IB Physics Average Speed Problems

A tutorial sheet on average speed problems.

1. A car travels at 50 km h^-1 for a distance of 150 km and then travels at 30 km h^-1 for another 150 km. What is the average speed for the entire trip?
2. A car travels to a town at an average speed of 40 km h^-1. The return journey on the same road is made with an average speed of 30 km h^-1. Find the average speed for the entire journey.
3. Two identical planes Mike and Ike race against each other. They start at the same place and both have an air speed of v km h^-1. A wind from the east of w km h^-1 blows, w < v. The planes start at the same point and time. Mike travels to a point d km east on the ground and returns. Ike travels to a point d km north on the ground and returns. Show that the average speed of Mike is (v² - w²)/v and the average speed of Ike is (v² - w²)^1/2.
4. Show that Ike always wins the race. Hint (v² - w²)^1/2 < v, v² - w² < v(v² - w²)^1/2. This problem is taken from Relativity for the Layman by James A Coleman, 1958, pp 32-33 and the solution is given in The Physics Teacher, vol 34, Oct 1996, pp 438-439.

IB Physics Entropy Change of Two Objects in Contact

A tutorial sheet on entropy change. Entropy change questions are often asked in HL Physics.

1. If a quantity of heat Δq is added reversibly to a body at Kelvin temperture T then the increase of the entropy of the body is Δs defined by Δs=Δq/T.

2. A reversible process is one where the body is in equilibrium at every stage of the process. In this case a small change in conditions may reverse the process exactly.In a reversible process the gain of entropy by one body is exactly equal to the loss of entropy by the other and the entropy of the whole system is unchanged.

3. An irreversible process does not consist of equilibrium states at each stage of the process. An irreversible process creates entropy as the entropy gain by one body is greater than the entropy loss of the other.

4. Two objects each of heat capacity C are placed in thermal contact. The final equilibrium temperature of both objects is T. Initially the temperature of the "hot" object is T_h and the temperature of the "cold" object is T_c . Show that the change in entropy for the combined system is C ln(T²/(T_hT_c)). Assuming that all of the heat energy lost by the hot object is transferred to the cold object, show that T_h = T + ΔT and T_c = T - ΔT. Hence show that the change in entropy for the system is C ln(T²/(T²-ΔT²)) and show that this is greater than 1. Use Δq = C Δθ where Δθ is the infinitesimal change in temperature. This problem is taken from Problems for Physics Students by K F Riley. The solution and additional notes on Boltzmann's constant can be found in the article by Jeffrey J Prentis in The Physics Teacher, vol 34, Oct 1996, pp 392-397.

IB Physics The Centrifuge

A tutorial sheet on the pressure difference in a rotating fluid providing a centripetal force, an often misunderstood concept.

1. In a centrifuge a column of fluid of density ρ rotates in a horizontal plane at an angular speed ⍵. Show that the pressure in the fluid P at a distance r from the axis of rotation is given by P(r) = P₀ +1/2 ρ ⍵²(r² - r₀²), where P₀ is the pressure at r = r₀.
2. Explain why a marble goes to the outside of the centrifuge and a cork to the inside. See The Physics Teacher, vol 34, October 1996, p 422, The Marble, Cork and Centrifuge by Thomas J Pickett.
3. If the object is denser than the fluid the pressure in the fluid is not great enough to maintain the circular motion at that distance and so the object will drift outward through the fluid to a larger value of r.

IB Physics Gravitational Force Between Objects

This tutorial sheet is on the gravitational force between two objects. The first 3 questions are SL/HL and the others are HL.

1. Two uniform solid spheres of masses M₁ and M₂ and radii R₁ and R₂ have their centres a distance r apart (r > R₁ + R₂). State the magnitude of gravitational force acting on each mass.
2. A satellite of mass m orbits a planet of mass M in a circular path of radius r with orbital period T. Find an expression for the gravitational field strength at the position of the satellite.
3. Two point masses m and M are placed at rest at a distance d apart. After release the masses move towards each other. Find an expression for the speed of the smaller mass when the speed of the larger mass is V.
4. A uniform spherical shell has a mass M and a radius R. i. What is the gravitational field strength at the centre of the shell? ii. A particle is placed at the centre of the shell and given an initial speed u. Find the time taken to reach the shell.
5. A uniform rod of mass M and length L is in the same straight line as another uniform rod of mass M and length L. The distance between the centres of the rods is 2L. i. Can we find the attraction between the rods by considering each rod to be a point particle of mass M at its centre of mass? ii. Show that the attraction between the rods is GM²/L² ln(4/3)

IB Physics Magnetic flux through a loop

This tutorial sheet studies the magnetic flux through a circular loop. This topic was a HL Paper 2 question in Zone 3 in May 2025.

1. What is the meaning of the term magnetic flux?

2. A constant current I flows in a long straight wire. Write down an expression for the magnetic field at a perpendicular distance r from the wire.

3. A small circular loop of radius R is in the plane of the wire with its centre at a distance r from the wire. Write down an expression for the magnetic flux through the loop. What assumption are we making?

4. If I=2.0 A, r=10.0 cm and R = 2.0 cm show that the magnetic flux through the loop is approximately 2.5x 10^-8 Wb. This assumes that a constant magnetic field acts through the coil. In a show that question all substitution, rearranging and cancellations must be shown. Give the answer to one more decimal place to show evidence of calculator usage.

5. In question 4 determine the magnetic flux through the coil if the variation of field strength through the coil with distance from the straight wire is included. In this case there is slightly more flux through the coil since the magnetic field is stronger in the side of the loop closest to the straight wire. Flux = 2.54 x 10^-8 Wb.

IB Physics Where does the Sun's energy come from?

A tutorial work sheet on the topic of the source of the Sun’s energy. As this is a misunderstood concept, two key study points are taken from the article by E G Thomas, What’s so special about E = m c2, separating the myth from the truth, Eur. J. Phys., 26, (2005), S125. These are SL/HL concepts.

1. The Sun is getting its energy by rearranging protons into a more stable form of a helium nucleus. In this process the energy that is released comes from the binding energy of the helium nucleus.
2. The Sun does not turn matter into glowing energy.

IB Physics Mass and Energy

A tutorial sheet on mass and energy. Some study points are listed. These are taken from the article by Keith Atkin in Physics Education 35, 5, Sep 2000, page 319. These are SL/HL concepts.

1. Is matter the same as mass? No, matter is a qualitative term meaning substance, mass is a defined physical quantity which is a measure of inertia.
2. E = mc² states that mass (inertia) and energy are equivalent not interconvertible.
3. In the Cockroft-Walton reaction a proton interacts with a lithium nucleus forming two helium nuclei with a gain in kinetic energy. Is there a loss in mass? No, mass and energy are equivalent. Both energy and mass are conserved in the process, there is no destruction of mass or creation of energy. There is merely a redistribution of a fixed amount of energy (and its equivalent mass).

IB Physics Diffraction

This tutorial sheet is about diffraction, a concept that is sometimes misunderstood.

1. State the definition of diffraction.
2. Why does diffraction occur when light passes through a single slit?
3. Explain qualitatively the pattern that we see when light passes through a single slit if i. the slit width is much greater than the wavelength ii. the slit width is much less than the wavelength.
4. Divide a single slit of width b into two sections. By considering a ray from the top of each section, show that destructive interference occurs when b sin𝜃 = 𝜆. Do this with four sections in the slit and show that destructive interference occurs when b sin𝜃 = 2𝜆. This can be generalized to b sin𝜃 = n𝜆, n=1,2,..
5. When light is now incident normally on a diffraction grating what does the equation d sin𝜃 = n𝜆, n=0,1,2,3.. predict?
6. The incident monochromatic light is not normal to the grating. Can we use the equation d sin𝜃 = n𝜆 in this situation?
7. In question 6 the angle of incidence of the light on the grating is ϕ. Show that the angle 𝜃 to the normal to the grating where intensity maxima occur are given by d ( sin(𝜃 - ϕ) - sinϕ ) = n𝜆.
8. Describe the difference between primary maxima and secondary maxima.
9. Describe the interference pattern when white light is incident normally on a diffraction grating.

IB Physics TOK What did Planck Quantize?

A tutorial sheet on the process of science in the development of quantum phenomena. See Physics Education, Nov 2000 p 381-386, A brief history of quantum phenomena by Gren Ireson.

1. In 1900 Max Planck quantized the energy of the oscillators in the radiating body rather than the radiation from the body.
2. Planck presented an argument that consisted essentially phenomenological curve fitting, relying on classical idea of entropy at long wavelengths and an ad hoc conhecture due to Wien for short wavelengths, but which fitted the data perfectly at all wavelengths. However he was unable to offer any theoretical justification for the results.
3. Planck regarded the walls of the cavity as harmonic oscillators which could absorb and emit energy only in discrete amounts, E, which is related to the frequency, f, of the absorbed or emitted radiation by E = hf, where h is Planck's constant.
4. In 1905 Albert Einstein took the notion of quantization further by suggesting that electromagnetic radiation exists in the form of packets of energy that we now call photons.
5. Application of the photon model supplied Einstein with the means to solve the photoelectric effect. Classical electromagnetic theory predicted that the energy available in light is proportional to the intensity and independent of the frequency, but experimental evidence pointed to the opposite result.

IB Physics Flipping Rod

A tutorial sheet on the problem of a uniform rod moving in a vertical plane.

A uniform rod of length 2a and mass m lies horizontal on a smooth horizontal surface. One end of the rod is given a vertical velocity V upwards.

1. Is energy conserved as the rod moves in a vertical plane?
2. Is linear momentum conserved as the rod moves in a vertical plane?
3. Is angular momentum conserved as the rod moves in a vertical plane?
4. The rod turns right over without losing contact with the table. Show that 6ag < V² < 7ag.

IB Physics Entropy Decrease

A tutorial sheet on the entropy change in a rust reaction is given below. It is taken from Entropy and Rust by Daniel F Styer, Am J. Phys., 78 (11), November 2010, p 1077.

The rust reaction is 4Fe +3O₂ →2Fe₂O₃. The entropy (at room temperature, 298.15 K and at a pressure of 10⁵ Pa) of 1 mole of Fe is 27.280 JK^-1, of 1 mole of O₂ is 205.147 J K^-1 and of one mole of Fe₂O₃ is 87.404 J K^-1.

1. Find the entropy change when 1 mole of Fe rusts.
2. Describe the entropy change in the surroundings when 1 mole of Fe rusts.

IB Physics Point Charges at the Corners of a Triangle

This tutorial sheet investigates a problem involving two positive and a negative charge placed in a plane. It is taken from Electricity and Magnetism, The Berkeley Physics Course Volume 2, Second Edition by Edward M Purcell.

1. Two positive ions and one negative ion are placed at the vertices of an equilateral triangle. Where can a fourth charge be placed so that the force on it will be zero? Is there more than one such place? (page 35 q 1.12)

IB Physics Rod Swinging in a Vertical Plane

This tutorial sheet is about a uniform rod swinging in a vertical plane.

A uniform rod of length 2L mass M can swing freely in a vertical plane about a horizontal axis through one end. The rod is released from rest when it is horizontal.

1. What are the acceleration components of the end of the rod when it makes an angle 𝜃 with the vertical?
2. Find the magnitude of the force exerted by the point of support of the rod when it makes an angle 𝜃 with the vertical.
3. Draw a graph showing the angular speed of the rod in terms of the angle that the rod makes with the vertical.
4. The rod is now released from the horizontal position and is given an initial angular speed. Find the least initial angular speed that will allow the rod to complete a full revolution.

IB Physics Mass on a Swinging Rod

A tutorial sheet on the problem of a mass on the end of a uniform rod swinging in a vertical plane. A question answered correctly by only a small percentage of the world.

A uniform rod of mass 2m and length L has a particle of mass m attached to its lower end. The rod is free to swing in a vertical plane about a horizontal axis through its upper end. The rod is released from rest at the horizontal.

1. Draw a free-body diagram showing the forces acting on the (i) particle, (ii) rod. The rod exerts an inwards force Y acting along the rod and a perpendicular force X on the particle along the tangent to the circular path. This question involves a rod and not a string. For a string X=0.
2. Use Newton's second law in terms of forces to write down the two equations of motion of the particle. The equations are written in terms of components parallel to the rod and perpendicular to the rod.
3. Use Newton's second law for rotational motion to write down the equation of motion for the system in terms of the net torque acting on it.
4. Solve the three equations simultaneously to find the force components exerted by the rod on the particle.
5. Show that X = mgsin𝜃/5 and Y = 17mgcos𝜃/5, where 𝜃 is the angle made by the rod with the vertical.
6. The force exerted by the rod on the particle is directed towards the centre of the circle only when the rod is vertical (𝜃=0°).

IB Physics Point Charges at the Corners of a Square

This sheet practices finding the electric potential of a system of point charges.

1. Define electric potential at a point in an electric field.
2. A point charge -q is placed at (-d/2,0) and a point charge +q is placed at (d/2,0). Find the electric potential at the point P that has coordinates (2d,0).
3. In question 2 the point P is moved to a very large distance x from the origin along the x-axis. Show that the potential at P is approximately d k q/x².
4. In question 2 find the electrostatic potential energy of the two charge system. What does this mean?
5. Point charges of +q are placed at the corners of a square of side of length d. Find the electric potential at the centre of the square.
6. In question 5 sketch a graph showing the variation in electric potential along the y-axis. The origin is at the centre of the square and the y-axis is parallel to the side of the square.
7. Show that the potential at the point (x,y) near the origin is approximately V = 8kq/d(1 + ( x² + y² )/d² + ..).
8. In question 5 a charge +q is placed at the origin and given a small displacement along the y-axis. Describe the subsequent motion of this charge and calculate its period. The charges at the four corners of the square are fixed in position.

IB Physics HL Mechanics

A sheet of questions on rolling objects, a topic in HL mechanics. These are explain questions requiring elaboration.

1. A sphere rolls from rest down an inclined plane. A block of the same mass slides the same distance down a smooth inclined plane of the same angle to the horizontal. Which object reaches the bottom first? Explain.
2. Why is friction necessary for rolling? Explain.
3. Can we use the equation F_f = µ F_N for rolling objects? Explain.
4. Does friction force do work as an object rolls? Explain.

IB Physics. What is conserved in the Compton effect?

The HL IB Physics course gives an equation for use in the Compton effect. What are the Physics principles expressed in this equation? These are general questions requiring elaboration in the answers.

1. Is momentum conserved in the Compton effect?
2. Is mass conserved in the Compton effect?
3. Is kinetic energy conserved in the Compton effect?
4. Is energy conserved in the Compton effect?
5. In the Compton effect the photon is scattered and in the photoelectric effect the photon is absorbed. Why is there a difference?

IB Physics Two blocks on a horizontal table

A tutorial sheet on two blocks on a table follows.

1. A 2.0 kg block sits on a 4.0 kg block that is resting on a frictionless table. The coefficients of static and dynamic friction between the blocks are 0.3 and 0.2 respectively. What is the maximum horizontal force that can be applied to the 4.0 kg block if the 2.0 kg block is not to slide on the 4.0 kg block? (Tipler Physics 3rd edition, p 133, q 47. )

2. A 60 kg block slides along the top of a 100 kg block with an acceleration of 3.0 m s ^-2 when a horizontal force of 320 N is applied. The 100 kg block sits on a smooth horizontal surface, but there is friction between the two blocks. Find (a) The coefficient of kinetic friction between the blocks. (b) The acceleration of the 100 kg block during the time that the 60 kg block maintains contact. (loc. cit, q 42)

IB Physics Relativistic train

A tutorial sheet on special relativity, a topic that most HL students find difficult. The tutorial questions are taken from the book University Physics by Harris Benson, Revised Edition, John Wiley and Sons, p 832. It is important to identify the proper time and proper length in a question. For questions where this choice is not obvious, apply the Lorentz transformations. Always find gamma first.

1. A train (frame S') of proper length 3.2 km moves at 0.6c relative to a platform (frame S). At t = t'= 0, two light pulses are emitted in opposite directions from the centre of the train. At what times do the pulses reach the ends of the train in (a) frame S' (b) frame S?
2. When it is 10 ⁸ m away in the Earth's frame (S), a rocket (frame S') travelling at 0.8c towards the Earth emits a flash. On receipt, it is immediately transmitted back to the rocket. How long does it take the flash return to the rocket according to the Earth frame?
3. A detector (frame S') moves away from the origin of frame S at a speed V along the +x axis. When it is at a distance x = L from the origin of S, a flash is emitted at the origin. How long does it take the flash to reach the detector according to observers (a) in S, (b) in S'?
4. A train of rest length 800 m approaches a platform of length 1 km at 0.6c. The front reaches the left end of the platform at t = 0 in the platform frame. At what time does the rear of the train reach the right end of the platform in the platform frame?

IB Physics Two climber problem

A tutorial sheet on the famous two climber problem follows. It is taken from Physics for Scientists and Engineers, Tipler, 3rd edition, p 133, q 44.

1. Two climbers are on an icy (frictionless) slope that makes 40.0° with the horizontal are tied together by a 30.0 m rope. One climber (Paul, of mass 52.0 kg) is hanging over the top of the slope and the other climber (Jay, of mass 74.0 kg) has dropped his ice pick and is on the slope. At time t=0 the speed of each is zero. (a) Find the tension in the rope as Paul falls and his speed just before he hits the ground if initially he is 20.0 m above the ground. (b) If Paul unties his rope after hitting the ground, find Jay's speed as he hits the ground. Initially Paul is hanging 5.0 m below the top of the slope.
2. In question 1 does the path followed by Jay after the rope is untied affect his speed at the ground?
3. Now assume that Paul does not untie his rope and that the coefficients of static and dynamic friction of Paul with the horizontal ground are 0.3 and 0.2 respectively. Find Jay's speed as he hits the ground.