IB Physics and Maths. Straight Line Motion

A tutorial sheet of problems on motion in a straight line, solved using IB Physics and Mathematics skills, is given below.

1. The acceleration of a particle is given by a = - k x², where k is a constant. Is the motion simple harmonic motion? Explain.
2. In question 1, k = 0.01 m^-1 s^-2 and the mass of the particle is 100.0 g. Using a graphical method, find the work done on the particle when it moves from x = ∛2 m to x = 0.
3. Find the speed of the particle at the origin if it is at rest when x = ∛2 m.
4. Show that the velocity of the particle is given by, -√( ( 2 - x³)/150 ).
5. Using a GDC show that the time taken to reach the origin is 15.3 s.

IB HL Physics. Spacetime diagrams

A tutorial sheet on HL topic A.4 special relativity is given below.

1. On a spacetime diagram the axes are inclined at 45° to each other. What does this mean?
2. A spacetime diagram is drawn for observers in reference frames that are moving at a constant velocity of 0.8c relative to each other. When drawn on paper the unit length interval on the x and ct axes is 2.4 cm. Is the length interval on the x' and ct' axes less than, equal to or greater than this? Explain why and give its value.

IB HL Physics. P-V diagrams

A tutorial sheet on P-V diagrams from Topic B.4 Thermodynamics is given below.

1. During a cyclic process on a P-V diagram is the entropy change always zero?
2. Does the efficiency of a heat engine depend on how rapidly the process is carried out?
3. State the definition of an adiabatic process.
4. On a P-V diagram the initial state is (P₁,V₁) and the final is (P₂, V₂). If the ratio of specific heats is ɣ and the specific heat capacity at constant volume is c_v, find the entropy change between the two states.

IB Physics. Centripetal Force

A tutorial sheet on centripetal force follows.

1. The Earth rotates on its axis once every 23 h 56 m 4 s. Why do objects remain at rest on the Earth (relative to the Earth) ?
2. Imagine that the Earth's period of rotation is 2 h. Would an object on the Earth stay at rest on the Earth? Explain.
3. A planet of mass M has a radius R and has a period of rotation about its axis of T. Find the weight, relative to the surface of the planet, of a mass m at latitude θ on the planet.
4. A centrifuge is spinning at a rate ω. Do heavier particles accumulate near the centre or the outside? Explain.
5. A mass m can slide on a smooth horizontal rod. The mass is placed at the centre of the rod. The rod rotates with a constant angular speed ω about an axis perpendicular to one end. Does the mass stay at rest relative to the rod, move inwards or outwards? Explain.

IB Physics. Motion in a Vertical Circle

A sheet of harder questions on a mass moving on a string in a vertical circle is given below.

1. A mass m hangs at rest on the end of a light inextensible string of length L. The mass is given a horizontal velocity U and the maximum vertical height to which the mass rises is L. Find U.
2. In the previous question find the tension in the string and the magnitude of the acceleration of the mass at its highest point.
3. A mass m is on the end of a string of length L that has its upper end fixed. The mass is released from rest and swings in a circular arc. Find an expression for the tension in the string when the string makes an angle 𝜃 with the vertical.
4. A mass hangs at rest on the end of a light inextensible string of length L. The mass is given a horizontal speed U. In its subsequent motion the string becomes slack and the mass hits the point of supprt of the string. Find the initial speed U.

HSC Physics Atwood's Machine

Atwood’s machine, the name given to two blocks connected by a light inelastic string passing over a smooth pulley, is used in many mechanics experiments.

1. A single Atwood's machine is suspended from the roof of an elevator. Masses of of m₁ and m₂ are connected by a light inelastic string that passes over the smooth pulley. Find the acceleration of the elevator if m₁ and m₂ are at rest relative to the elevator.
2. A double Atwood’s machine consists of a fixed pulley with a string connected to a mass m₁ passing over it, with another Atwood’s machine connected to the other end of the string passing over the first pulley. On the second Atwood’s machine there are masses of m₂ and m₃ connected by a light inelastic string. We neglect the mass of each pulley.Show that the acceleration of the second pulley is given by a = g(4 m₂ m₃ - m₁(m₂+ m₃))/(4 m₂ m₃ + m₁(m₂ + m₃))

HSC Physics Elastic Collision

A sheet of harder mechanics questions appears below.

An elastic collision occurs between an alpha partice of mass m moving at a speed u and a stationary nucleus of mass M. After collision the alpha particle moves at speed v at an angle 𝜃 to its initial direction and the nucleus moves at speed V at an angle ϕ to the initial direction of the alpha particle.

1. Show that v = u sinϕ/sin(ϕ + 𝜃).
2. Show that V = m u sin𝜃/( M sin(ϕ + 𝜃)).
3. Show that m/M = sin(2ϕ + 𝜃)/sin𝜃.

HSC Physics Harder Circular Motion

A sheet of harder questions on circular motion follows.

1. A railroad car is moving around a horizontal circular track. On which rail, the inner or the outer, does a greater force act on the wheels of the car?
2. A railroad car is moving around a horizontal circular track of radius r with a speed v. The distance between the rails is d. If the height of the centre of gavity of the car above the rails is h, show that the ratio of the normal reaction reaction force exerted by the outer rail to the inner rail is (dgr + 2hv²)/(dgr - 2hv²).
3. A thin ring of radius R and mass M rotates at an angular speed ⍵. Find the tension in the ring. (a) Why is the tension in the ring not zero? (b) Show that the tension in the ring is M R ⍵²/(2𝜋).

HSC Physics Harder Projectile Motion

A sheet of harder questions on projectile motion is given below.

1. A particle is projected from a vertical height of 120.0 m at 30.0 m s^-1. Find the angles of projection to the horizontal if the horizontal range of the projectile is 100.0 m. Neglect air drag.
2. A stone is thrown at a speed U at 45° to the horizontal from a cliff of height h above sea level. The maximum height of the stone is 98.0 m and the horizontal displacement of the sone when it strikes the sea is 98.0 m. Find U and h. Take g = 9.8 m s^-2 and neglect air drag. (22.69 m s^-1, 84.87 m)

IB Physics Doppler effect

A tutorial sheet of practice questions on the Doppler effect is given below.

1. A car moves at 20.0 m s^-1 to the east. The driver blows the horn of the car. If the speed of sound in air is 340 m s^-1, what is the speed of the sound waves that an observer measures if they are: (a) at rest to the west of the car, (b) at rest to the east of the car, (c) moving towards the car from the east at 20.0 m s^-1.
2. A car moves at a velocity u to the east. Sound waves of frequency f0 are made by the car. The sound waves reflect from a vertical wall and travel back to the car. What is the frequency of the sound waves received by the car? The speed of sound in air is c.

IB Physics Power

A tutorial sheet of questions on power is given below.

1. Is power the gradient of the work-time graph?
2. Is work done equal to the area under the power-time graph?
3. Is work done equal to the average power multiplied by the time taken?
4. A particle moves in SHM of period 12.0 s and amplitude 8.0 cm. Find the average power of the resultant force acting on the mass as it moves from x = +4.0 cm to the equilibrium position.

IB Physics Vectors

A sheet of practice questions on vectors is given below.

1. A force of magnitude 5.0 N and a force of magnitude 4.0 N cannot be added together to give a force of magnitude (a) 0.5 N, (b) 1.5 N, (c) 3.0 N, (d) 7.0 N
2. A block of mass 2.0 kg is at rest on a rough inclined plane that makes an angle of 20.0° with the horizontal. The coefficient of static friction between the surfaces is 0.30. What is the magnitude of the force of static friction acting on the block?
3. A block of mass 1.50 kg is projected up a rough inclined plane of angle of elevation 25.0° at 12.0 m s ^-1. The coefficient of static and dynamic friction between the surfaces are 0.40 and 0.30 respectively. Find the time taken by the block to return to its starting point.

IB Physics Radioactive decay

A tutorial sheet on radioactive decay in Topic E follows.

1. Choose the best definition of half-life. (a) The time taken for one-half of the initial mass to decay (b) The average time taken for one-half of the original number of nuclei to decay (c) The time taken for one-half of the original number of nuclei to decay (d) The average time taken for one-half of the original number of nuclei to undergo one decay reaction.
2. The activity of a radioactive sample is A. The rate of decay of the sample at this time is (a) A, (b) -A, (c) A ln2, (d) A/ln2
3. The decay constant is equal to the probability that a nucleus will undergo radioactive decay. True or false?
4. The decay constant is inversely proportional to the probability that a nucleus will undergo radioactive decay per unit time. True or false?
5. During an experiment with a new alpha particle emitting sample in the laboratory the reading on a Geiger counter is 2.6 after 0.3 h. The reading is next taken 0.2 h after the first measurement and its value is 1.8. Find the time interval when the reading is 0.8.

IB Physics Mass and energy

A tutorial sheet of questions on mass and energy from topic E follows.

1. Can mass be "converted" into energy?
2. Can energy be "converted" into mass?
3. A Higgs boson has an approximate energy of 2 TeV. What is the mass associated with this energy? Give the answer in u.
4. A neutron has a mass of 1.00727 u. What is the rest mass of a neutron in GeV c^-2?
5. When a nuclear fission reaction occurs is mass "converted" into energy?
6. Where does the energy "come from" in a nuclear fission reaction?
7. Is mass "converted" into energy when an electron and a positron annihilate each other?
8. Is energy "converted" into mass when a gamma ray undergoes a par production reaction?
9. The rest mass of an electron is 0.5 MeV c^-2. What does this mean?
10. Is the binding energy of a nucleus positive or negative in sign?

IB Physics Gravitational fields

A tutorial sheet of questions on Topic D gravitational fields, HL, appears below.

1. Equipotential curves are drawn around a point mass. The difference in potential between the curves is constant. Do the equipotential curves become closer in distance, further in distance or the same separation as the distance from the point mass increases?
2. When the potential is maximum the field strength is zero. True of false?
3. When the field strength is maximum the potential is maximum. True or false?
4. Equal masses are placed at the vertices of an equilateral triangle. Sketch the gravitational field lines around the masses.
5. Explain why gravitational potential is negative in sign.
6. Two equal point masses M are placed a distance d apart. A point mass m is moved from infinity at a constant speed and is placed at the midpoint of the line joining the masses. Find the work done by an external force in moving the mass m from infinity to its final position. Does the work depend on the path taken?
7. A uniform solid sphere has a mass M and radius R. State the gravitational potential and field strength for (a) r >R (b) r < R. Sketch graphs for each case.
8. A uniform spherical shell has a mass M and radius R. State the gravitational potential and field strength for (a) r > R (b) r < R. Sketch graphs for each case.
9. Find the gravitational potential energy of a uniform solid sphere of mass M and radius R.
10. Find the gravitational potential energy of a uniform spherical shell of mass M and radius R.

IB Physics Rutherford model of the atom

A tutorial sheet of questions on aspects of the Rutherford model of the atom is given below.

1. The Rutherford model of the atom has protons and neutrons at the centre of an atom. True or false?
2. Marsden fired neutrons at a thin gold sheet and measured the number that passed through. True or false?
3. When alpha particles are scattered by a thin metal sheet the number detected at a scattering angle 𝜃 is (state true or false) a) proportional to the thickness of the foil b) proportional to the kinetic energy of the alpha particle c) proportional to the atomic number of the metal d) proportional to the cosine of 𝜃/2 squared.
4. Where are the electrons in the Rutherford model of the atom?
5. Sketch the path of an alpha particle of charge +2e as it passes close to a nucleus of charge +Ze. Assume that the mass of the nucleus is much greater than that of the alpha particle.
6. Sketch the path of an alpha particle of charge +2e as it passes close to a charge -Ze. Assume that the mass of the negative charge is much greater than that of the alpha particle.
7. What is the scattering statistic in this experiment?

IB Physics Magnetic fields

A tutorial sheet on topic D magnetic fields appears below.

1. What produces a magnetic field?
2. Two parallel wires carry equal currents in the same direction. Sketch a graph showing the magnetic field strength on a line through each wire perpendiculr to the wires.
3. Sketch the magnetic field lines in the plane perpendicular to each wire.
4. Three parallel wires carry equal currents I. The wires are at the vertces of an equilateral triangle of side d. Find the magnetic force per unit length acting on each wire.

IB Physics Simple harmonic motion

A tutorial sheet of simple harmonic motion (SHM) questions for IB SL and HL appears below.

1. A simple pendulum always swings in SHM. True or false?
2. A simple pendulum has a mass on the end of a string of length L. The mass hangs at rest. It is given a small horizontal velocity u. If the initial speed is doubled, which case, high initial speed or low initial speed, has the greater a) period of oscillation, b) energy, c) tension in the string.
3. A particle moves in SHM of period 6.00 s and amplitude 12.0 cm. Find the least time taken by the particle to move from x = +8.00 cm to x = +4.00 cm.

IB Physics Photons

A tutorial sheet of questions on photons is given below.

1. Define the term photon.
2. Does a photon have a wavelength?
3. Does a photon have an amplitude?
4. Does a beam of photons have an intensity?
5. Can photons be polarised?
6. What is the difference between an electron neutrino and a photon?

IB Physics Angular momentum

A tutorial sheet of questions on angular momentum is given below.

1. Define the angular momentum of a particle about a point.
2. Define the angular momentum of a rigid body about its axis of rotation.
3. State the condition for the angular momentum of a particle about a point to be conserved.
4. Linear momentum is always parallel to the linear velocity...true or false?
5. Angular momentum is always parallel to the angular velocity...true of false.