Oct/Nov 2016

What is the order of magnitude of the Young modulus for a metal like copper?

Stress and strain

A beach-ball is dropped straight down from a high hotel window. Air resistance is not negligible. Which graph shows how the acceleration $a$ of the ball varies with time $t$?

Non-uniform motion

The mass of a car is $m$. To produce an acceleration of $a$ for the car, a person must push it with force $F$. To produce an acceleration of $3a$, the person must push the car with force $2F$. Which expression gives the constant resistive force opposing the motion of the car?

Momentum and Newton's laws of motion

A box is depicted at rest on the ground. Newton’s third law shows that there are four forces of equal magnitude. These forces are called P, Q, R and S. P and Q act on the box, whereas R and S act on the Earth. To make the diagram clearer, the forces are drawn a little apart. Which statement about the forces is correct?

Momentum and Newton's laws of motion

Two spheres move in the same straight line with velocities $u_1$ and $u_2$. They collide, and afterwards their velocities are $v_1$ and $v_2$. Which collision is not elastic?

Linear momentum and its conservation

A submarine is fitted with circular windows with a diameter of $0.30\,\text{m}$. These windows can withstand a highest external pressure of $660\,\text{kPa}$ before cracking. What minimum external force is required to crack the windows?

Density and pressure

There are four beams of equal length, and each beam has three forces acting on it. Which beam has both zero resultant force and zero resultant torque acting on it?

Equilibrium of forces

An air-conditioning unit is held up by a rigid beam PQ, as illustrated. Which diagram shows the directions of the horizontal and vertical forces acting at the two ends of the beam?

Equilibrium of forces

A hydroelectric power station converts the gravitational potential energy of water into electrical energy. In one specific power station, the mass of water passing each unit time is $1.5 \times 10^5\,\text{kg s}^{-1}$. The water drops through a vertical distance of $120\,\text{m}$. The electrical power output is $100\,\text{MW}$. Calculate the efficiency of the power station.

Gravitational potential energy and kinetic energy

A heat engine changes thermal energy into mechanical work. It absorbs thermal energy $Q_{\text{in}}$ from a heat source and releases thermal energy $Q_{\text{out}}$ to a heat sink, thereby producing useful work $W$. Calculate the efficiency of this engine.

Energy conservation

A truck with mass $500\,\text{kg}$ starts from rest at the top of a stretch of track that is $400\,\text{m}$ long and $30\,\text{m}$ high, as shown. A frictional force of $250\,\text{N}$ acts on the truck for the whole journey. What is the final speed of the truck?

Gravitational potential energy and kinetic energy

For two point charges $q_1$ and $q_2$ separated by a distance $r$, the force $F$ is described by the equation $F = \dfrac{k q_1 q_2}{r^2}$ in which $k$ is a constant. What are the SI base units of $k$?

Electric current

What condition has to be satisfied for the work done by an expanding gas to equal $p\Delta V$, with $p$ as the gas pressure and $\Delta V$ as the change in volume?

Density and pressure

A metal wire is pulled until it reaches breaking point, and a force-extension graph is drawn. Which graph shows the elastic region, the plastic region and the area that represents the work done in stretching the wire until it breaks correctly labelled?

Elastic and plastic behaviour

A copper wire is suspended vertically from a fixed support. A load is hung from the bottom end of the wire, causing an extension $x$. The wire follows Hooke’s law. Which single change would produce an extension of $2x$?

Stress and strain

The table lists the wavelengths of five electromagnetic waves. Which row correctly gives the principal radiation for each of these wavelengths?

Electromagnetic spectrum

The diagram illustrates an experiment used to create a stationary wave in an air column. A tuning fork positioned above the column oscillates and generates a sound wave. By changing the amount of water in the tube, the length of the air column can be adjusted. The tube is first filled, and then the water is permitted to flow out. The first two stationary waves are formed when the air column lengths are $0.14\,\text{m}$ and $0.42\,\text{m}$. What is the wavelength of the sound wave?

Stationary waves

The graph illustrates how the displacement $X$ of a gas molecule changes with time as a continuous sound wave travels through a gas. The speed of sound in the gas is $330\,\text{m s}^{-1}$. Every graph below uses the same zero time as the graph above. What is the displacement-time graph for a molecule that is $0.165\,\text{m}$ farther from the source of the sound?

Progressive waves

An ambulance’s warning signal has a frequency of $600\,\text{Hz}$. The speed of sound is $330\,\text{m s}^{-1}$. The ambulance moves at a constant velocity of $25\,\text{m s}^{-1}$ towards an observer. What overall change in the observed frequency occurs from when the ambulance is far behind the observer to when it is far in front of the observer?

Doppler effect for sound waves

Diagrams X and Y illustrate water waves moving around an obstacle and passing through a gap. The thick lines act as barriers to the waves, and each thin line shows a wavefront. Which statement is correct?

Diffraction

The diagram illustrates a long rope that is fixed at one end. The free end is then moved up and down, creating a stationary wave. Determine the phase difference between the oscillations at X and Y?

Stationary waves

A diffraction grating is employed to determine the wavelength of monochromatic light. The slit spacing in the grating is $1.15 \times 10^{-6}\,\text{m}$. The angle between the first order diffraction maxima is $60.0^\circ$, as illustrated in the diagram. What is the wavelength of the light?

The diffraction grating

An aircraft is able to travel with velocity $X$ in still air. If it is flying in wind, its velocity relative to the ground is $Y$. Which vector diagram illustrates the magnitude and direction of the wind velocity $W$?

Scalars and vectors

Which path indicates a possible route taken by an electron in the electric field shown?

Momentum and Newton's laws of motion

The diagram depicts an electric field pattern produced by two positive and two negative point charges, each with equal magnitude, positioned at the four corners of a square. In which direction does the force on an electron at point $X$ act?

Scalars and vectors

Two broad horizontal metal plates are spaced $4\,\text{mm}$ apart. The lower plate is held at a potential of $-80\,\text{V}$. What potential must be applied to the upper plate so that the electric field between the plates has a strength of $60\,000\,\text{V m}^{-1}$ upwards?

Potential difference and power

An electric kettle is labelled $3.10\,\text{kW}$. It operates from an electrical supply of $240\,\text{V}$. What current flows through the kettle, and what is its electrical resistance while it is operating?

Potential difference and power

A thick copper wire and a thin copper wire are connected in series with a cell, as shown. What is much smaller in the thick wire than in the thin wire?

Resistance and resistivity

What is a representative order-of-magnitude value for copper’s resistivity?

Resistance and resistivity

In the circuit diagram, the ammeter gives a zero reading. The four resistors are of different resistance values $R_1$, $R_2$, $R_3$ and $R_4$. Which equation is correct?

Kirchhoff's laws

In the circuit diagram, currents $I_1$, $I_2$, $I_3$, $I_4$ and $I_5$ are shown in different branches. Which equation is correct?

Kirchhoff's laws

What is meant by a proton?

Fundamental particles

Which descriptions correctly apply to a $\gamma$-ray and a $\beta^-$ particle?

Atoms, nuclei and radiation

The voltmeter produces readings that are greater than the actual values, and it has a systematic error that depends on the voltage. Which graph represents the calibration curve of the voltmeter?

Errors and uncertainties

Within a radioactive decay chain, three decays happen one after another, and each one emits a particle. The first decay emits a $\beta^-$ particle. The second decay emits an $\alpha$ particle. The third decay emits another $\beta^-$ particle. Nuclides $P$ and $S$ are then compared. Which statement is correct?

Atoms, nuclei and radiation

A student employs a cathode-ray oscilloscope (c.r.o.) to determine the period of a signal. She adjusts the time-base on the c.r.o. to $5\ \text{ms cm}^{-1}$ and sees the trace shown. The trace measures $10.0\ \text{cm}$ in length. Determine the period of the signal.

Practical circuits

A cyclist moves along a raised horizontal track. At the track’s end, he leaves it travelling horizontally through the air and lands on a track that is vertically $2.0\ \text{m}$ below. While in the air, the cyclist covers a horizontal distance of $6.0\ \text{m}$. Air resistance is negligible. Determine the horizontal velocity $v$ of the cyclist at the end of the upper track?

Equations of motion

An astronaut is on the Moon, where there is no air resistance, and throws a ball. The ball starts with a vertical velocity component of $8.00\ \text{m s}^{-1}$ and a horizontal velocity component of $4.00\ \text{m s}^{-1}$, as shown. The acceleration of free fall on the Moon is $1.62\ \text{m s}^{-2}$. What is the ball’s speed $9.00\ \text{s}$ after it has been thrown?

Equations of motion

A car moves with constant velocity. When $t = 0$, the driver notices an obstacle in the road and then applies the brakes until the car comes to rest. The graph shows how the car’s velocity varies with $t$. What distance does the car cover in the $5.0\ \text{s}$ after the driver notices the obstacle?

Equations of motion

A car is at rest at traffic lights. When the lights turn green, the driver depresses the accelerator pedal sharply. The resulting horizontal force on the car changes with time as shown. Which graph shows how the car’s speed varies with time?

Non-uniform motion

Concrete has a density of $2400\,\text{kg m}^{-3}$. What mass of concrete would occupy a rectangular space measuring $8.0\,\text{cm} \times 90\,\text{cm} \times 110\,\text{cm}$?

Density and pressure

To allow a train to halt safely, it always passes a signal with a yellow light before it encounters a signal with a red light. At the yellow light, drivers apply the brake, causing a steady deceleration so that the train stops exactly at the red light. The separation between the red and yellow lights is $x$. If the train's speed is raised by $20\%$, while its deceleration remains unchanged, what is the least possible distance between the lights?

Equations of motion

Two frictionless trolleys travel towards one another on the same horizontal straight line. Their masses and velocities are given. The trolleys collide and remain joined together. What is the velocity of the trolleys after the collision?

Linear momentum and its conservation

A bullet of mass $8.0\,\text{g}$ has a speed of $300\,\text{m s}^{-1}$ before it strikes a target. It then comes to rest after $100\,\mu\text{s}$. What is the average force exerted on the bullet by the target?

Momentum and Newton's laws of motion

A low-mass ball is descending vertically through air. The graph shows how the resistive force $F_R$ varies with time $t$. At what times is the ball’s speed zero, when is its speed greatest, and when is its acceleration zero?

Non-uniform motion

Which diagram most accurately represents the forces acting on a ball that is falling through a liquid at constant velocity?

Equilibrium of forces

To open a jar, a smallest torque of $20\,\text{N m}$ has to be exerted on its lid. The lid has a radius of $4.0\,\text{cm}$. What is the least force $F$ that must act on each side of the lid so that it opens?

Turning effects of forces

The diagram illustrates a car’s brake system. The pipes contain incompressible liquid. When a force is exerted on the brake pedal, the pressure in the liquid rises and produces a force on each of the four wheels. The area of the piston attached to the brake pedal is $8\,\text{cm}^2$. The area of each piston attached to the brakes is $12\,\text{cm}^2$. The foot applies a force of $800\,\text{N}$ to the brake pedal. What force is applied to each brake?

Density and pressure

A rigid cross-shaped arrangement with four arms PO, SO, QO and RO, each measuring $1.00\,\text{m}$ in length, is hinged at O. As illustrated, forces act at the ends of the arms and at the midpoints of the arms. What is the magnitude of the resultant moment on the structure about O?

Turning effects of forces

At the surface of a planet, $30\,\text{J}$ of work is done against gravity in lifting a mass of $1.0\,\text{kg}$ by a height of $10\,\text{m}$. How much work is needed to lift a mass of $4.0\,\text{kg}$ by a height of $5.0\,\text{m}$ on this planet?

Gravitational potential energy and kinetic energy

A car's speed rises from $10\,\text{m s}^{-1}$ to $15\,\text{m s}^{-1}$, causing its kinetic energy to increase by $E_1$. At a later time, its speed then rises from $15\,\text{m s}^{-1}$ to $25\,\text{m s}^{-1}$, causing its kinetic energy to increase by $E_2$. Find the ratio $\dfrac{E_2}{E_1}$?

Energy conservation

The speed $v$ of sound in a gas is described by $v = \sqrt{\frac{\gamma P}{\rho}}$, where $P$ represents the gas pressure, $\rho$ represents its density, and $\gamma$ is a constant. What are the SI base units of $\gamma$?

SI units

A car moves up a slope at a steady speed of $25\,\text{m s}^{-1}$. The engine-driven wheels exert a forward force of $3000\,\text{N}$. A drag force from air resistance and friction acts with a magnitude of $2100\,\text{N}$. The component of the car’s weight down the slope is $900\,\text{N}$. At what rate is thermal energy being dissipated?

Energy conservation

Which force-extension graph represents plastic deformation of a sample of material?

Elastic and plastic behaviour

An object of weight $10\,\text{kN}$ is carried equally by four solid steel rods. Each rod has a length of $2.0\,\text{m}$ and a cross-sectional area of $250\,\text{mm}^2$. As a result of the object's weight, the rods shorten by $0.10\,\text{mm}$. Determine the Young modulus of steel.

Stress and strain

A liquid carries high-frequency sound waves of frequency $2.0\,\text{MHz}$ at a speed of $2.0\,\text{km s}^{-1}$. What is the minimum separation between a compression and a rarefaction (expansion) in the liquid?

Transverse and longitudinal waves

A transverse progressive wave with wavelength $\lambda$ is formed on a stretched string. The graph illustrates how displacement $y$ changes with distance $x$ at one specific moment. At $x = \dfrac{\lambda}{8}$, the displacement is $y_1$. What are the next two values of $x$ for which the displacement $y$ once again has the value $y_1$?

Progressive waves

A man beside a train that is at rest hears a sound of frequency $400\,\text{Hz}$ coming from the train’s horn. The train then travels directly away from the man and blows its horn when it is moving at a speed of $50\,\text{m s}^{-1}$. The speed of sound is $340\,\text{m s}^{-1}$. What is the change in frequency of the sound heard by the man between the two cases?

Doppler effect for sound waves

A stationary wave exists on a stretched string. The diagram shows the string at one moment when the string’s displacement is at its greatest. The wave has frequency $250\,\text{Hz}$. Point $P$ on the string has a vertical displacement of $-1.0\,\text{mm}$. What is the vertical displacement of point $P$ after $5\,\text{ms}$?

Stationary waves

Visible interference fringes are formed with light from a double slit. At first, the light emerging from each slit has the same intensity. The intensity of the light coming from one slit is then decreased. What effect does this have on the interference pattern?

Interference

Monochromatic light with wavelength $450\,\text{nm}$ is passed through two parallel slits that are $0.30\,\text{mm}$ apart. A screen is positioned $2.0\,\text{m}$ away, where bright fringes are formed. What is the spacing between the bright fringes on the screen?

Interference

A microwave transmitter is positioned a fixed distance away from a flat reflecting surface, as illustrated. A microwave detector is then moved at a constant speed along a straight path from $X$ to $Y$. A sequence of intensity maxima and minima is recorded. The separation between neighbouring maxima is $1.5\,\text{cm}$. What is the frequency of the microwave radiation?

Interference

An object starting from rest and accelerating at a constant acceleration $a$ can be described by the equation below. $v^2 = 2as$. Which row states the quantities represented by the symbols $v$ and $s$?

Equations of motion

Two circular metal plates, $X$ and $Y$, are parallel to each other. Each plate has a diameter of $18\,\text{cm}$, and the gap between the plates is $9.0\,\text{cm}$. A potential difference of $9.0\,\text{V}$ is applied across them. Point $P$ lies $6.0\,\text{cm}$ from the surface of plate $X$ and $3.0\,\text{cm}$ from the surface of plate $Y$. Determine the electric field strength at $P$.

Potential difference and power

An oil drop of mass $m$ and charge $q$ is suspended motionless in an electric field between two parallel horizontal plates separated by distance $d$, as shown. The potential difference across the plates is $V$, and the acceleration of free fall is $g$. What is the charge-to-mass ratio $\frac{q}{m}$ for the oil drop?

Potential difference and power

The diagram illustrates a junction in a circuit at which three wires $P$, $Q$ and $R$ join. The currents in $P$ and $Q$ are $1\,\text{A}$ and $3\,\text{A}$, respectively, in the directions indicated. What quantity of charge flows past a fixed point in wire $R$ during a time of $5\,\text{s}$?

Electric current

A current of $2.0\,\text{A}$ flows through a wire for $1.0\,\text{hour}$. How many electrons pass a point in the wire during this interval?

Electric current

The diagram illustrates an electric circuit in which the external resistor has resistance $2R$ while the source has internal resistance $R$. What is the ratio $\frac{\text{power in internal resistance}}{\text{power in external resistor}}$?

Potential difference and power

The graph illustrates how the current $I$ in components $X$, $Y$ and $Z$ changes with potential difference $V$. Which row correctly names the components?

Resistance and resistivity

Four statements concerning either potential difference or electromotive force are given. 1. It is the conversion of electrical energy into other forms. 2. It is the conversion of other forms of energy into electrical energy. 3. It is the energy transferred per unit charge to drive charge around a complete circuit. 4. It is the work done per unit charge by charge moving from one point to another. Which statements relate to potential difference and which relate to electromotive force?

Potential difference and power

For the circuit illustrated, a current of $3.0\,\text{A}$ flows through the $2.0\,\Omega$ resistor. Determine the current $I$ supplied by the power supply and the voltage $V$ across it.

Kirchhoff's laws

In the circuit shown below, P is a potentiometer with a total resistance of $10\,\Omega$ and Q is a fixed resistor with a resistance of $10\,\Omega$. The battery has an e.m.f. of $4.0\,\text{V}$ and negligible internal resistance. The voltmeter has a very high resistance. The slider on the potentiometer is shifted from X to Y, and a graph of voltmeter reading $V$ is drawn against slider position. Which graph is obtained?

Potential dividers

Nuclide $^{42}_{20}\text{Ca}$ is produced through $\beta^{-}$ decay. What are the nucleon (mass) number and proton (atomic) number of the unstable nuclide that decayed by $\beta^{-}$ emission to produce the calcium nuclide?

Atoms, nuclei and radiation

A cathode-ray oscilloscope (c.r.o.) shows a waveform as illustrated. The time gap between two neighbouring peaks of the waveform is $0.006\,\text{s}$. What is the c.r.o. time-base setting?

Practical circuits

Which diagram shows the structure of an antineutron?

Fundamental particles

The acceleration of free fall on Earth is stated as $(10 \pm 2)\,\text{m s}^{-2}$. Which of the following statements is correct?

Errors and uncertainties

An experiment is being used to find atmospheric pressure $P$ by applying the relation $P=\rho gh$, where $\rho=(13600\pm100)\,\text{kg m}^{-3}$, $g=(9.81\pm0.02)\,\text{m s}^{-2}$ and $h=(0.762\pm0.005)\,\text{m}$. What is the value of $P$, together with its uncertainty, expressed to an appropriate number of significant figures?

Errors and uncertainties

A lorry is moving at a steady speed, then it decelerates until it comes to rest. Which graph shows the distance travelled by the lorry as time changes?

Equations of motion

The graph shows the vertical velocity of a parachutist during the first $20\,\text{s}$ of her jump. Approximately how far does she descend before opening the parachute?

Non-uniform motion

A girl is bouncing on a trampoline. Which graph shows how the girl’s velocity $v$ changes with time $t$?

Equations of motion

For a metal such as copper, what order of magnitude would you give for the Young modulus?

Stress and strain

A beach-ball drops straight down from a window high up in a hotel. Air resistance is not negligible. Which graph shows how the acceleration $a$ of the ball varies with time $t$?

Non-uniform motion

The mass of a car is $m$. A person must apply a force $F$ to the car so that it accelerates at $a$. The person must apply a force $2F$ to the car so that it accelerates at $3a$. Which expression represents the constant resistive force acting against the car's motion?

Momentum and Newton's laws of motion

A box is illustrated at rest on the ground. According to Newton’s third law, four forces of equal magnitude are present. These forces are labelled P, Q, R and S. Forces P and Q act on the box. Forces R and S act on the Earth. To make the diagram easier to follow, the forces are drawn with small gaps between them. Which statement about the forces is correct?

Momentum and Newton's laws of motion

Two spheres move along the same straight line with velocities $u_1$ and $u_2$. They collide, and after the collision their velocities are $v_1$ and $v_2$. Which collision is not elastic?

Linear momentum and its conservation

A submarine is fitted with circular windows with diameter $0.30\,\text{m}$. These windows may withstand a greatest external pressure of $660\,\text{kPa}$ before they crack. Calculate the least external force required to crack the windows?

Density and pressure

Each of four beams is of equal length and has three forces applied to it. Which beam has both zero resultant force and zero resultant torque acting?

Equilibrium of forces

An air-conditioning unit is held up by a rigid beam PQ, as illustrated. Which diagram indicates the directions of the horizontal and vertical forces acting at the two ends of the beam?

Equilibrium of forces

A hydroelectric power station converts the gravitational potential energy of water into electrical energy. In one specific power station, the mass of water passing each unit time is $1.5 \times 10^5\,\text{kg s}^{-1}$. The water descends by a vertical distance of $120\,\text{m}$. The electrical power produced is $100\,\text{MW}$. What is the efficiency of the power station?

Gravitational potential energy and kinetic energy

A heat engine changes thermal energy into mechanical work. It receives thermal energy $Q_{\text{in}}$ from a heat source and transfers thermal energy $Q_{\text{out}}$ to a heat sink, so that useful work $W$ is produced. State the efficiency of this engine?

Energy conservation

A truck with mass $500\,\text{kg}$ starts from rest at the top of a stretch of track that is $400\,\text{m}$ long and $30\,\text{m}$ high, as shown. The frictional force on the truck is $250\,\text{N}$ for the whole journey. Determine the truck's final speed.

Gravitational potential energy and kinetic energy

For two point charges $q_1$ and $q_2$ separated by a distance $r$, the force $F$ is described by the equation $F = \frac{k q_1 q_2}{r^2}$, where $k$ is a constant. What are the SI base units of $k$?

SI units

Under what condition is the work done by an expanding gas equal to $p\Delta V$, where $p$ is the pressure of the gas and $\Delta V$ is the change in its volume?

Energy conservation

A metal wire is pulled until it reaches breaking point, and a force-extension graph is drawn. Which graph is labelled correctly with the elastic region, the plastic region, and the area that shows the work done in stretching the wire until it breaks?

Elastic and plastic behaviour

A copper wire is suspended vertically from a stationary support. A load is fixed to the bottom end of the wire, causing an extension $x$. The wire follows Hooke’s law. Which one change would produce an extension of $2x$?

Stress and strain

The table gives the wavelengths of five electromagnetic waves. Which row correctly matches the principal radiation for each of these wavelengths?

Electromagnetic spectrum

The diagram illustrates an experiment for creating a stationary wave in an air column. A tuning fork above the column vibrates, generating a sound wave. The length of the air column may be changed by adjusting the amount of water in the tube. The tube is filled and then the water is allowed to drain from it. The first two stationary waves are produced when the air column lengths are $0.14\,\text{m}$ and $0.42\,\text{m}$. What wavelength does the sound wave have?

Stationary waves

The graph illustrates how the displacement $X$ of a gas molecule changes with time as a continuous sound wave travels through a gas. The speed of sound in the gas is $330\,\text{m s}^{-1}$. All the graphs below use the same zero time as the graph above. What is the displacement-time graph for a molecule that is $0.165\,\text{m}$ farther from the source of the sound?

Progressive waves

An ambulance emits a warning signal with a frequency of $600\,\text{Hz}$. The speed of sound is $330\,\text{m s}^{-1}$. The ambulance moves towards an observer at a steady velocity of $25\,\text{m s}^{-1}$. What total change in the observed frequency occurs from the moment when the ambulance is far behind the observer to the moment when it is far ahead of the observer?

Doppler effect for sound waves

Diagrams X and Y illustrate water waves travelling around an obstacle and passing through a gap. The thick lines act as barriers for the waves, and each thin line shows a wavefront. Which statement is correct?

Diffraction

The diagram depicts a long rope secured at one end. The free end is moved vertically, producing a stationary wave. What is the phase difference between the oscillations at X and Y?

Stationary waves

A diffraction grating is employed to determine the wavelength of monochromatic light. The separation of the slits in the grating is $1.15 \times 10^{-6}\,\text{m}$. The angle between the first order diffraction maxima is $60.0^\circ$, as illustrated in the diagram. Calculate the wavelength of the light.

The diffraction grating

An aeroplane is able to travel at velocity $X$ in still air. In windy conditions, its velocity relative to the ground is $Y$. Which vector diagram represents the magnitude and direction of the wind velocity $W$?

Scalars and vectors

Which trajectory could an electron follow in the electric field shown?

Momentum and Newton's laws of motion

The diagram illustrates an electric field pattern produced by two positive and two negative point charges, each with equal magnitude, positioned at the four corners of a square. In which direction does the force act on an electron at point $X$?

Scalars and vectors

A pair of large horizontal metal plates has a separation of $4\,\text{mm}$. The lower plate is at a potential of $-80\,\text{V}$. What potential should be applied to the upper plate to produce an upward electric field of strength $60\,000\,\text{V m}^{-1}$ in the region between the plates?

Potential difference and power

An electric kettle is labelled $3.10\,\text{kW}$. It operates from an electrical supply of $240\,\text{V}$. What current flows in the kettle and what is the kettle’s electrical resistance when it is operating?

Potential difference and power

A thick copper wire is joined in series to a thin copper wire with a cell, as illustrated. What is much smaller in the thick wire than in the thin wire?

Resistance and resistivity

What would be a representative order-of-magnitude value for the resistivity of copper?

Resistance and resistivity

In the circuit diagram, the ammeter shows a reading of zero. The four resistors have different resistances $R_1$, $R_2$, $R_3$ and $R_4$. Which equation is correct?

Potential dividers

In the diagram, the currents $I_1$, $I_2$, $I_3$, $I_4$ and $I_5$ are shown in separate branches of a circuit. Which equation is the correct one?

Kirchhoff's laws

What does the term proton mean?

Fundamental particles

Which descriptions are correct for a $\gamma$-ray and a $\beta^-$ particle?

Atoms, nuclei and radiation

A voltmeter produces measurements that are higher than the actual values, and it has a systematic error that changes with voltage. Which graph represents the calibration curve for the voltmeter?

Errors and uncertainties

Within a radioactive decay chain, three decays happen one after another, with a particle emitted at each step. The first decay emits a $\beta^-$ particle. The second decay emits an $\alpha$ particle. The third decay emits another $\beta^-$ particle. Nuclides $P$ and $S$ are compared. Which statement is correct?

Atoms, nuclei and radiation

A student is using a cathode-ray oscilloscope (c.r.o.) to determine the period of a signal. She adjusts the time-base on the c.r.o. to $5\,\text{ms cm}^{-1}$ and sees the trace shown below. The trace extends over $10.0\,\text{cm}$.\n\nWhat is the period of the signal?

Practical circuits

A cyclist moves by pedalling along an elevated horizontal track. At the track’s end, he continues horizontally into the air and lands on a track that is $2.0\,\text{m}$ lower vertically. While in the air, the cyclist covers a horizontal distance of $6.0\,\text{m}$. Air resistance is negligible. What is the horizontal velocity $v$ of the cyclist at the end of the upper track?

Equations of motion

An astronaut on the Moon, where there is no air resistance, throws a ball. The ball begins with a velocity that has a vertical component of $8.00\,\text{m s}^{-1}$ and a horizontal component of $4.00\,\text{m s}^{-1}$, as shown. The acceleration of free fall on the Moon is $1.62\,\text{m s}^{-2}$. Determine the speed of the ball $9.00\,\text{s}$ after it has been thrown?

Equations of motion

A car moves with constant velocity. At time $t = 0$, the driver spots an obstacle in the road and then applies the brakes until the car comes to rest. The graph shows how the velocity of the car varies with $t$. How far does the car travel in the $5.0\,\text{s}$ after the driver sees the obstacle?

Equations of motion

A car is at rest at traffic lights. When the traffic lights turn green, the driver pushes the accelerator down quickly. The horizontal resultant force acting on the car changes with time as shown. Which graph shows how the speed of the car varies with time?

Momentum and Newton's laws of motion