containing air at a low pressure when a high voltage is applied between the electrodes.
  2. German scientists believed that cathode rays were a wave-like disturbance in the aether like light. Heinrich Hertz found that cathode rays could pass through thin sheets of gold and were not deflected by electric fields. Hertz left too much gas in his tube causing it to be ionised and so a weak resultant electric field existed between his deflecting plates....too weak to produce a noticeable deflection of the cathode ray beam.
  3. J.J. Thomson in 1897 used a lower pressure in his discharge tube and delected a beam of cathode rays towards the positively charged plate showing that cathode rays are negatively charged particles. Thomson applied a magnetic field perpendicular to his deflecting electric field using a set up known as Helmholtz coils. The magnetic field deflected the beam perpendicular to its velocity and by adjusting the strength of the field he was able to allow the cathode rays to pass through both fields in a straight line, the electric force balancing the magnetic force. In this case v = E/B, where v is the speed of the cathode ray, E is the strength of the electric field and B is the strength of the magnetic field.
  4. Thomson switched off the magnetic field and allowed the cathode rays to be deflected only by the electric field. He measured the angle 𝜽 at which the beam was deflected when it left the electric field; tan𝜽 = qEL/(mv 2 ), where L is the length of the electric field, v is the speed of the cathode ray and q/m is the charge to mass ratio of the cathode ray. If the sideways deflection y of the beam is measured instead of 𝜽 the equation connecting y and q/m is y = qB 2 L 2 /(2mE)
  5. Thomson found that the charge to mass ratio of cathode rays was a large number and was independent of the type of metal in the cathode. He concluded that cathode rays are small negatively charged partices that are present in all matter. His work established the existence of the electron as a fundamental particle of matter provided the basis for further advances in Physics such as quantum theory, semiconductor technology and superconductivity.

Some facts about cathode rays.

  1. The first observation of the presence of cathode rays was made by Julius Plucker in 1858 who noticed a green fluorescence coming from the wall of the glass tube near the anode. This colour is determined by the chemical composition of the glass.
  2. When a small paddle-wheel balanced on a pair of horizontal rails is placed in a discharge tube the vane always turns away from the cathode. This led William Crookes to (incorrectly) conclude that cathode rays were particles with momentum. H Starke later showed that the rotation of the vane was due to the heating of only one side of the vane by the cathode rays. The gas next to the vane had an increased pressure and so the vane was pushed away from the cathode. Thomson showed that the momentum of the beam was not sufficient to produce the observed motion. The paddle wheel experiment shows that cathode rays have a heating effect rather than momentum.

Circular Motion

Question 22 (SL) and Question 14 (HL) in the May 2016 IB Physics Paper 1  involved a mass on the end of a rod moving in a vertical circle in such a manner that the speed of the mass was constant. This question received the lowest percentage of correct responses in both papers and so it is worthwhile to discuss the Physics involved in this question. The question asks about the force exerted by the rod on the mass. The forces acting on the mass are its weight due to the Earth's gravitational field and the contact force of the rod pulling on the mass. Since the mass is moving at a constant speed in uniform circular motion the resultant force acting on the mass must always be directed towards the centre of the circle and must be constant in magnitude. As the mass moves around the circle the weight force is always directed downwards and so the direction of the contact force must change so that the vector sum of the weight force and the contact force is always directed towards the centre of the circle. At the top of the circle both forces point towards the centre of the circle and so the contact force has its minimum value at this position. Therefore the answer is D.

Speed of Light

This is a phrase that often appears in student responses in Physics examinations. Let's look at various versions of it and see if they are correct. We will start from the most basic.

  1. Light is constant. This is incorrect as the property of light has not been identified.
  2. The speed of light is always constant. This is incorrect. The speed of light in water is less than the speed of light in a vacuum.
  3. The speed of light in a vacuum is a constant value. This is not fully correct as the frame of reference has not been included.
  4. The speed of light in a vacuum is the same value in any inertial frame of reference. Correct. This was one of Einstein's postulates in 1905.
  5. The speed of light in a vacuum is the same value in any frame of reference. Incorrect. In accelerating (non-inertial) frames of reference the speed of light in a vacuum is not always c.

Here are some other misconceptions about the speed of light.

  1. The speed of light in a vacuum is given the symbol c because c is the first letter of constant. Incorrect. The c comes from the Latin word celeritas for speed.

  2. The Michelson and Morley experiment showed that the speed of light was always constant. Incorrect. There is no mention of the constancy of the speed of light in their paper describing the experiment. Einstein proposed this in 1905. M and M were not able to detect the motion of the Earth relative to the aether (this is a null result)

  3. Light waves are different to sound waves. The speed of sound in air at 20 degrees C is 343m/s. Imagine that you move towards a source of sound at 20 m/s. What is the speed of the sound waves relative to you? [363 m/s]
  4. The Michelson-Morley experiment found that the light waves in their interferometer always arrived in phase. Incorrect. The rays of light produced an interference pattern after travelling on perpendicular paths. This pattern did not change when the apparatus was rotated through 90 degrees. This is called no fringe shift.
  5. The first determination of the speed of light was made by the Dutch physicist Christian Huygens in 1677 using astronomical measurements made by Olaus Roemer. The value obtained was 2.3x108 m/s. The French physicist Hippolyte Fizeau using an Earth based method determined the speed of light as 3.1x108 m/s in 1849.
To Tom...for always and in all ways
— Elizabeth, Catherine and Stephen


Damping of Forced Vibrations

In the May 2015 TZ1 IB Physics Paper 1 SL and HL there was a question (13SL,10HL) on the effect of damping on an oscillating system experiencing a driving force of variable frequency. The IB Examination Report states that "as damping is increased and friction is introduced into the system so the time per oscillation will increase, answer is B". This may not be intuitively obvious so a mathematical route to the solution may be helpful.

Let the frequency of vibration of the system when no damping occurs (usually just called the natural frequency) be F. The frequency of the driving force that acts on the system is f. The amplitude of the forced oscillations (this is the greatest displacement of the system from its equilibrium position) caused by the action of the driving force is A. Damping means that a resistive force is acting on the system as it vibrates causing its energy to decrease.

  1. Driving force with no damping. When damping is not present a huge vibration known as resonance ocurs when the frequency of the disturbing force equals the natural frequency of vibration. As the amplitude is huge we can predict that the amplitude of oscillation must be inversely proportional to the difference in the frequencies. When f - F approaches zero A approaches infinity. A mathematical solution of the differential equation describing the system without damping gives A = 1/(f2-F2). How can a catastrophic vibration be avoided when f = F? Including a damping term in the equations removes some energy from the system allowing it to be unavailable to participate in a large vibration.

  2. Driving force with damping. When a damping term is present the differential equation describing the system contains an additional term 2kv, where k is the damping coefficient and v is the velocity of the mass. The solution for A with damping is A = 1/√((f2-F2)2+ 4k2f2 ). Notice the additional term in the denominator. When f = F we have A = 1/(4k2f2) giving a finite amount of vibration when f = F. Catastrophe is avoided! Let us examine the equation

    A = 1/√( (f2-F2)2+ 4k2f2 )

If we plot A versus f we obtain the graph shown on the 2015 examination paper. By differentiating A with respect to f we find that A has a maximum value of A0 when f has the value f0

f0 = √( F2-2k2 )

A0 =1/( 2k √(F2-k2) )

To answer the question, as k increases A0 decreases and f0 decreases so alternative B is the correct answer.



Velocity-Time Graph

Question 16 in the 2016 HSC Mathematics examination involved calculating the distance travelled by a particle given its velocity as a function of time. The velocity during the first second of the motion was negative. This trapped many students. To find the total distance travelled we must add up the absolute values of all of the areas under the v-t graph. Be careful! If you have done it correctly the answer is 10-4ln2. If you obtain 14-12ln2 this is the change in displacement or the final position of the particle measured from the starting point; this is the length of the arrow from the starting point to the finishing point and is not the distance travelled which is the total amount of ground covered.


Question 5 in the 2003 HSC Physics examination was a multiple choice question on time dilation and length contraction. Unfortunately, no correct answer was given as an alternative. Students doing revision often ask about this question. As the mark for the question was apparently not included in the final mark it could probably be ignored. However, an answer involves taking into account the travel time of the light coming from the Earth as the question says "when seen from the astronaut's spaceship"...seen implying making an observation using light .  From the point of view of the astronaut in the spaceship the Earth is moving away at 0.8c. The time for the journey in the reference frame of the spaceship is 10 years. The distance of the journey in the reference frame of the spaceship is 8 light years and so a ray of light would take a time interval of 2 years in the spaceships reference frame to reach the spaceship. To determine the corresponding time interval shown by the clock on the Earth we solve the time dilation equation for t0 putting tv as 2 and v as 0.8c. This is because the astronaut considers the Earth to be moving away carrying its clock with it. This works out to be 1.2 years.


Simple Pendulum

The simple pendulum is one of the oldest Physics demonstrations and examination questions. A simple pendulum consists of a mass tied to one end of a string, the other end of which is fixed, and the mass is allowed to swing freely in a vertical plane. The important physical concept involved is energy. At any point of its motion the energy (meaning the "total" energy) of the pendulum is constant, provided frictional forces are negligible. Energy is said to be a constant of the motion. In Physics problems we always look for constants. Constants allow us to determine many properties of the motion of a system. Here is a list of some pendulum problems that students usually find difficult.

  1. Determine the magnitude of the acceleration of the mass when it is at the lowest point of its swing. Is it zero? Is it g?
  2. What is the direction of the acceleration vector of the mass at the lowest point of its swing?
  3. Determine the magnitude of the acceleration of the mass at the highest point of its swing. Is it zero?
  4. Imagine that a simple pendulum of mass m and length L is set moving so that it just reaches the vertical position over the point of support. Determine the energy of the pendulum in terms of g, L and m. Neglect frictional forces.[2.5mgL]
  5. Imagine that the mass is set moving and the string becomes slack before it reaches the vertical position. The mass then falls on a path that passes through the point of support. Determine the energy of the mass in this situation in terms of g, L and m. Neglect friction forces. [1.86603mgL]
  6. As in question 5 but now the path of the falling mass passes through the lowest point of the swing of the pendulum.[1.75mgL]
  7. As in question 5 but now the path of the falling mass passes through the horizontal through the point of support at a distance L from the point of support. [2.29904mgL]

Motors and Generators

The Motors and Generators in the NSW government syllabus is usually answered poorly in Year 12 examinations. What are the reasons for this? Firstly, magnetic fields are abstract things....we cannot see them but we can measure their effects when we do experiments. Secondly, the direction of the magnetic force vector acting on a current carrying conductor is perpendicular to both the magnetic field vector and the current vector and this presents challenges in thinking. Finally, students' exam responses sometimes become confused due to a lack of understanding of the basic terms used in this topic. Here is a list of some of the basic facts in this topic.

  1. Magnetic field and magnetic force are not the same thing.
  2. Current is the rate of flow of charge through a conductor.
  3. Current is measured in ampere (A). Charge is measured in coulomb (C)
  4. The potential difference between two points is the work done in moving a +1 C charge between the points.
  5. Potential difference is measured in volts (V).
  6. Power is the rate at which work is done.
  7. Work is measured in joules (J). Power is measured in watts (W).
  8. Current direction is the opposite to the dirction of electron flow.
  9. A current carrying conductor experiences a magnetic force when it is placed in a magnetic field.

  10. When a conductor moves through a magnetic field a potential difference is induced across the conductor.

  11. When a current carrying conductor is placed in an external magnetic field the interaction of the external magnetic field and the magnetic field of the conductor does not exert a force on the wire.