HSC Physics Projectiles

A tutorial sheet of harder questions on projectiles is given below. Unless otherwise indicated, neglect air resistance and take g = 9.8 ms ^-2 .

1. A ball is thrown at 65 m/s at 32° to the horizontal. At what height does it strike a vertical wall 53 m from the point of projection? [28.6m]
2. A stone is projected at 24 m/s and strikes a wall 37 m from the point of projection at a height of 15 m above the level of projection. What are the angles of projection to the horizontal? [47.8°,64.3°]
3. A stone is thrown at 47 m/s at 35° above the horizontal from the edge of a cliff. The stone strikes the sea at an angle of 14° below the horizontal. What is the height of the cliff? [32.4m]
4. A projectile is thrown at 13° below the horizontal from the edge of a cliff. It hits the sea at 135 m/s at an angle of 23° below the horizontal. What is the speed of projection? [127.5m/s]
5. A projectile is thrown from a cliff and strikes the sea 56 m from the foot of the cliff at 97 m/s at 49° below the horizontal. What is the speed of projection? [90.7m/s]
6. If a projectile strikes the sea at 140 m/s at 35° below the horizontal after being in flight for 12.0 s, what is the angle at which it was projected? [+18.0°]
7. A projectile strikes the sea 65.0 m from the base of a cliff of height 127 m after being projected at 92.0 m/s. What is the angle of projection to the horizontal? [-60.9°]
8. When a projectile lands below its initial level the maximum horizontal range is obtained at an angle of projection less than 45°. In shotput the shot leaves the hand at a height h above the ground at a speed u. Show that the angle of projection above the horizontal for maximum range is given by tan𝜽=1/(√(1+2gh/v²)).
9. A projectile is thrown at an angle of 45° to the horizontal. Sketch, on the same axes, the path of the projectile when (i) air resistance is neglected, (ii) air resistance is included.
10. A horizontal tunnel has a height of 3.00 m. A ball is thrown inside the tunnel with an initial speed of 18.0 m/s. What is the greatest horizontal distance the ball can travel before it bounces for the first time?[25.5m]

IB Physics Electric and Magnetic Fields

A tutorial sheet on electric and magnetic fields follows.

1. A charge +Q is at rest in the laboratory. Show the electric field around the charge in the laboratory reference frame.
2. A charge +Q moves to the right at a constant velocity v relative to the laboratory. Draw the electric field of the charge (i) in the reference frame of the charge, (ii) in the laboratory reference frame.
3. Two charges, +Q and +Q, both move to the right at a constant velocity v relative to the laboratory on parallel paths. In the reference frame of the charges, the line joining the charges is perpendicular to the velocity of the charges and has length d. Determine the magnitude of the force between the charges in (i) the reference frame of the charges, (ii) the laboratory reference frame.
4. A current I flows in the same direction in each of two long parallel wires. Determine the force between the wires in (i) the laboratory reference frame, (ii) a refernce frame moving parallel to the wires at the speed of the charges.
5. An electric field exists in the laboratory reference frame S. A reference frame S' moves at a constant velocity relative to the laboratory frame. (i) is an electric field present in s' ? (ii) is a magnetic field present in S' ?
6. A magnetic field exists in the laboratory reference frame S. A reference frame S' moves at a constant velocity relative to the laboratory frame. (i) is an electric field present in S' ? (ii) is a magnetic field present in S' ?

HSC Physics Exam 2018

Here are some final study notes for the HSC Physics examination on Thursday 1st November 2018. This list will be updated during the time up to the exam.

Space

1. Weight and gravitational force are the same.
2. Work done is the change in gravitational potential energy.
3. Work done is the area under the gravitational force versus distance graph.
4. Gravitational force is the negative gradient of the gravitational potential energy versus distance graph.
5. "g-force" is not a force. The net force that accelerates an astronaut upwards is the force of the seat pushing upwards minus the weight of the astronaut pulling downwards. g-force is the ratio of the seat force to the weight force.
6. A train is moving to the east and slowing down with deceleration g. A person in the train drops a ball. Relative to the person in the train the ball moves with a vertical acceleration component g and a horizontal acceleration component g and appears to fall forward in a straight line at 45° below the horizontal.
7. The escape speed from a point in a gravitational field is the speed with which a mass is projected so that its total energy is zero.
8. An object is said to be weightless when it is in a reference frame that is moving at the acceleration due to gravity.
9. Time dilation is when the time interval measured on a moving clock is less than the time interval measured on a clock at rest.

Motors and Generators

1. The torque on a coil carrying a current is maximum when it is parallel to the magnetic field.
2. The torque acting on one side of a square coil carrying a current in a magnetic field is one half of the total torque acting on the coil.
3. When a conductor moves relative to a uniform magnetic field an emf is induced in the conductor. If the emf allows a current to flow a force opposing the change is exerted by the magnetic field on the current.
4. When a conductor moves relative to a uniform electric field no emf is induced in the conductor.
5. In induction effects, the external magnetic field exerts a force on the induced current that opposes the change.
6. The presence of the iron core in a transformer allows the primary coil to produce a stronger magnetic field than with an air core. The iron core carries the magnetic flux from the primary coil through the secondary coil.

From Ideas to Implementation

1. The electric force acting on an electron in a uniform electric field is in the opposite direction to the field lines.
2. The magnetic force acting on a moving charge is perpendicular to both the velocity vector and the magnetic field direction.
3. For a constant intensity of light, the number of electrons released per second in the photoelectric effect decreases as the frequency increases.
4. For a constant frequency of light, the number of electrons released per second increases as the intensity of the light increases.
5. The Planck radiation curve has a peak since relatively few atoms in the wall of a hot object are vibrating at high frequencies (each sending out a high energy photon) and many are vibrating at lower frequencies (each sending out a low energy photon).
6. In the photovoltaic effect (in a solar cell) an electron in the valence band of the p-type semiconductor absorbs a photon (whose energy is greater than the band gap) creating a hole in the valence band and an electron in the conduction band. An electric field exists across the p-n junction and this pulls electrons to the n side where they can flow out of the cell if it is connected to a load resistor.

Quanta to Quarks

1. The scattering of a small number of alpha particles through a large angle by a thin gold foil is experimantal evidence for a small positively charged nucleus with most of the volume of the atom empty space.
2. The line spectrum of hydrogen is evidence for quantised energy levels in the hydrogen atom.
3. Chadwick collided neutrons with hydrogen and nitrogen atoms and measured the speed of each target atom after collision. The mass of the neutron was determined by applying the laws of conservation of momentum and kinetic energy to the elastic collisions.
4. Binding energy is the energy released when protons and neutrons combine to form a nucleus. Energy is released in nuclear fission because the total binding energy after reaction is greater than the total binding energy before reaction.
5. "mass and energy are both but different manifestations of the same thing", Einstein quote.
6. The anti-neutrino and electron given off in beta decay of a neutron share the released energy and momentum. In this process a down quark in a neutron is converted to an up quark by the release of a W minus boson which decays into an electron and an anti-neutrino. This decay happens as the nucleus is unstable due to it having too many neutrons for the number of protons present.

IB Physics Longitudinal Waves

A tutorial sheet of  longitudinal wave questions is given below.

1. A longitudinal progressive wave moving from left to right has a frequency f and wavelength λ. Two particles, P and Q, have equilibrium positions one-half a wavelength apart. At a certain instant P is at rest and is displaced to the left of its equilibrium position.(a) What is the amplitude of oscillation of P? (b) What is the displacement of Q from its equilibrium position?
2. Do we have nodes in longitudinal progressive waves?
3. In a longitudinal standing wave at which points in the pattern is the pressure greatest?
4. In a longitudinal standing wave at which points in the pattern is the density greatest?
5. In a longitudinal standing wave do all particles have the same frequency of vibration?
6. In a longitudinal standing wave are all of the particles vibrating in phase?
7. In a longitudinal standing wave the pressure mimima (rarefactions) are positions where the particles have zero displacement from their equilibrium position. Why is this?
8. Are the pressure maxima (compressions) at a position of zero particle displacement?
9. A closed pipe of length 1.5m is sounding its third harmonic. If the maximum possible displacement of a particle in the pipe from its equilibrium position is a what is the maximum displacement of a particle 0.25 m from the closed end of the tube? The speed of sound is 343 m/s and neglect the end correction.
10. Where would you hear a louder sound, at the anti-node or at the node of displacement of a standing wave?

HSC Physics Quanta to Quarks

With the old Quanta to Quarks elective being examined for the last time this November a list of true-false questions on concepts that are often misunderstood is given below. This list will be updated during the next six weeks.

Rutherford Model of the Atom

1. Rutherford's model of the atom has a central charge concentration made of protons and neutrons.
2. The alpha particles that bounce back from the gold foil hit the nuclei of the atoms in the foil.
3. Rutherford's model did not have electrons orbiting the nucleus in rings
4. In Rutherford scattering the number of alpha partices scattered through 60 degrees is one-half the number scattered through 30 degrees.
5. If the thickness of the gold foil is doubled the number of alpha particles scattered through each angle is halved.
6. In the Geiger and Marsden 1910 scattering experiment the number of alpha particles scattered through an angle greater than 90 degrees was 1 in 800.

Radioactivity

1. Alpha particles released in the decay of Ra-226 have different kinetic energies.
2. Beta particles given off in the decay of Sr-90 have the same kinetic energies.
3. Gamma rays are released when an electron makes a transition to a lower energy level in Co-60.
4. Gamma rays can be detected using a cloud chamber.
5. Alpha particle tracks in a cloud chamber are thicker and longer than those of beta particles.
6. In beta minus decay an electron is ejected from the nucleus.
7. Half-life is the time for exactly one half of the original number of nuclei to decay.
8. Technetium-99m is a radioisotope of half-life 6 h that emits gamma radiation and is used as a tracer in nuclear medicine.

Hydrogen Spectrum

1. The line spectrum of hydrogen is evidence for quantised energy levels in the hydrogen atom.
2. The longest wavelength in the Balmer series for hydrogen is 656.1 nm.
3. The shortest wavelength in the Balmer series for hydrogen is 364.5 nm.
4. The wavelengths in the Balmer series become closer together when placed in order from longest to shortest.
5. The four longest wavelengths in the Balmer series can be seen by the human eye.
6. The energy required to remove an electron from the ground state of the hydrogen atom is 13.6 eV.
7. The energy of the photon released when an electron makes a transition from n _i =5 to n _f =3 is 1.0 eV.
8. The shortest wavelength in a certain spectral series for hydrogen is 2.28 μm. The longest wavelength in this series is 7.46 μm.

Modifications of the Bohr Model of the Atom

1. The Bohr postulates can be applied to an atom with more than one electron.
2. The energy required to remove the electron from the ground state of a helium atom with one electron only is 54.4 eV.
3. The difference in intensity of spectral lines is explained using additional quantum numbers to n. This predicts extra states for the electron to exist in. This allowed the development of selection rules and the calculation of transition probabilites.
4. The state of the electron in the hydrogen atom is now described by 4 quantum numbers. These are n (1,2,3..), l (0,1,2,..n-1), m (-l, -2,-1,0,1,2,...l) and s (-1/2 or 1/2).
5. The Zeeman effect in hydrogen is the splitting of spectral lines that occurs when a magnetic field is applied to the gas. The magnetic field interacts with the orbiting electron creating extra energy levels allowing more electron transitions.In the Balmer series, this creates 2 extra spectral lines equally spaced on either side of the spectral line observed with no magnetic field.

Neutrons

1. When beryllium is bombarded with alpha particles a highly penetrating radiation is given off that can eject protons with considerable velocities from matter containing hydrogen.
2. Neutron scattering is a non-destructive technique to probe materials such as turbine blades for defects as neutrons have no charge and have a wavelength comparable to the spacing between atoms and so are diffracted producing an interference pattern from which the arrangement of atoms can be determined.

Heisenberg

1. The Heisenberg uncertainty principle limits us measuring the exact position of an electron.
2. Matrix mechanics uses matrices to represent observable quantities and the eigenvalues of the matrix are the observable values.
3. The uncertainty principle is a consequence of the wave nature of an electron.

Pauli

1. Pauli proposed in 1930 the existence of an uncharged particle of very small mass that carried energy and momentum to explain the continuous spectrum of beta decay. This was later called the neutrino.
2. The Pauli exclusion principle states that no two electrons in an atom can have the same set of four quantum numbers.

Fermi

1. Fermi found that slower moving neutrons could produce more radioactivity in silver than faster moving neutrons. He deduced that slower moving neutrons, produced by collisions in paraffin wax, were more easily captured than faster moving neutrons.
2. Fermi was in charge of the group that carried out the first sustained controlled fission reaction of U-235 using graphite blocks as a moderator and cadmium control rods on December 2 1942.

Particle Accelerators

1. The drift tubes in a linear accelerator increase in length to allow allow an alternating voltage of constant frequency to be be applied across each tube so that the speed of the beam increases.
2. The LHC uses superconducting magnets as these produce very strong magnetic fields using low currents.
3. A cyclotron uses magnetic fields to increase the speed of the charges.
4. A synchrotron uses a time varying magnetic field to allow for the increase in relativistic mass of a charge as it travels faster so that it can cross the dees at regular time intervals.

Standard Model

1. The mediator of the strong nuclear force is a gluon.
2. In beta decay the quark composition of the particles does not change.
3. The strong nuclear force holds protons and neutrons together.
4. The strong nuclear force holds quarks together.

HSC Physics Ideas to Implementation

With the old Ideas to Implementation topic being examined for the last time this November a list of true-false questions on concepts that are often misunderstood is given below. This list will be updated during the year.

Cathode Rays

1. A paddle wheel spins showing that cathode rays have momentum.
2. A paddle wheel will spin if the pressure in the tube is zero.
3. Cathode rays are not emitted when positive ions in a discharge tube impact on the cathode.
4. Cathode rays cause glass to phosphoresce.
5. Heinrich Hertz found that cathode rays could not travel through a metal foil.
6. Heinrich Hertz observed that cathode rays were deflected by an electric field.
7. When the pressure in a gas discharge tube is reduced the order of formation of structures in the tube is Faraday dark space, positive column, striated positive column, Crookes dark space, negative glow.
8. Dark spaces in a discharge tube are caused by destructive interference.
9. Cathode rays have their greatest speed in the bright areas.

Electric and Magnetic Fields

1. In J J Thomson's original experiment he used perpendicular electric and magnetic fields to give equal magnitude forces on a cathode ray causing them to move in a straight line.

Blackbody Radiation Curve

1. An example of a blackbody is a piece of iron painted black.
2. In the blackbody spectrum there are not many photons released at low frequencies.
3. In the blackbody spectrum there are many photons released at high frequencies.

Photoelectric Effect

1. The frequency of light is the number of photons passing a point in one second.
2. If the frequency of the light increases there are more photons passing a point in one second.
3. If the frequency of the light increases the intensity of the light remains constant.
4. The photoelectric current does not change if the intensity of the light is kept constant and the frequency is increased.
5. Heinrich Hertz found that when ultraviolet light was directed on a spark gap a spark was not produced when the width of the gap was increased.
6. Photoelectrons ejected by exposure to bright light have a greater maximum kinetic energy than those ejected by dimmer light of the same frequency.

Conduction in Metals

1. The crystal lattice is composed of positively charged ions. Conduction electrons are attracted to the lattice ions and this causes resistance in a metal.
2. Resistance in a copper wire is due to collisions between the conduction electrons and the stationary copper atoms in the wire.

Band Theory

1. The valence band in an insulator is not full.
2. Intrinsic silicon has no electrons in the conduction band at room temperature.
3. Conduction in intrinsic silicon is due to electrons moving in the valence band.

Bragg Experiment

1. The x-ray diffraction pattern produced by a crystal is a series of alternating bright and dark fringes.

Superconductors

1. Magnetic fields cannot pass through all superconductors.

IB Physics Data Booklet

Here are notes to assist students in using the IB Physics Data Booklet. These notes will be added to and arranged in syllabus order during the year as other topics are taught in schools.

Topic 10 Fields

1. Electrostatic potential due to a single point charge, . Enter the sign of the charge when substituting for q.
2. Electrostatic potential energy of two point charges, . Enter the sign of each charge when substituting for q. Negative potential energy means the charges attract and positive work must be done to separate the system to a state where the charges do not influence each other.
3. Electric field strength due to a single point charge, . Enter the sign of the source charge when substituting for q. A negative field value means towards the source charge, a positive value means away.

HSC Physics Motors and Generators

With the old Motors and Generators topic being examined for the last time this November a list of true-false questions on concepts that are often misunderstood is given below. This list will be updated during the year.

DC Motor

1. A common answer is "a DC motor converts electrical energy into kinetic energy". This means that the heat energy released by the current flowing in the coils is equal to the kinetic energy gained by the coils.
2. A 12 V battery has zero internal resistance. It is connected to a coil of resistance 4Ω that can spin freely in a magnetic field. In one second the coil gains 36 J of kinetic energy.
3. The back emf in a motor increases when the speed of the coils decreases.

AC Generator

1. A common answer is "an AC generator converts kinetic energy into electrical energy". This means that the kinetic energy of the coils is transformed into the heat energy given off by the current flowing in the load resistor.
2. The work done by an external force in turning the handle of an AC generator in one second is 40 J. If there is no friction in the axle as the coil turns the potential difference across the generator terminals is 40 V.
3. The kinetic energy of the coils of a generator is doubled. The size of the induced emf is doubled.

Eddy Currents

1. The induced eddy currents in a spinning metal disk in a uniform magnetic field experience a magnetic force that slows down the disk.
2. A metal disk is spinning in a uniform magnetic field with all of its area in the field. The plane of the disk is perpendicular to the field lines. No eddy currents are induced in the disc.
3. A copper disk is spinning clockwise. The north pole of a magnet is held above the disc. The induced eddy currents circulate clockwise in the disc.
4. A copper disc is at rest and can spin on a smooth axle. The north pole of a bar magnet is moved clockwise over the disc. The disc moves counterclockwise.

AC Induction Motor

1. In an AC induction motor a rotating magnetic field passes through the squirrel cage. The squirrel cage turns because it is repelled by the increasing magnetic flux.

Transformer

1. The iron core of a transformer increases the magnetic flux entering the secondary coil.

Electromagnetic Induction

1. A straight copper wire is moving with its length and velocity vector both perpendicular to a uniform electric field. An induced emf occurs in the wire.
2. When a conductor moves relative to a magnetic field with its velocity vector parallel to the magnetic field vector an emf is induced in the conductor.

3. When a reference frame moves relative to a magnetic field there is no electric field in the reference frame.

4. When a conductor moves through a magnetic field a current is induced in the conductor that produces a magnetic field that exerts a force on the conductor.

5. Imagine a rapidly flowing salt water river flowing from west to east through the Earth's magnetic field. A voltmeter is placed on a bridge over the river. One terminal of the voltmeter is connected to a wire placed in the water at the north bank and the terminal is connected to a wire placed in the water at the south bank. The voltmeter gives zero reading.

HSC Physics Two Dimensional Collisions

A tutorial sheet of two dimensional collision problems is given below.

1. A particle A of mass m is at rest on a smooth horizontal surface. It is struck off centre by a moving particle B of mass M. The magnitude of the change in momentum of B due to the collision is ∆p. What is the magnitude of the change in momentum of A?
2. A particle of mass m has a momentum vector p to the north. An identical particle has a momentum vector of 2p to the east. (a) What is the magnitude of the total momentum of this system? (b) The particles collide and join together. What is the kinetic energy of the combined mass after collision?
3. A ball of mass m moving at a velocity u to the east strikes an identical ball that is at rest. After collision one ball moves to the north-east at a speed u/2. What is the speed of the second ball after collision? [0.737u]
4. Two objects of the same mass having the same initial speed collide and join together. If the comined mass moves away at one-half their initial speed, what is the angle between the initial velocity vectors of each object? [120°]
5. Two particles of equal mass undergo a glancing perfectly elastic collision. If one of the particles was initially at rest, determine the angle between the velocity vectors after collision. [90°]

IB Physics Low Speed Relativity?

A student says in an answer "the effects of Einstein's theory of special relativity are only noticeable at speeds slightly less than the speed of light". Is this correct? Is there a situation where the effects of special relativity can be measured at very low speeds such as 1 cm/s? Yes. What is it?

IB HSC Physics Doppler Effect for Sound

A tutorial sheet of  Doppler effect questions for sound is given below.

1. The speed of sound in still air is v. A train blowing its whistle is moving to the east at a speed v_s. What is the speed of sound at a point (a) east of the train, (b) north of the train, (c) west of the train, (d) south of the train.
2. When a source of sound waves moves towards you do you measure an increase or decrease in the speed of the waves?
3. When the moving source emitting sound waves is directly opposite the observer is there an observed frequency shift in the sound? [no]
4. A train sounding its whistle moves to the east at a speed v_s. An observer moves at a velocity v_o towards the train. Is the observed frequency the same as the case when the observer is at rest and the train is approaching at a speed v_s+v_o?
5. Draw the wave pattern when (a) v_s < v, (b) v_s = v and (c) v_s > v. In the last case show the bow wave.
6. A car traveling at 10 m/s sounds its horn, which has a frequency of 500 Hz, and this is heard in another car which is travelling behind the first car in the same direction at 20 m/s. The sound can also be heard in the second car by reflection from a bridge. If the speed of sound in air is 340 m/s what frequencies will the driver of the second car hear? [514 Hz,545 Hz]
7. An observer in a mountain town hears a train whistle and 3.0 s later hears the start of the echo from a cliff. The echo's frequency is 0.90 that of the sound heard directly.(a) how far is the train from the cliff? (b) how fast and in what direction is the train moving? [510 m, 17.9 m/s towards observer, train is between cliff and the observer]
8. A transmitter sends out waves of frequency f and speed v.A target moves towards the transmitter at a speed u. Show that the frequency of the reflected waves received back at the transmitter is f(v+u)/(v-u). If u is much smaller than v show that this expression becomes f(1+2u/v).

HSC Physics Formulae Sheet

Here are some notes to assist students in using  the new HSC Physics Formulae Sheet that will be used in HSC examinations from 2019. These notes will be updated during 2018 and 2019 as the topics are taught in schools.

1. The weight (F) of an object is given by F=mg, where m is mass and g is acceleration due to gravity.
2. The force of static friction (F) between two surfaces is given by F≤μ_sN, where μ_s is the coefficient of static friction and N is the normal reaction force between the two surfaces.
3. Linear momentum (p) is given by p = mv, where m is mass and v is velocity.
4. Linear momentum is conserved in all collisions or explosions. This means that for a system of two masses
5. Kinetic energy is only conserved in elastic collisions. This means that for a system of two masses
6. The Doppler effect equation for sound waves is , where f^' is the frequency measured by the observer, f is the frequency of the sound waves emitted by the source, v is the speed of sound and v_o and v_s are the velocities of the observer and source respectively. Note: Draw the arrow from the observer to the source. This is the positive direction for choosing the signs of the velocity vectors, v_o and v_s
7. The heat conduction equation is where the negative sign indicates that the heat flow ∆Q is from the high temperature end to the lower temperature end and the change in temperature ∆T is the final temperature minus the initial temperature. The thermal conductivity of the material is k, the cross sectional area that the heat flows through in a time ∆t is A and ∆x is the distance between the end points.

Year 11 Physics Momentum and Kinetic Energy

A question asked by students in Year 11 Physics  is "what is the difference between momentum and kinetic energy?" Moving objects have both momentum and kinetic energy but each quantity plays a different role in Physics. A good description of why we need both momentum and kinetic energy is given by Serway and Jewett in Physics for Scientists and Engineers (eighth edition page 236)......There are clear differences between kinetic energy and momentum. First, kinetic energy is a scalar and momentum is a vector. Consider a system of two equal masses heading towards each other on a line with equal speeds. There is kinetic energy associated with this system because members of the system are moving. Because of the vector nature of momentum however, the momentum of this system is zero. A second major difference is  that kinetic energy can transform to other types of energy, such as potential energy or internal energy. There is only one type of linear momentum, so we see no such transformations when using a momentum approach to a problem...

Momentum can be thought of as the tendency of an object to keep moving in a straight line at the same speed. Kinetic energy is  the work done (energy provided) by an external force in moving the object from rest to its final speed.

From a mathematical perspective, in classical physics momentum is defined as mass multiplied by velocity, p=mv and kinetic energy is given by E_k=1/2mv². Notice that If we differentiate 1/2mv² with respect to v we get mv which is of course the momentum. This generalisation is one of the first steps in the long road to the development of quantum mechanics. A tutorial sheet on momentum and kinetic energy follows.

1. Express E_k in terms of p and m.
2. Two objects P and Q, have masses in the ratio of 2:1 respectively. If each has the same momentum which has the greater kinetic energy?
3. Two cars are moving along a road. The mass of one car is twice that of the other but it is moving at half the speed of the smaller car. What is the ratio of the kinetic energy of the larger car to that of the smaller car?
4. Two objects A and B are in motion. The kinetic energy of A is one quarter that of B and the momentum of B is one half that of A. What is the ratio of the speed of A to the speed of B?
5. A trolley of mass 452g is moving in a straight line on a smooth horizontal laboratory bench. A block of plasticine of mass 146g is initially at rest. Determine the change in kinetic energy of the system when (i) the block is on the bench and the trolley collides with and sticks to the block (ii) the block is dumped on the trolley from a small height as the trolley passes underneath. Describe what has happened in each case to the missing kinetic energy.
6. A large mass M is at rest on a smooth horizontal table. A smaller mass m moving at a velocity u collides with the larger mass. If the collision is perfectly elastic determine the velocity of the smaller mass after the collision.
7. In the previous question initially the larger mass M is moving at a velocity U and the smaller mass m is at rest. Determine the velocity of m after the collision.
8. A trolley of mass M contains a mass m of sand. The loaded trolley moves at a velocity U along a smooth horizontal laboratory bench. The sand starts to leak from the trolley at a constant rate R. Determine the velocity of the trolley when one half of the sand has leaked out.
9. *Three perfectly elastic spheres of masses m₁,m₂ and m₃ lie in that order and not in contact in a smooth horizontal groove. If m₁ is projected towards m₂ with velocity U find the velocities of each sphere after two impacts have occurred and show that there will not be a third if m₂(m₁+m₂+m₃)>3m₁m₃

HSC Physics Space

With the old Space topic being examined for the last time this November a list of true-false questions on concepts that are often misunderstood is given below. This list will be updated during the year.

Gravity

1. A satellite has a greater gravitational potential energy than a grain of dust in the same circular orbit about the Earth.
2. Gravitational potential energy is the energy needed to bring masses together from a state where they are not influencing each other.
3. A gravitational sling-shot of a spacecraft by Jupiter causes the spacecraft to leave Jupiter at a greater speed. [false, spacecraft can increase speed relative to the Sun by "taking" kinetic energy from Jupiter in an interaction in which the spacecraft has no change in kinetic energy in Jupiter's reference frame but an increase in KE in the Sun's reference frame due to Jupiter slowing down and giving KE to the spacecraft. The final spacecraft speed can be increased by almost twice the speed of Jupiter if the spacecraft moves directly towards the approaching planet whose gravitational field sweeps it around increasing its speed relative to the Sun]
4. Two large equal masses M are placed a distance r apart. A smaller mass m is placed at the midpoint of the line joining the larger masses. The gravitational potential energy of this system is zero.
5. Two large masses M are placed a distance r apart. The work done in moving a mass m from a very large distance to the midpoint of the line joining the larger masses depends on the path taken.
6. Gravitational potential energy increases as a mass moves closer to the Earth since the gravitational force increases.
7. A mass is tied to a string of length 120 cm and moves freely in a vertical circle in the Earth's gravitational field. The speed of the mass at its lowest point is 8.0 ms ^-1 . The magnitude of the acceleration of the mass at this instant is 53.3 ms ^-2 .[false,54.2 ms ^-2 ]

Projectiles

1. A projectile moving upwards has a negative acceleration and when it moves downwards its acceleration is positive.
2. A cannon is fired horizontally from a tall mountain. The projectile can strike the Earth on the hemisphere opposite to the direction of firing if its initial speed is sufficient.
3. An object is dropped from the Eiffel Tower. Neglecting air resistance the object hits the ground at a point to the east and south of its starting point. An object dropped from Centre Point Tower (neglecting air resistance) will be deflected to the west and north of its starting point.
4. A ball is thrown at initial speed U on horizontal ground. The maximum range of the ball is R. If the new initial speed is 2U the maximum range (neglecting air resistance) is 2R.

Orbits

1. The two forces acting on a satellite moving in a circular path around a planet at a constant speed with no air drag are the gravitational force and the centripetal force.
2. When atmospheric drag acts on a satellite its speed decreases.
3. Apollo 13 could re-enter the Earth's atmosphere at an angle 𝜽 to the vertical where 5.3° < 𝜽 < 7.7°.
4. A spacecraft that bounces off the atmosphere enters an orbit around the Sun.
5. A satellite is in a low Earth circular orbit. The radius of the orbit decreases. The gain in orbital kinetic energy of the satellite is equal to the loss in gravitational potential energy of the satellite.
6. A satellite in a high Earth circular orbit has a total energy E. If the satellite is placed in a circular orbit of twice the radius its total energy is 2E.
7. A satellite in a circular orbit of period 23h 56m 4s that passes over Sydney always appears directly overhead.

Relativity

1. An electron cannot move through water at a speed greater than the speed of light in water.
2. A rocket moves at a constant velocity of 0.90c relative to the Earth. The crew of the rocket play a CD that lasts for 1 hour. A person on the Earth plays an identical CD that lasts for a longer time interval than one hour.
3. A particle accelerator is 2.0 km long. A proton starts from rest and moves through the accelerator striking the end at 0.8c. The distance travelled by the proton in its own reference frame is 1.2km.
4. A certain star is 66.5 light-years away from the Earth. A spacecraft leaves the Earth and travels at a constant speed of 0.95c to the star. The time taken to travel to the star according to a clock on the spacecraft is 70 years.
5. A train is moving to the east. A ball is rolled across the smooth floor of the train initially perpendicular to the south side of the train at 1 ms ^-1 .A person in the train sees the ball move in a parabolic arc towards the east of focal length 1 m. The acceleration of the train is 0.5 ms ^-2 to the east.
6. A white hot metal rod is cooled to room temperature.Its mass does not change.
7. In Michelson and Morley's interferometer the light rays interfere destructively. This is called a null result.
8. In the aether theory the time taken by light to travel along each of the equal arms of the interferometer is the same.
9. Interference fringes are not caused by the reflections from the half silvered mirror in the Michelson-Morley experiment.

10. The result of the Michelson-Morley experiment is that the time taken by light to travel a given path depends on the direction of the light ray.

11. Simultaneous events are seen to happen at the same time instant in the same reference frame.

12. Michelson and Morley measured a change in fringe spacing when they rotated their apparatus through 90°
13. Michelson and Morley expected to measure a change in fringe spacing when they rotated their apparatus through 90°

Year 11 Physics Vectors Sheet 1

This is a sheet of harder questions on vectors.

1. A river flows at 3.0 km/h. The river is 100.0 m wide and a boat is to arrive on the opposite bank 80.0 m downstream from its starting point. What is the velocity of the boat relative to the water if the time of crossing is 5.0 minutes? [2.4km/h at 31° to the upstream bank]
2. A river 1.0 km wide flows due north at 8.0 km/h. A motor launch travels at 6.0 km/h relative to the water. A person starts from the west bank and wishes to reach the point directly opposte on the east bank. If the person can walk at 3.0 km/h find the direction in which the motor launch should head so that the person can make the journey in the minimum time.[E33°S]
3. Relative to a cyclist travelling to the west at 40km/h the wind appears to be coming from the south. On doubling their speed the wind appears to be coming from the south-west. What is the velocity of the wind?[56.6km/h NW]
4. A cyclist travelling on a straight road at 10 km/h is subject to air resistance proportional to the square of their speed. By what factor must they increase their power output to maintain their speed if a 20 km/h cross wind develops?[5^1/2]
5. An ocean liner is travelling in a straight line at a speed of 20km/h that takes it 1.0 km from a port. A boat that can travel at 12km/h is to leave the port at the last possible time and move in a straight line to meet the ocean liner. What is the distance travelled by the boat when it reaches the liner? [1.25km]

IB Physics Mass and Spring

A tutorial sheet of questions on a mass and a spring is given below.

1. Two springs each of force constant k are connected in series and held vertically. A mass M is placed on the lower end of the combination. What is the extension produced?
2. A mass M rests on a smooth horizontal surface. Identical springs of force constant k are attached to opposite sides of the mass. The other ends of the springs are held at rest. What is the period of oscillation of the mass when it is released after being displaced (a) along the line of the springs, (b) perpendicular to the line of the springs.
3. A spring of force constant k is held vertically with its upper end fixed. A mass M is placed on the lower end of the spring. The mass is then pulled down a distance A and released from rest. (a) Explain why the period of oscillation does not depend on g. (b) Does the period of oscillation does depend on A? (c) Instead of being released from rest the mass is given an initial velocity u downwards at the pulled down position. What is the period of the oscillation in this case?
4. Does a mass oscillating on a spring in a vertical plane have gravitational potential energy?
5. A light spring is hanging loosely from the ceiling. A mass is placed on the free end of the spring and released from rest. The mass moves downwards a distance of 40 cm before starting to rise again. What is the period of the simple harmonic motion?[0.90s]
6. A block of mass M is connected to a light spring of force constant k. The block is placed on a smooth inclined plane of angle of elevation 𝜽. The other end of the spring is held at rest with the spring parallel to the inclined plane. The mass is set moving in simple harmonic motion. Does the period of oscillation depend on 𝜽?
7. A block of mass M slides a distance d from rest down a smooth inclined plane making an angle 𝜽 with the horizontal. It hits a light spring of natural length L and force constant k at the bottom of the incline. Determine the amount that the spring is compressed when the block comes to rest.
8. A bungee jumper of mass M is attached to an elastic cord of unstretched length L and force constant k. If they jump from rest how far do they fall before they come to rest?

Year 11 Physics Kinematics Sheet 1

A tutorial sheet of harder questions on kinematics is given below.

1. A car travels back and forth between two towns. The speed during the forward journey is v1. If the speed during the return journey is v2, what is the average speed for the entire trip?[2v₁v₂/(v₁+v₂)]
2. A car travels back and forth between two towns. The average speed during the forward journey is 50km/h. What is the speed for the return journey if the average speed for the entire trip was 40 km/h?
3. An object moves from rest with constant acceleration for 4.0 s then with uniform velocity for 5.0s, the total distance travelled being 224 m. What was the acceleration?
4. Two airports, A and B, are 850 km apart with B due east of A. At 10 am a jet takes off from A and travels at a constant velocity of 400 km/h to the east. At 11 am an aircraft takes off from B and travels at a constant velocity of 500 km/h to west. At what time do they pass each other?
5. Two camels leave the Sphinx at times 52.5 s apart. The first moves off with a uniform acceleration of 1.30 ms^-2 which it maintains for 1.92 s. It then continues with the acquired speed. The second camel moves off with a uniform acceleration of 1.45 ms^-2 which it maintains for 2.84 s. It then continues with the acquired speed. Calculate the time taken by the second camel to overtake the first camel and the distance travelled in this time.[82.9 s, 336 m]
6. A moving trolley is observed to have the following positions at equal intervals of 1 second; 5.10, 1.60, 1.50, 4.80, 11.5 and 21.6 cm. Show that the acceleration is uniform and determine its magnitude. What is the next number in the list? [3.40 cms^-2, 35.1 cm]
7. An elevator can increase its speed with an acceleration a and slow down with a deceleration b. What is the least time that it can travel a distance d if it starts and finishes at rest?
8. A stone is dropped down a well. The sound of the splash is heard after a time interval t. What is the depth of the well if the speed of sound is vs? Give the answer in terms of g, t and vs.

HSC Physics Transformers

Most HSC students can apply the transformer equation, but often the Physics principles are misunderstood. A tutorial sheet on transformers is given below.

1. What is the role of a transformer in the transmission of electricity?
2. Define one volt.
3. Define the term emf.
4. Is voltage is the same as emf?
5. What is the role of the iron core in a transformer?
6. What is meant by a soft iron core? Why is the soft iron core laminated?
7. Can a transformer operate using DC? Sketch a graph showing the primary and secondary voltage (on different axes) when the DC voltage applied to the primary coil is switched on and then after a short time switched off.
8. A common examination response is that "the induced emf in a coil equals the rate of change of the magnetic flux through the coil". Why is this incorrect?
9. When AC enters the primary coil of a transformer in which coil is an emf induced? Primary, secondary or both?
10. Assuming that the primary coil has low resistance, is the voltage applied to the primary coil equal to the counter emf induced in the primary coil? Is a counter emf induced in the secondary coil?
11. Explain how an emf is induced in the secondary coil.
12. The transformer equation uses the symbols Vp and Vs. Since transformers use AC, in which the current varies with time, what do these symbols represent?

HSC Physics Newton's Cannon

A tutorial sheet of harder problems on Newton's cannon is given below. Neglect air resistance, the rotation of the Earth and the movement of the Earth about the Sun.

1. Define escape speed.
2. Derive the equation for escape speed in terms of G, M and r.
3. Express escape speed in terms of g, G and r.
4. Does escape speed depend on the mass of the projectile m? Explain why in words.
5. Does escape speed depend on the launch angle?
6. Calculate the value of the escape speed from the surface of the Earth.
7. A cannon on a tall mountain fires a projectile horizontally at a small speed. Explain why the projectile falls to the Earth.
8. A projectile is fired from the surface of the Earth at 5 kms^-1 at 45° to the horizontal. Does this projectile go into orbit around the Earth?
9. The escape speed from the surface of a planet of radius R is V. A projectile is thrown vertically upwards at a speed V/2. Determine the maximum height reached by the projectile.
10. A tall mountain has an altitude h. The radius of the Earth is R and its mass is M. A cannon fires a shell horizontally at a speed u from the top of the mountain. Find the speed with which the shell strikes the Earth.
11. *A projectile is given an initial speed of 5 km/s at 45° to the horizontal from the surface of the Earth. Find the range on the surface of the Earth and the time of flight. What launch angle gives maximum range on the surface of the Earth? Take g=9.81 m/s² and R=6378 km [3121km, 1052s, 38°, 3219km 2Rsin^-1[v²/(2gR-v²)]]
12. *In the previous question the projectile is fired from a point on the equator towards the east. Taking into account the rotation of the Earth, how are the previous answers modified? [decreases (2706km), takes longer (1135s), lower angle (33.6°), decreases (2972km)]

HSC Physics Magnetic Force

When a current flows in a conductor that is placed in a magnetic field a magnetic force arises. Does the magnetic force act on the conductor or on the current?