Synoptic Exam Questions (Paper 2) (DP IB Physics: HL): Exam Questions

A prototype magnetic levitation or Maglev train uses powerful electromagnets on the track to induce currents in coils on the train's underside, creating a repulsive force for levitation. A separate system of electromagnets provides propulsion.

An electromagnet on the track creates a magnetic field. As the train moves over it, the magnetic flux through a coil on the train changes.

(i) State Faraday's law of induction.

[1]

(ii) Use Lenz's law to explain why this induced current creates a repulsive force on the train.

[2]

(iii) The train has a mass of .

Calculate the minimum total magnetic repulsive force required for levitation.

[1]

The train accelerates uniformly from rest. It passes through a speed test platform with timing gates at each end, and . The timing gates are positioned apart.

The elapsed time between passing and is recorded to be . The timing gate recorded​ the train’s speed to be .

(i) Derive an equation for the acceleration of the train.

[2]

(ii) Determine the acceleration of the train.

[2]

(ii) Calculate the minimum power output of the propulsion system when the train is travelling at .

[2]

The electromagnets in the tracks are cooled by liquid helium.

Explain, in terms of molecular motion, why the copper wires must be continuously maintained at a low temperature.

A theoretical future design of the train proposes that a speed of could be reached.

(i) An observer on the proposed train measures the length of the train carriage to be as it passes through the speed test platform at .

Calculate the length of the carriage as measured by an observer standing on the speed test platform.

(ii) A clock at the speed test platform measures the total journey time of the proposed train to be .

Calculate the total journey time as measured by a clock on the train.

A ballistic pendulum is used to determine the speed of a projectile. A projectile of mass is fired into a large block of wood of mass , which is suspended by a light wire of length . The projectile embeds itself in the block, and the combined system swings upwards.

(i) The collision between the projectile and the block is inelastic.

State what is meant by an inelastic collision and explain why momentum is conserved, but kinetic energy is not.

[3]

(ii) Immediately after the collision, the combined block and projectile system moves with a common speed . The projectile's initial speed was .

Show that ​.

[2]

After the collision, the system swings up to a maximum vertical height .

The swing can be assumed to be frictionless.

(i) By considering the conservation of energy after the collision, derive an expression for the speed in terms of and .

[2]

(ii) The system swings through an angle to reach the maximum height .

Determine the height of the swing.

[2]

(iii) Calculate the initial speed of the projectile.

[3]

The following graph shows the velocity of the oscillation as a function of time if the pendulum system were to oscillate in simple harmonic motion.

On the axes below, sketch the graph for the acceleration of the pendulum system as a function of time, assuming simple harmonic motion.

In reality, the pendulum system would not oscillate in simple harmonic motion. Use the idea of damping to explain why this is the case.

An experiment to determine the charge of an electron is shown.   

Oil drops are sprayed into a chamber above two parallel metal plates which are separated by a distance d. The oil drops become charged before entering the region between the plates.

A potential difference V is applied between the plates.

(i) Explain why the oil drops become charged.

[1]

(ii) Draw the electric field lines between the plates.

[2]

An oil drop is observed to be stationary between the plates when the potential difference is . When the potential difference is increased to , the drop is observed to move upwards with a constant velocity .

(i) State the sign of the charge on the oil drop.

[1]

(ii) Draw the forces acting on the oil drop when and when .

[3]

Show that the electric charge on the oil drop is given by

where  is the viscosity of air and is the radius of the oil drop.

The following measurements are made for the oil drop:

The viscosity of air between the plates is  and the separation of the plates is .

Deduce, using the equation in part (c), whether the value of the charge for the oil drop is consistent with the currently accepted value of the elementary charge.

The voltage supply connected to the parallel plates is switched off. The oil drop falls with a constant velocity .

Show that  is about 0.2.

The oil drop collides with another oil drop of charge +14e, where e is the elementary charge.

Deduce the net charge on each oil drop after the collision.

The Bohr model was developed in order to explain the atomic spectrum of hydrogen.

Outline the Bohr model and give a limitation of it.

Bohr modified the Rutherford model by introducing the condition: 

. 

Outline the reason for this modification.

The Bohr model for hydrogen can also be applied to a helium atom which has lost one of its electrons through ionisation.

The one remaining electron has a mass of m and moves in a circular orbit of radius r. Deduce an expression for

(i) the kinetic energy of the electron

[2]

(ii) the electric potential energy

[1]

(iii) the total energy of the atom

[1]

Using your answer to (c), describe the predicted effect on the orbital radius of the electron when it

(i) absorbs an electromagnetic wave

[1]

(ii) emits an electromagnetic wave.

[1]

The radius of the electron's orbit in the helium atom is 2.43 × 10⁻¹⁰ m.

Determine the principal quantum number of the energy level occupied by the electron.

The total energy of an electron in a stable orbit of a hydrogen atom is given by:

State and explain what physical quantity is represented by the constant K.

In 1908, the physicist Friedrich Paschen first observed the photon emissions resulting from transitions from a level n to the level n = 3 of hydrogen and deduced their wavelengths were given by:

where A is a constant.

Justify this formula on the basis of the Bohr theory for hydrogen and determine an expression for the constant A.

Two coherent sources, A and B, which are in phase with each other, emit UV rays of wavelength 280 nm. The amplitude of waves from source B is twice that of source A.

A detector is placed at the point P where it is 1.68 μm from A and 2.24 μm from B. The centre axis is normal and a bisector to the straight line joining A and B.

With reference to the phase of the UV rays, deduce the magnitude of the detected signal at P and explain your reasoning.

Deduce, with suitable calculations, how the detected signal varies as the detector is moved from P to O.

Another ultraviolet source is positioned such that it is incident on a zinc plate. The zinc plate is situated within an evacuated chamber a few millimetres under a collecting plate, as shown in the diagram.

Photoelectrons are emitted from the zinc plate and move towards the positive collecting plate due to the potential difference, V, between the plates. When the potential difference, V, is varied, it is observed that the photoelectric current varies as shown on the graph. 

(i) Explain why the photoelectric current reaches a maximum value despite further increases in potential difference.

[2]

(ii) The battery connections are reversed so that the potential difference across the plates is negative. As a result, the photoelectrons are now repelled by the collecting plate, although some still make it across.  

Explain this observation. 

[2]

The zinc plate experiment is repeated using a different ultraviolet lamp which has a lower intensity and wavelength. 

(i) Sketch a second curve on the graph in part (a) to show the new variation between photoelectric current and potential difference.

[2]

(ii) Explain the difference between the two graphs.

[2]

The work function of zinc is 3.74 eV. 

Determine the wavelength of the ultraviolet light incident on the zinc plate.

When scientists develop climate models for planets other than Earth, the value of the solar constant  must be adjusted.

(i) Explain why is a constant and how it can be adjusted for different planets in the Solar System.

[2]

(ii) Outline two assumptions made in the calculation of solar constant.

[2]

Different climate models consider the energy absorbed by the Earth with and without an atmosphere.

(i) Explain why the average power absorbed per unit area of the Earth is less than in both models.

[2]

(ii) Draw an energy balance diagram to illustrate the model in which Earth has no atmosphere. 

[2]

(iii) Discuss one limitation of this model in terms of the greenhouse effect.

[1]

A simplified energy balance model of the Earth with an atmosphere is shown in the diagram.

In this model, the Earth's surface is assumed to be a black body radiator at constant temperature . It receives both solar radiation and radiation emitted from the atmosphere. The atmosphere is modelled as a body with albedo and average equilibrium temperature .

(i) Draw arrows to show the energy exchanges between the Earth's atmosphere and surface.

[1]

(ii) Determine the value of  used in this model.

[1]

(ii) Calculate the average equilibrium temperature of the Earth's surface . 

[4]

Carbon dioxide and water vapour are both known to be greenhouse gases.

Compare and contrast the roles of carbon dioxide and water vapour in the greenhouse effect. 

Suggest why the burning of fossil fuels may lead to an increase in global warming by the enhanced greenhouse effect.

A generator in a hydroelectric plant features a coil rotating in a magnetic field with a constant angular velocity.  

The power output varies over time for a generator rotating with a maximum power output of P₀ and a frequency of 20 Hz.

(i) Sketch the variation of power output with time for a single complete revolution of the coil. Indicate any key values on your axes.

[2]

(ii) Sketch the variation of voltage with time for a single complete revolution of the coil. Indicate any key values on your axes.

[2]

Using Faraday's Law, show that the new power output is 16P₀ if the frequency of the rotation of the coil increases to 80 Hz. 

You may use the following equation

A graph showing the variation in power over time for a different hydroelectric generator is shown below. 

In this generator, when the rate of flow of water from the dam doubles, the frequency of revolution of the coil also doubles.

On the diagram above, sketch a curve showing the new variation in power over time when the flow rate halves.

The braking system of the hydroelectric generator also utilises electromagnetic induction.

The components of the electromagnetic braking system are shown in the diagram. A metal disc is attached to the rotating axle of a vehicle. An electromagnet is mounted with its pole pieces placed on either side of the rotating disc, but not touching it. 

When the brakes are applied, a direct current is passed through the coil of the electromagnet and the disc slows down.

Explain, with reference to appropriate laws of electromagnetic induction, how this design can produce a braking effect.

A conventional braking system has friction pads that are brought into contact with a moving metal surface when the vehicle is to be slowed down. 

Suggest one advantage and one disadvantage of an electromagnetic brake compared to a conventional brake.

The principle of mutual induction is used in the transmission of alternating current from a hydroelectric power plant. An arrangement of coils in two separate circuits, P and Q, is shown in the diagram.

When the switch is closed there is a current in the coil in circuit P. The current is in a clockwise direction as viewed from position O. Circuit Q is also viewed from position O. 

Outline how Lenz’s law predicts the direction of the induced current when the switch is opened and again when it is closed.

In a comparison of two stars, A and B, the following data was collected

Surface temperature of star A = 25 000 K

Surface temperature of star B = 4300 K

The radius of star B was determined to be 1.1 × 10⁵ times larger than the radius of star A.

(i) Outline what is meant by the luminosity of a star.

[1]

(ii) Calculate the ratio of the luminosity of star B to the luminosity of star A.

[3]

Determine the wavelengths of light for which the maximum rate of emission occurs from stars A and B.

The graph shows the variation of rate of emission against wavelength for the Sun.

On the graph, sketch the variation of rate of emission against wavelength for stars A and B.

Under the right conditions, four hydrogen nuclei can fuse to make a helium nucleus in a process known as the proton–proton cycle.    

Show that 4 × 10^–12 J of energy is released as a result of the fusion of four hydrogen nuclei.

Fusion occurs naturally in the core of stars.

Explain why very high densities of matter and very high temperatures are needed to bring about and maintain nuclear fusion in stars.

While on the main sequence, the Sun maintains a constant luminosity of 3.86 × 10²⁶ W. It is predicted that the Sun will spend a total of 10¹⁰ years in this phase of its evolutionary cycle. 

Show that the Sun will convert a total mass of 2 × 10²⁹ kg of hydrogen into helium during its time on the main sequence. 

One day, the Sun will leave the main sequence and move on to the next stage of its evolutionary cycle.

Discuss what will happen to the Sun.

In your answer, you should outline

• the conditions that will initiate this change

• the nuclear processes that will occur 

• the physical changes that the Sun will undergo.

The gravitational field strength on the Moon's surface is 1.63 N kg^–1. It has a diameter of 3480 km.  

(i) Calculate the mass of the Moon.

[2]

(ii) Outline an assumption made in this calculation.

[1]

A rocket of mass 2.00 × 10⁶ kg travels from the Earth to the Moon. The first fuel tank burns enough propellant to provide thrust for the first 124 seconds and allows the rocket to accelerate from launch at a constant rate of 5.25 m s^–2.

The mass of the Earth is 5.97 × 10²⁴ kg and the mean radius is 6370 km.

(i) Calculate the work done by the rocket during the first 124 seconds after launch.

[3]

(ii) Outline an assumption made in this calculation.

[1]

In reality, less work is required to move the rocket away from the Earth's gravitational field than the value calculated in part (a).

(i) Discuss a possible reason for the difference in value.

[2]

(ii) The goal of the mission is to release a spacecraft from the rocket that will achieve a stable orbit around the Moon.

Explain why no work is done by the spacecraft when it maintains a stable orbit around the Moon.

[2]

The distance between the centre of the Earth and the centre of the Moon is 385 000 km. At a point along the rocket's journey, there is a point where the resultant gravitational field strength is zero.

Calculate the distance from the Earth where there is no resultant gravitational field strength acting on the rocket.

The gravitational field strength lines between the Earth and the Moon can be represented as shown in the diagram.

Point P is the neutral point between the Earth and the Moon where there is no resultant gravitational field.

Sketch the equipotential lines between the Earth and the Moon.

Calculate the gravitational potential at the surface of the Moon in terms of the gravitational potential on the surface of the Earth.