Angle Questions

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A tutorial sheet on HSC/IB Physics questions involving angles is given below.

  1. A metal bar of length 1.5 m points to the north. The bar can turn about an axis through the origin. A rope is tied to the end of the bar. Determine the torque exerted by the rope when (a) the rope pulls to the north with a force of 6.0 N, (b) the rope pulls to the east with a force of 4.0 N, (c) the rope pulls in the direction E40°S with a force of 3.0 N, (d) the rope pulls in the direction N16°W with a force of 5.0 N.
  2. A uniform magnetic field of 3.0 mT comes out of the page. A straight wire of length 30.0 cm carries a current of 600 μA in the direction N23°E. Determine the magnetic force acting on the wire.
  3. A uniform rod of length 2.0 m is placed with its upper end against a smooth vertical wall and its lower end on smooth horizontal ground. The rod's upper end initially makes an angle of 45° with the wall. The rod is released from rest. What is the angle at which the rod loses contact with the wall as its slips?
  4. A cannon can fire a projectile at 150 m/s. The cannon is situated on the horizontal ground level. The target is on a horizontal plateau 800 m above the ground and is located at a distance of 100 m from the edge of the plateau. At what angles to the horizontal can the projectile be fired if it is to hit the target? Neglect air resistance and take g=9.81 m/s2. [87.7° at 41.5m from the cliff down to 61.4° 1168 m from the cliff]
  5. In the previous question the cannon can now fire at any speed. What is the least speed of firing if the target is to be hit, what is the angle of firing to the horizontal and the distance from the cliff where this occurs? [132 m/s, 72.4°, 465 m]
  6. A wall is 20 m tall and 10 m wide. A ball is thrown from ground level. What is the least speed of projection of the ball if it is to pass over the wall? What are the angle of projection to the horizontal and the distance of the point of projection from the wall? [22.7m/s, 63.8°, 15.9 m]
  7. A wall has the form of a semi-circle of radius 10 m. What is the least speed at which a ball can be thrown from ground level and pass over the wall? What is the angle of projection and what is the distance from the wall at which it is thrown? [16.7m/s,57.8°,12.9m ]
  8. A wall has the shape of a circle of radius 5.0 m. What is the least speed of a particle if it is to pass over the wall from ground level? [15.7 m/s, 63.7°, 10.1 m]

HSC Potential Difference

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A tutorial sheet on the concept of potential difference is given below.

  1. Two wires, one of resistance R and the other of resistance 2R are connected in parallel to a 12 V battery of zero internal resistance. Compare the potential differences across each wire.
  2. Two wires are made of the same material and have the same diameter. One wire has a length L and the other wire a length 2L. Thw wires are connected in series with a 12 V battery. (a) Which wire has a greater potential difference across its ends? (b) Which wire releases the most heat energy in one second?

IB Physics Internal Resistance

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A sheet on topic 6.3 is given below

  1. A battery of emf 6.0 V is connected to an 8 Ω resistor causing a current of 0.5 A to flow. What current flows when a 4 Ω is placed in the circuit?
  2. A battery of emf 12 V has an internal resistance of 2 Ω. The battery is connected to a 6 Ω load resistor. (a) What is the power of the battery? (b) What is the power of the load resistor? [13.5W, 13.5W]
  3. A battery of emf 12 V has an internal resistance r. When the battery is connected to a 8 Ω resistor the power of the 8 Ω is 11.5 W. What is the value of r? [2 Ω]
  4. Is the power of the load resistor always equal to the power of the battery?
  5. Is the power of the internal resistance always equal to the power of the load resistor?

Mathematical Tripos Dynamics and Relativity 2019

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Listed below are my answers to the MT Dynamics and Relativity questions in Paper 4 of Part 1A held in June 2019. Answers to MT D&R questions will be added each October to correspond to the start of Michaelmas Term.

  1. Question 3A. uln2
  2. Question 4A. t = √ (m/(ɣg) ) e-2ɣh/m tanh-1( √(1-e-2ɣh/m) )
  3. Question 9A. A=-1/4, B=3/4
  4. Question 10A. (a) x = 1-r+rcos(⍵t), y = rsin(⍵t), z = vt, where r = mv/( qB √ (1-2v2/c2 ) ) and ⍵=v/r.
  5. Question 10A. (b) (i) (0,0), three saddle points also exist where the equilibrium is stable in one direction (ii) stable along x and y axes. At (0,0) ∂V/∂x=0, ∂V/∂y=0, ∂2V/∂x2>0, ∂V/∂y=0,∂2V/∂y2>0 (iii) A=35/4/(23/2√𝜋). At saddle point ⍵=1.389q/√(m𝜀) taking a=1

IB Physics Series and Parallel Resistors

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A tutorial sheet on series and parallel resistors is given below.

  1. A 2 Ω and a 4 Ω are place in series with a battery. Which resistor has the greater power?
  2. A 2 Ω and a 4 Ω are placed in parallel across a battery. Which resistor has the greater power?
  3. A 2 Ω and a 4 Ω are connected in parallel. In series with this parallel group is a 1 Ω. When a battery of zero internal resistance is connected across this combination, which resistor has (a) the greatest power? and (b) the least power? [1 Ω,4 Ω]
  4. Two 5 Ω resistors are placed in parallel. In series with this combination is a 10 Ω. The power of the 10 Ω is 20 W when the entire combination is connected across a battery of zero internal resistance. What is the power of the 10 Ω when one of the 5 Ω resistors is removed? [13.9 W]

IB Physics MeV in Relativity Option

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A tutorial sheet of IB questions on units is given below.

  1. An electron has a momentum of 4.0 MeVc-1. What is the energy of the electron?
  2. A particle has a rest energy of 2.0 MeV. The momentum of the particle is 3.0 MeVc-1. What is the total energy of the particle?
  3. A particle has a mass of 2.0 MeVc-2. What is its momentum if its speed is 0.90c?
  4. A particle of mass 0.8MeVc-2 is accelerated from rest through a potential difference of 2.0 GeV. What are the final energy and momentum of the particle in the laboratory reference frame?
  5. A proton has a speed of 0.995c relative to the laboratory. What is the energy of this particle in the rest reference frame and the laboratory reference frame?

IB Physics Electric Current

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A tutorial sheet of electric current questions is given below.

  1. The density of copper is 8960 kgm-3. If the molar mass of copper is 63.5 g, determine the number of free electrons per cubic metre of copper if each atom provides one free electron. [8.5x1028]
  2. Determine the electron drift speed in a copper wire of diameter 2.0 mm carrying a current of 1.0 A.
  3. List some common metals that have a free electron density greater than that of copper.[aluminium, iron, magnesium, tin, lead, zinc, magnesium]
  4. What is meant by a free electron?
  5. Explain why a wire heats up when a current passes through it.
  6. A student in an answer states that "resistance in a copper wire is due to collisions between the electrons and the positively charged copper atoms". Analyse this statement.
  7. Two metal wires are made of the same material and are at the same temperature. The potential difference across each wire is the same. If the length of the second wire is one-half that of the first wire and the diameter of the first wire is two times that of the second wire in which wire does a greater current flow?

IB Coulomb's Law with Dielectrics

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A tutorial sheet of problems with dielectrics separating the charges is given below

  1. Two point charges, +2.0 nC and +2.0 nC are placed 5.0 cm apart in a vacuum. Draw the electric field around the charges and determine the electric force between the charges.
  2. The point charges in question 1 are now placed in a material of relative permittivity 4. Draw the electric field lines. Give a reason why the electric force between the charges increases/decreases/stays the same.
  3. A point charge -4.0 nC is at a height of 6.0 cm above a deep, still, freshwater lake. Draw the electric field lines in air and water. If the dielectric constant of water is 81 determine the electric force on the charge.[See p184 Electromagnetism by Lorrain and Corson, attraction, k(K-1)/(K+1)q2/(4d2), 9.75x10-6N]
  4. Two point charges +6.0 μC and -6.0 μC are placed 12.0 cm apart in a vacuum. An infinite rectangular slab of dielectric material of thickness 6.0 cm and relative permittivity 4 is placed with its surface 3.0 cm from each charge perpendicular to the line joining the charges. Draw the electric field lines and determine the electric force acting on each charge.

HSC Physics Atoms to Universe

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  1. Atoms emit discrete wavelengths of light. Explain why a heated iron bar changes colour as its temperature changes.
  2. The energy of an electron in the ground state of a hydrogen atom is -13.6 eV. (a) How can an electron have a negative energy? (b) What is the energy of an electron in the first excited state? (c) determine the value of the three longest wavelengths in the Balmer series for hydrogen.

  3. A proton moves at a constant speed of 0.90c. The proton moves once around the tube of a particle accelerator of circumference 20.0 km. (a) What are the momentum and the energy of the proton in the laboratory reference frame? (c) What is the distance travelled by the proton in its own reference frame?

  4. more to come

HSC Physics Photoelectric Effect

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A tutorial sheet of problems on the photoelectric effect follows.

  1. What factors determine the intensity of light shining on a surface?
  2. If the light shines at 30° to the surface of the metal does this change the number of photoelectrons released compared to when the light shines perpendicular to the surface?
  3. The frequency of light is increased but the intensity of the light is kept constant. Describe how this affects the rate at which electrons are released from the metal surface on which the light falls.
  4. Sketch a graph showing the maximum kinetic energy of the escaping photoelectrons versus the wavelength of the incident light.
  5. Why is the maximum kinetic energy calculated in the photoelectric effect? Do some escaping electrons have more kinetic energy than others?

IB Energy Topics

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A tutorial sheet on topic 8.1 energy sources and 8.2 thermal transfer is given below.

  1. The intensity of the Sun's radiation at the Earth's orbit is I. If the Earth's albedo is 𝛼 determine the average intensity over the surface of the entire Earth. [I(1-𝛼)/4]
  2. An Earth-like planet is discovered orbiting a distant star at an average distance of 2.7x1012m. If the power of the star is 1.3x1028W, calculate the surface temperature of the planet. Take the albedo and emissivity of the planet as 0.3 and 0.61 respectively. [163.7K]
  3. The solar constant is 1361 Wm-2. The albedo of the Earth is 0.33 and its emissivity is 0.61. Determine the surface temperature of the Earth if the albedo increases by 10% and the emissivity decreases by 10%. [292.5K]
  4. The solar constant is 1361 Wm-2 at the Earth's distance from the Sun. At what distance from the centre of the Sun is the solar constant 15 Wm-2? What planet is at this distance? [Saturn]
  5. A lake full of water has an area of 5.1x106m and a depth of 40 m. The base of the lake is 34 m above the turbine in a power station. Determine the greatest possible output power of the station if 1000 kg of water flows through it every second. [1.08x1014 W]
  6. In a nuclear power station 7.64x1019 fission reactions of U-235 occur per day. Each reaction releases 190 MeV of energy. Determine the specific energy and energy density of U-235. Assume that the sample is pure U-235 of density 19.1 gcm-3 and atomic mass 235.0439 u. [7.78x1013Jkg-1, 1.49x1018 Jm-3]
  7. In the previous question U-235 only occupies 3% by volume of the fuel rod which has a uniform density throughout. Determine the specific energy and energy density of the fuel rod.[2.33x1012,4.46x1016Jm-3]

IB Thermal Concepts

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A tutorial sheet of harder questions on sub-topic 3.1 thermal concepts is given below.

specific heat capacity of ice = 2200 J/Kg/°C, specific latent heat of fusion of ice=334000 J/kg, specific heat capacity of water=4200J/kg/°C.

  1. 25.0 g of ice is at a temperature of -10 °C.The ice is placed in 300 g of water at 20°C. What is the temperature when thermal equilibrium is reached? [11.9°C]
  2. 300.0 g of ice at 0°C is placed in 100.0 g of water at 15°C. What fraction of the ice melts?
  3. 500.0 g of ice at 0°C is placed in water at 20°C. What is the mass of the water if one half of the ice melts?

IB Physics Capacitors

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A tutorial sheet of capacitor questions starts below

  1. The distance between the parallel plates of a capacitor with an air gap is doubled, the potential difference between the plates remaining constant. Does the electric field strength between the plates change?
  2. The distance between the parallel plates of a capacitor with an air gap is doubled, the charge on each plate remaining constant. Does the electric field strength between the plates change?
  3. Does the capacitance increase, decrease or stay the same when a slab of dielectric material is placed between the plates which are connected to a battery of constant voltage?
  4. Does the capacitance increase, decrease or stay the same when a slab of dielectric material is placed between the plates on which the charge is kept constant?
  5. Why does the presence of a dielectric material between the plates change the capacitance?
  6. Does the force between the plates of a parallel plate capacitor increse, decrease or stay the same when a parallel sided dielectric slab half fills the distance between the plates, the plates being connected to a battery of constant voltage? When is the total energy of the capacitor greatest, before or after the slab is inserted? Explain the difference.
  7. A parallel plate capacitor is charged and then isolated from the supply. The plates are then moved further apart. State the changes that occur in the potential difference between the plates, the energy stored in the capacitor, the electric field strength between the plates and the capacitance.[increases,increases,constant,decreases]
  8. A parallel plate capacitor is maintained at a constant voltage. The plates are then moved further apart. State the changes that occur in the charge stored on the plates, the energy stored by the capacitor, the electric field strength between the plates and the capacitance.[decreases, decreases, decreases, decreases]

HSC Physics Interference of Waves

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A tutorial sheet on double slit interference is given below.

  1. Coherent, monochromatic light passes through a single narrow rectangular slit. Describe the intensity pattern that forms on a screen at a large distance from the slit.
  2. Coherent, monochromatic light passes through two parallel narrow rectangular slits. Describe the intensity pattern that forms on a screen at a large distance from the slits.
  3. Coherent red light of wavelength 650 nm passes through a double slit of separation 0.2 mm. Determine the distance between successive bright fringes on a screen 3.0 m from the double slit.
  4. What is the path difference when the first order maximum forms on a screen?
  5. In a double slit experiment one of the slits is covered up. Is the central maximum brighter when one of the slits is covered?
  6. Microwaves have a wavelength of 3.0 cm. A micowave detector is placed alongside the microwave source. The microwaves are aimed perpendicular at thin parallel perspex and metal sheets. Some microwaves reflect back from the perspex and all are reflected back by the metal sheet. What is the least distance between the sheets when constructive interference occurs in the reflected microwaves?

HSC Physics Polarisation

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A tutorial sheet of polarisation problems is given below

  1. When is a beam of light polarised?
  2. A beam of unpolarised light of intensity 4000 Wm-2 strikes a polarising filter. What is the transmitted intensity?
  3. Unpolarised light of intensity I passes through three polarising filters placed in a line. The polarising directions of the filters are are inclined at 45° to each other. Determine the intensity transmitted by the third filter.
  4. Polarised light of intensity I passes through three polarising filters placed in a line. The angle between the plane of polaristion of the light and the polarising direction of the first filter is 45°. If the polarising directions of the filters are inclined at 45° to each other, determine the intensity transmitted by the third filter.
  5. Light is polarised with its electric field in the horizontal plane. The light strikes two polarising filters, one behind the other. The first filter has its polaring direction at 25° to the horizontal and the second at 50° to the horizontal. What percentage of the intensity of the original light passes through the second filter?

HSC Physics Electric Field Lines

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Electric field patterns are commonly drawn incorrectly. A tutorial sheet of field line questions is given below.

  1. Equal point charges +Q and +Q are placed a distance 2d apart in a vacuum. Draw the electric field pattern around these charges. Do the electric field lines approach the perpendicular bisector to the line joining the charges? [see the cover of W J Duffin Electricity and Magnetism]
  2. Point charges +4Q and -Q are placed a distance d apart in a vacuum. Draw the electric field lines around these charges.
  3. Draw the electric field lines of an electric dipole when it is seen close up.
  4. Draw the electric field lines of an electric dipole when it is measured from a large distance (a distance much greater than the charge separation). Is the field zero at a large distance?
  5. Point charges -Q, +2Q and -Q are placed in a straight line in a vacuum. The end charges are each a distance d from the middle charge. Draw the electric field lines around this combination.
  6. A long metal cylinder of inner and outer radii a and b respectively carries a total charge +Q. Draw the electric field lines of this arrangement.
  7. A long metal cylinder of inner and outer radii a and b respectively is uncharged. The cylinder is placed in a uniform electric field that is perpendicular to the axis of the cylinder. Draw the electric field lines of this combination. What is the electric field strength inside the cylinder?

HSC Physics Electricity and Magnetism

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In the Electricity and Magnetism section of the HSC Physics Formuae Sheet the equations involving an angle 𝜽 do not all have the angle measured in the same way. A tutorial set of substitution questions is given below.

  1. A charge of +2.0 μC has a velocity of 3.0×107 ms-1 to the right of the page. The particle is in a uniform magnetic field of 1.0 mT acting out of the page. Determine the magnetic force acting on the charge.
  2. A coil of area 10 cm2 has its plane at an angle of 30° to a uniform magnetic field of 100 mT. What is the magnetic flux through the coil?
  3. A coil of cross sectional area 30 mm2 containing 100 turns carries a current of 20 mA. The axis of the coil makes an angle of 20° with a uniform magnetic field of 2.0x10-2 T. Determine the size of the torque acting on the current.
  4. A straight wire of length 52 cm carries a current of 300 μA in a uniform magnetic field of 350 mT. If the wire makes an angle of 123° with the magnetic field lines, find the size of the magnetic force acting on the current.
  5. The Earth's magnetic field vector at Sydney is 57 μT N12°36'E at 64°19' below the horizontal. At a certain instant an electron is moving in this magnetic field towards the east at a speed of 3.0x107 ms-1. Determine (a) the magnitude of the magnetic force acting on the electron at this instant (b) the direction of the magnetic force acting at this instant, and (c) the period of the motion of the electron in the uniform magnetic field.

IB Physics Static and Kinetic Friction

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A tutorial sheet on static and kinetic friction problems from subtopic 2.2 forces is given below

  1. A 3.0 kg block is at rest at rest on each of two rough inclined planes. One incline makes an angle of 37° with the horizontal, the other 53°. On which block is a greater force of static friction acting?
  2. A block of mass 2.0 kg is on a rough horizontal table. The coefficient of static friction between the block and the table is 0.4. A horizontal force of 5.0 N to the right is applied to the block. What is the force of static friction between the block and the table?
  3. A block of wood of mass 4.0 kg has a brick of mass 2.0 kg sitting on it. The block rests on a smooth horizontal surface and the block and brick are initially at rest. A constant horizontal force of 12.0 N is applied to the block. What are the speeds of the block and the brick after 12.0 s? Assume that the brick stays on the block and that the coefficients of static friction and kinetic friction between the surfaces are 0.2 and 0.1 respectively.

IB Physics Equations of Motion

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Below is a tutorial sheet of harder problems on subtopic 2.1

  1. A ball falls from rest near the surface of the Earth. The ball falls 1.0 m in the last second of its fall. From what vertical height was the ball released? Neglect air resistance.
  2. A stone is released from rest at a height of 200.0 m above the surface of the Earth. At the same instant a ball is projected vertically upwards from the ground from directly below the stone. If they meet after 4.0 s at what speed was the ball projected? Neglect air resistance.
  3. A ball is projected vertically upwards from the surface of the Earth. The ball is above a height of 125.0 m for a total time of 3.0 s. At what speed was the ball projected? Neglect air resistance.
  4. A car of length L moves at a constant velocity u to the east. A truck of length T moves at a constant velocity v to the east. What is the time taken by the car to overtake the truck?
  5. A car of length L moves with a constant acceleration a to the east. A truck of length T moves at a constant velocity v to the east. When the velocity of the car is u it starts to overtake the truck. What is the time taken to overtake the truck?
  6. A particle moves with a constant acceleration a. If its maximum speed is v what is the least time to travel a distance d if it starts from rest?
  7. A particle is initially at rest. Its acceleration increases uniformly from zero to a in a time interval t. What is the distance travelled in this time interval? [at2/6]

IB Physics Vectors

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Below is a tutorial sheet on sub topic 1.3 vectors.

  1. What is the component of a force of 5.0 N in a direction at 30° to itself?
  2. What is the component of a force of 4.0 N in a direction at 90° to itself?
  3. An object of weight W is held at rest on a smooth inclined plane of angle of elevation 𝜽 by a horizontal force H. What is the value of H?
  4. An object of weight W is held at rest on a rough inclined plane of angle of elevation 𝜽 by a horizontal force H. If the coefficient of static friction is μ, determine the possible values of H.
  5. Two light inextensible strings are tied to an object of weight W at the same point. The strings make angles of 30° and 60° with the vertical. Determine the tension in each string.
  6. Three light strings of equal length are tied to the same point on an object of weight W. The other ends of the strings are tied to hooks on the ceiling, the strings forming the sides of a regular tetrahedron. What is the tension in each string?