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. more to come

IB 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 vs. 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 vs. An observer moves at a velocity vo 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 vs+vo?
  5. Draw the wave pattern when (a) vs < v, (b) vs = v and (c) vs > 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]

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≤μsN, where μs 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 vo and vs are the velocities of the observer and source respectively. The positive direction is from the observer towards the source.
  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 Ek=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 Ek 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 Questions

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.

  1. A satellite has a greater gravitational potential energy than a grain of dust in the same circular orbit about the Earth.
  2. A projectile moving upwards has a negative acceleration and when it moves downwards its acceleration is positive.
  3. 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.
  4. When atmospheric drag acts on a satellite its speed decreases.
  5. An electron cannot move through water at a speed greater than the speed of light in water.
  6. Gravitational potential energy is the energy needed to bring masses together from a state where they are not influencing each other.
  7. 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.
  8. 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.
  9. 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.
  10. 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.
  11. 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]
  12. 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.
  13. A 200 g 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]
  14. 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.
  15. A white hot metal rod is cooled to room temperature.Its mass does not change.
  16. 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.
  17. 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.
  18. 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.
  19. In Michelson and Morley's interferometer the light rays interfere destructively. This is called a null result.
  20. Gravitational potential energy increases as a mass moves closer to the Earth.
  21. Apollo 13 could re-enter the Earth's atmosphere at an angle 𝜽 to the vertical where 5.3° < 𝜽 < 7.7°.

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?[51/2]
  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 Blackbody Radiation

The term black body radiation sometimes causes confusion in examination answers. Below is a tutorial sheet on this topic.

  1. Define the term blackbody. Is the "blackbody" the object, a cavity in the object or a small hole in the wall of the object?
  2. Define the term radiation as used in this context.
  3. Is the Sun a perfect blackbody? Is a lump of hot coal a perfect blackbody? Is the filament of a light globe a perfect blackbody? Is a hot oven a perfect blackbody?
  4. Sketch a graph showing the energy released per unit wavelength on the Y axis and wavelength on the X axis for a blackbody at a constant temperature. Is this graph the same shape as the "normal curve"? Is this graph the same shape as the distribution of particle speeds curve in an ideal gas?
  5. Sketch a graph showing the number of oscillators (vibrating atoms in the walls of a hot object) versus the energy of each oscillator at a constant temperature. This is a key difference between the quantum theory of light and the wave theory of light. The classical wave theory of light assumes that every oscillator has the same kinetic energy at a given temperature and this (incorrect) assumption leads to the ultraviolet catastrophe.
  6. Sketch a graph showing the energy released per unit frequency versus frequency for a blackbody at a constant temperature.
  7. Sketch a graph showing the peak wavelength in the black body spectrum versus the temperature of the object.
  8. What does the equation E=hf mean?
  9. Quantum theory predicts that an oscillator can only have certain particular energies. These are given by E=(n+1/2)hf where n=0,1,2,3.... Why is this result different to E=hf?
  10. *A perfect blackbody has a temperature of 5778 K. What fraction of the total energy released is contained between the wavelengths of 380 nm and 700 nm? This is the range of visible wavelengths coming from a blackbody at the same temperature as the photosphere of the Sun. [39%]
  11. In the previous question the temperature is doubled. Is the percentage of radiation emitted as visible light increased, decreased or the same? [decreased, 31%]

IB Physics Relativity

Here is part of a question on Special Relativity taken from Columbia University's Physics Qualifying Examination in 2016. It was set by renown physicist and author Brian Greene. HL students aiming for a 7 must do extra reading to broaden their knowledge of Physics. Professor Greene's books make a good start. An asteroid is on a collision course with a space station located 5000 light minutes from the Earth. The asteroid is moving away from the Earth toward the space station at a speed 3/5c along a trajectory which is a straight line connecting the Earth and the space station. To save the station, NASA launches a missile from Earth at 4/5c. When the missile is launched, NASA determines that the asteroid is 400 light-minutes from Earth. How many minutes should NASA set on a timer located on the missile so that it will explode just as it catches the asteroid? [1200 minutes]

HSC Physics Assessment Task

A common Assessment Task in HSC Physics is to release a ball bearing from rest on a track inclined at a small angle to the horizontal and measure the time taken (t) to move various distances (d). The average speed is then calculated (v=d/t) and a graph of v-t is drawn. A common mistake is to then say that the gradient of this graph is the acceleration of the ball. Why is this incorrect? How do we determine the acceleration of the ball?

HSC Physics Binding Energy

One of the most misunderstood concepts in the quanta to quarks section of the current NSW HSC Physics syllabus is binding energy. Listed below are some tutorial points on this concept. 

  1. The binding energy of a nucleus is the work that must be done on the separate nucleons to assemble them from an initial state where they do not influence each other into the final nucleus.
  2. Binding energy has a negative sign.
  3. A lone proton or neutron has no binding energy.
  4. The total energy of a nucleus is the sum of the rest energy of each component particle and the binding energy of the nucleus.
  5. Energy is released in a nuclear reaction when the product nuclei are more strongly bound (more stable) than the initial nuclei (less stable).

HSC Physics Band Theory

One of the most difficult and misunderstood concepts in the ideas to implementation section of the current NSW HSC Physics syllabus is band theory. Listed below are some tutorial points on this concept. 

  1. Bands are not the same as the orbits of electrons around a nucleus (these are called shells).
  2. Bands refer to an entire material not a particular atom.
  3. The valence band is the set of possible energy states an electron can have if it is bonded to an atom. In a full valence band conduction is not possible as there are no states available for an electron to move to (no net flow of electrons).
  4. The conduction band is the set of possible energy states that an electron can have if it is free of an atom. In a full conduction band conduction is not possible.
  5. In a conductor at room temperature there is a partial overlap of the valence and conduction bands. The valence band is full and the conduction band is partially filled. Electrons can be moved easily by an applied electric field and enter nearby unoccupied states in the conduction band. In a semiconductor at room temperature there is a small energy gap between the valence and conduction bands. The valence band has some unoccupied states and some electrons occupy states in the conduction band. An electron in the valence band can gain thermal energy and enter the conduction band creating a hole in the valence band that behaves like a positive charge carrier. In an insulator there is a large energy difference between the valence and conduction bands. The valence band is full and the conduction band is empty.