# IB Physics MeV units

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

- An electron has a momentum of 4.0 MeVc
^{-1}. What is the energy of the electron?

What are the concepts in Physics and Mathematics that students find difficult? In this blog I will post tutorial points that I hope will stimulate thinking and so broaden the knowledge and understanding of students allowing them to write thorough examination responses. Tutorial sheets, structured from a student's point of view, will be posted on the HSC, IB and university level topics of Relativity, Electromagnetism, Mechanics, Quantum Physics and Calculus. The overall purpose of these pages is to encourage and promote learning in Physics and Mathematics and so open **new horizons** in learning.

Permission is granted to use the material on this blog provided that recognition is given to its source,

the Sydney Physics and Mathematics Tutor

the Sydney Physics and Mathematics Tutor

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

- An electron has a momentum of 4.0 MeVc
^{-1}. What is the energy of the electron?

A tutorial sheet of electric current questions is given below.

- 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. [8.5x10^{28}] - Determine the electron drift speed in a copper wire of diameter 2.0 mm carrying a current of 1.0 A.
- List some common metals that have a free electron density greater than that of copper.[aluminium, iron, magnesium, tin, lead, zinc, magnesium]
- What is meant by a free electron?
- Explain why a wire heats up when a current passes through it.
- 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?

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

- 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.
- 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.
- A point charge -4.0 nC is at a height of 6.0 cm above a deep, still, freshwater lake. If the dielectric constant of water is 81 determine the electric force on the charge.
- 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. Determine the force acting on each charge. Draw the electric field lines.

- Atoms emit discrete wavelengths of light. Explain why a heated iron bar changes colour as its temperature changes.
- 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.
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?

more to come

A tutorial sheet of problems on the photoelectric effect follows.

- What factors determine the intensity of light shining on a surface?
- 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?
- 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.
- Sketch a graph showing the maximum kinetic energy of the escaping photoelectrons versus the wavelength of the incident light.
- Why is the maximum kinetic energy calculated in the photoelectric effect? Do some escaping electrons have more kinetic energy than others?

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

- 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]
- An Earth-like planet is discovered orbiting a distant star at an average distance of 2.7x10
^{12}m. If the power of the star is 1.3x10^{28}W, calculate the surface temperature of the planet. Take the albedo and emissivity of the planet as 0.3 and 0.61 respectively. [163.7K] - 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] - 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] - A lake full of water has an area of 5.1x10
^{6}m 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. [1.08x10^{14}W] - In a nuclear power station 7.64x10
^{19}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. [7.78x10^{13}Jkg^{-1}, 1.49x10^{18}Jm^{-3}] - 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.[2.33x10
^{12},4.46x10^{16}Jm^{-3}]

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.

- 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]
- 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?
- 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?

A tutorial sheet of capacitor questions starts below

- 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?
- 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?
- 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?
- 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?
- Why does the presence of a dielectric material between the plates change the capacitance?
- 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.
- 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]
- 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]

A tutorial sheet on double slit interference is given below.

- 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.
- 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.
- 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.
- What is the path difference when the first order maximum forms on a screen?
- In a double slit experiment one of the slits is covered up. Is the central maximum brighter when one of the slits is covered?
- 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?

A tutorial sheet of polarisation problems is given below

- When is a beam of light polarised?
- A beam of unpolarised light of intensity 4000 Wm
^{-2}strikes a polarising filter. What is the transmitted intensity? - 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.
- 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.
- 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?

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

- 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*] - Point charges +4Q and -Q are placed a distance d apart in a vacuum. Draw the electric field lines around these charges.
- Draw the electric field lines of an electric dipole when it is seen close up.
- 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?
- 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.
- 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.
- 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?

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.

- A charge of +2.0 μC has a velocity of 3.0×10
^{7}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. - A coil of area 10 cm
^{2}has its plane at an angle of 30° to a uniform magnetic field of 100 mT. What is the magnetic flux through the coil? - A coil of cross sectional area 30 mm
^{2}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. - 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.
- 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 3.0x10
^{7}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.

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

- 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?
- 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?
- 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.

Below is a tutorial sheet of harder problems on subtopic 2.1

- 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.
- 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.
- 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.
- 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?
- 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?
- 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?
- 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? [at
^{2}/6]

Below is a tutorial sheet on sub topic 1.3 vectors.

- What is the component of a force of 5.0 N in a direction at 30° to itself?
- What is the component of a force of 4.0 N in a direction at 90° to itself?
- 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?
- 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.
- 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.
- 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?

A tutorial sheet on sub topic 1.2 is given below.

- The mass of a pencil is measured once. The value is 4g. What is the uncertainty in this measurement?
- A ball is released from rest and the time to fall a fixed distance is measured. The times are 0.5s, 0.5s, 0.6s and 0.6s. What is the uncertainty in the time of fall?
- A student measures the following value for g in ms
^{-2}: 9.81, 9.79, 9.84, 9.81, 9.75, 9.79, 9.83. Give the scientific value of g including its uncertainty. [9.80 ± 0.01 ms^{-2}] - A toy car moves in a straight line along a horizontal laboratory bench. The time taken to move a distance of 350cm is measured 5 times. The values are 6.2s, 6.5s, 6.4s, 6.3s and 6.0s. What is the average speed of the car?
- In the previous question the distance is measured 5 times. The values are 340cm, 360cm, 345cm, 365cm, 355 cm. Using the previous time values, what is the average speed of the car?
- The mass of a marble is measured five times. The values are 52g, 51g, 52g, 53g, 52g. The diameter is measured five times. The values are 35mm, 33mm, 36mm, 34mm and 35mm. Determine the density of the marble.
- A uniform rod can oscillate freely about a horizontal axis through its end point. The time of small oscillations about its equilibrium position is given by T = 2𝜋√[I/(mgh)], where m is the mass of the rod, g the acceleration due to gravity, h the distance from the point of support to the centre of the rod and I is the moment of inertia of the rod about its point of support. The following data sets are obtained for the measurement of m, h and I respectively; {210g, 208g, 209g, 211g, 212g}, {0.50m, 0.49m, 0.51m, 0.48m, 0.49m}, {0.42kgm
^{2}, 0.40kgm^{2}, 0.46kgm^{2}, 0.50kgm^{2}, 0.50kgm^{2}}. Determine g from this data. - The radius of a circle is 14.6±0.5cm. Determine the area of the circle to the correct number of significant figures. [(6.70±0.46)×10
^{2}cm^{2}] - What is the circumference of the circle in the previous question? [91.7±3.1cm]
- If R=1800±36Ω and I=2.1±0.1mA, what is the value of RI? [3.8±0.3V]

A tutorial sheet of **true-false** questions on the spacetime diagram is given below.

ɣ=1/√(1-v^{2}/c^{2})

- Albert Einstein was not the first person to use a spacetime diagram.
- The path of a particle in the (x,ct) plane on a spacetime diagram is called its world line.
- A rigid rod is at rest in the S frame. At t=0 the spacetime coordinates of the ends of the rod in S are A=(0,0) and B=(L
_{0},0). The worldlines of A and B have the equations x=0 and x=L_{0}respectively. - In question 3 take ɣ = 5/4 and L
_{0}as 2. Using a spacetime diagram the coordinates of A in S' when ct' = 4 are (-2.5,4) and the coordinates of B are (-0.83,4), the length of the rod in S' being 1.7 approximately. - A rigid rod is at rest in the S' frame. At t'=0 the spacetime coordinates of the ends of the rod in S' are P=(0,0) and Q=(L
_{0},0). The worldlines of P and Q have the equations x=0 and x=L_{0}respectively.

A tutorial sheet of **true-false** questions on relativity is given below.

- The speed of light (according to the local observer) near a black hole is 3.0x10
^{8}m/s. A distant observer considers the speed of light to be much less than this. - The speed of light changes (according to a distant observer) as it passes through a gravitational field.
- The speed of light is the same for all observers in a flat space.
- Space can expand at a rate greater than c.
- Nothing can escape from inside a black hole.
- Particles can escape from the event horizon of a black hole.
- Light leaving the horizon of a black hole undergoes a gravitational red shift and has an infinite wavelength at infinity and so cannot be detected.
- The time coordinate of an event is the same value at all locations in the same inertial reference frame.
- If an event occurs at x' at time t' in the inertial reference frame S' the event occurs at time ɣ(t' + v x'/c
^{2}) in another inertial frame S. - The proper time interval is the least time interval between two events as reckoned from any inertial reference frame.
- The proper time interval is the time interval between two events in the inertial reference frame where the events occur at the same position.
- The proper length of a rod is the length of the rod in the inertial reference frame where the rod is at rest.
- The rest reference frame for a moving object is the reference frame in which the object is at rest.
- On a spacetime diagram the units on each axis have the same scale.
- On a spacetime diagram the worldline of a particle of non-zero rest mass cannot have a gradient less than 1.

A tutorial sheet of **true-false** questions on thermal physics concepts is given below.

- Particles of an ideal gas do not collide with each other.
- Particles of an ideal gas all have the same speed.
- The ideal gas approximation works best at high temperatures and pressures.
- The pressure exerted by a gas is due to the momentum of the particles.
- No heat energy flows between two objects at the same temperature.
- A large mass at a low temperature has the same amount of heat energy as a smaller mass at a higher temperature.
- To find the Kelvin temperature we add 273.16 to the celsius temperature.
- An object of higher specific heat capacity takes a longer time interval to undergo a given temperature change than one of lower specific heat capacity.
- Heat energy is the amount of energy a substance possesses.
- The SI unit for thermal conductivity is the Jm
^{-2}s^{-1}K^{-1} - A flat sheet of iron of mass m is left in the Sun and its temperature changes by T. If a flat sheet of iron of mass 2m is left in the Sun for the same time interval its temperature change is T/2.

A tutorial sheet of harder problems on Coulomb’s law is given below.

- Point charges +4Q and -Q are placed a distance d apart in a vacuum. Where is the resultant electric field zero?
- Draw the electric field lines around the charges in question 1.
- Two point charges +4Q and +Q are placed a distance d apart in a vacuum. Where is the resultant electric field zero?
- Draw the electric field lines around the charges in question 3.
- Three equal point charges +Q are placed at the vertices of an equilateral triangle of side d. Is the resultant electric field ever zero?
- Draw the electric field lines around the charges in question 5.
- Four equal point charges +Q are placed at the corners of a square of side d. Is the resultant electric field ever zero?
- Draw the electric field lines around the charges in question 7.
- Four equal point charges +Q are placed at the corners of a regular tetrahedron of side d. Calculate the magnitude of the resultant force acting on one of the charges. [F√6, where F is the force between two of the charges]
- Eight equal point charges +Q are placed at the corners of a cube of side d. Is the resultant electric field zero at the centre of the cube?
- *In question 10 what is the magnitude of the resulant electric field at a small distance from the centre of the cube?

Welcome to Sydney Physics Tutor, my name is Stephen McAndrew. I have taught Physics and Mathematics in independent schools in Sydney and the UK for 38 years. I offer expert individual tutoring to allow students to fulfil their academic promise. I focus on the individual student and prepare structured work to address their particular deficiencies in knowledge and skills and develop these deficiencies into strengths. I use traditional methods of instruction where students write their answers in examination style format and are tested regularly to build their confidence and so develop a love of learning in Physics and Mathematics.

STEPHEN MCANDREW

MA, MSc, DipEd, CPhys, MInstP, MAIP, MAustMS, FRAS

Sydney Physics and Mathematics Tutor

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