Feb/March 2017

Which expression has SI base units that are the same as those of pressure?

SI units

A firework at rest bursts into three fragments. The masses and velocities of the three fragments immediately after the explosion are shown. What are speed $v_1$ and speed $v_2$?

Linear momentum and its conservation

A spherical object travels through water at constant speed as it falls. Three forces act on the object. Which diagram, showing these three forces to scale, is correct?

Equilibrium of forces

A uniform metre rule with weight $2.0\,\text{N}$ is supported on a pivot at the $60\,\text{cm}$ mark. A $4.0\,\text{N}$ load is hung from one end, so that the rule turns around the pivot. When the rule is horizontal, what is the resultant moment about the pivot?

Turning effects of forces

The upward forces from the ground acting on a van that is stationary are shown. The van is $2.50\,\text{m}$ long, with the wheels $0.600\,\text{m}$ from the front of the van and $0.400\,\text{m}$ from the rear of the van. How far horizontally is the van’s centre of gravity from the front of the van?

Turning effects of forces

An object is suspended using two cords wrapped around two rods, as illustrated. The object is in equilibrium under the action of the forces $F_1$ and $F_2$. The object has a weight of $10\,\text{N}$. Friction between the rods and the cords is negligible. Angle $\theta$ is $90^{\circ}$. Which row in the table gives an angle $\theta$ of $90^{\circ}$?

Equilibrium of forces

Which force is produced solely by a difference in pressure?

Density and pressure

A process has a total energy input $E_{in}$, with part of it being converted into useful energy output $U$ and the rest being transferred to wasted energy $W$. What efficiency does the process have?

Energy conservation

A gas is trapped in a cylinder that has a frictionless piston fitted to it. At the start, the gas occupies a volume $V_1$ and is in equilibrium with the external pressure $p$. The gas is then heated gradually so that it expands while the pressure remains constant, forcing the piston to move back until the gas volume has risen to $V_2$. How much work is done by the gas in this expansion?

Energy conservation

A projectile is launched at an angle to the ground. At a particular moment, the projectile's horizontal velocity is $23.0\,\text{m s}^{-1}$ and its vertical velocity is $-10.1\,\text{m s}^{-1}$. What is the projectile's speed at this moment?

Scalars and vectors

A car with a mass of $1400\,\text{kg}$ is moving along a straight, level road at a steady speed of $25\,\text{m s}^{-1}$. The engine’s output power is $30\,\text{kW}$. The car then moves uphill on a slope of $2^\circ$ to the horizontal, while still keeping the same steady speed. What is the output power of the car’s engine when it is travelling up the slope?

Gravitational potential energy and kinetic energy

What approximate value would you give for the speed of sound in air?

Progressive waves

Wires X and Y are constructed from different metals. The Young modulus of wire X is twice the Young modulus of wire Y, and the diameter of wire X is half the diameter of wire Y. Both wires undergo the same strain and both obey Hooke’s law. What is the ratio $\dfrac{\text{tension in wire X}}{\text{tension in wire Y}}$?

Stress and strain

A $120\,\text{kN}$ load is applied to the top of a metal column. This causes the column’s length to decrease by $0.25\,\text{mm}$. The column follows Hooke’s law while it is being compressed. How much energy is stored in the compressed column?

Elastic and plastic behaviour

How does the amplitude of a wave relate to its intensity?

Progressive waves

Which statement concerning light waves and sound waves is correct?

Transverse and longitudinal waves

The diagram depicts two waves, R and S. For wave R, the amplitude is $8\,\text{cm}$ and the period is $30\,\text{ms}$. Determine the amplitude and the period of wave S.

Progressive waves

A source of sound waves is moving as illustrated. In which case would the stationary observer notice the greatest drop in the observed frequency?

Doppler effect for sound waves

M and N are each electromagnetic waves. The ratio $\dfrac{\text{wavelength of M}}{\text{wavelength of N}} = 10^5$. What might M and N be?

Electromagnetic spectrum

A progressive wave is incident normally on a flat reflector. The reflected wave overlaps the incident wave, so a stationary wave is produced. At an antinode, what might be the ratio $\dfrac{\text{displacement of the incident wave}}{\text{displacement of the reflected wave}}$ at any instant?

Stationary waves

A monochromatic plane wave, moving with speed $c$ and wavelength $\lambda$, is diffracted by a small aperture. The diagram shows successive wavefronts. How long will it take for some part of wavefront GH to reach point P?

Diffraction

To show two-source interference of light, a light beam is divided into two beams by two slits $0.50\,\text{mm}$ apart. The two beams fall on a laboratory wall that is $4.0\,\text{m}$ away. The wavelength of the light is $550\,\text{nm}$. What is the separation of two neighbouring interference fringes produced on the laboratory wall?

Interference

A horizontal force $H$ keeps a pendulum bob at rest. The diagram shows the three forces acting on the bob. The tension in the pendulum string is $T$. The weight of the pendulum bob is $W$. The string is inclined at an angle of $30^\circ$ to the vertical. Which statement is correct?

Equilibrium of forces

Two positive charges and one negative charge, each with the same magnitude, are placed at the vertices of an equilateral triangle. Which diagram gives the best representation of the electric field around the charges?

Scalars and vectors

A steady potential difference is maintained across two horizontal metal plates. An electrically charged oil droplet is kept stationary by the electric field between the plates. When part of the oil evaporates, the droplet’s mass decreases and it begins to accelerate. Its charge stays the same. In which direction will the droplet accelerate, and what change must be made to the separation of the plates to stop this acceleration?

Equilibrium of forces

An electric current $I$ appears in the list of formulae on page 3 as $I = Anvq$. What does each symbol stand for in the expression for an electric current in a metal wire?

Electric current

The potential difference across a resistor is $12\,\text{V}$. The current through the resistor is $2.0\,\text{A}$.\n\nA charge of $4.0\,\text{C}$ moves through the resistor.\n\nWhat is the energy transferred in the resistor and the time taken for the charge to move through the resistor?

Potential difference and power

A coil is made from $N$ turns of insulated copper wire wrapped around a cylindrical iron core whose diameter is $D$. The copper wire has diameter $d$. The resistivity of copper is $\rho$. Diameter $D$ is much greater than diameter $d$. What is the total resistance between the two ends of the coil?

Resistance and resistivity

Two cells are joined to a load resistor with resistance $3.0\,\Omega$. The electromotive force (e.m.f.) and internal resistance for each cell are shown. What current flows through the load resistor?

Practical circuits

Six resistors, each with resistance $R$, are arranged as illustrated. Their total resistance is $66\,\text{k}\Omega$. Determine the value of $R$.

Resistance and resistivity

A potential divider is made up of two resistors with resistances $R_1$ and $R_2$ joined in series across a source of potential difference $V_{in}$. The p.d. across $R_1$ is $V_{out}$. What alterations to $R_1$ and to $R_2$ would make $V_{out}$ larger?

Potential dividers

Which row gives the relative ionising power and the relative penetration power per unit length in air for $\alpha$-particles and $\gamma$-rays?

Atoms, nuclei and radiation

A sodium-21 nucleus, $^{21}_{11}\text{Na}$, undergoes decay to produce a different nucleus made up of 10 protons and 11 neutrons. Which leptons are released from the sodium-21 nucleus in this decay?

Atoms, nuclei and radiation

A student is examining an electrical signal with a cathode-ray oscilloscope (c.r.o.). The signal has a frequency of $50\,\text{kHz}$. Which time-base setting should be selected on the oscilloscope?

Practical circuits

A neutron undergoes decay to produce a proton. Which particle does not take part in the decay process?

Atoms, nuclei and radiation

A student wants to determine a distance of about $10\,\text{cm}$ with a precision of $0.01\,\text{cm}$. Which measuring instrument ought to be used?

Errors and uncertainties

An aircraft, starting from rest on a runway, reaches a speed of $85\,\text{km h}^{-1}$ over a distance that does not exceed $1.20\,\text{km}$. What minimum constant acceleration is required for the aircraft?

Equations of motion

A radio-controlled toy car moves in a straight line for $15\,\text{s}$. The graph shows how the velocity $v$ of the car changes with time $t$. What is the average velocity of the toy car for the journey represented by the graph?

Equations of motion

On Pluto, the acceleration of free fall is $0.66\,\text{m s}^{-2}$. A certain object weighs $6.0\,\text{N}$ on Earth. What would its weight be on Pluto?

Momentum and Newton's laws of motion

Water emerges from a pipe and strikes a wall. As the jet impacts the wall, its horizontal velocity is $v$ and its cross-sectional area is $A$. The water has density $\rho$. The water does not bounce back from the wall. What force is exerted on the wall by the water?

Momentum and Newton's laws of motion

Complete Fig. 1.1 by placing a tick (✓) in the correct column to show whether each listed quantity is a scalar or a vector.

Equilibrium of forces

State what the principle of conservation of momentum says.

Linear momentum and its conservation

State the meaning of velocity.

Equilibrium of forces

State the meaning of the Doppler effect.

Doppler effect for sound waves

An electron moves in a straight line through a vacuum at a constant speed of $1.5 \times 10^{7}\,\text{m s}^{-1}$. It enters a uniform electric field at point A, as shown in Fig. 5.1. It keeps travelling in the same direction until the electric field brings it to rest at point B. The distance AB is $2.0\,\text{cm}$.

Equations of motion

Three resistors with resistances $R_1$, $R_2$ and $R_3$ are arranged as in Fig. 6.1. The current through the resistor network is $I$ and the potential difference across it is $V$. Show that the overall resistance $R$ of the network is given by the equation $\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$.

Potential difference and power

A bismuth-212 nucleus $\left(^{212}_{83}\text{Bi}\right)$ undergoes decay by emitting an $\alpha$-particle together with $\gamma$-radiation.

Atoms, nuclei and radiation

Define the gravitational potential at a point.

Gravitational potential

State what the term photon means.

Energy levels in atoms and line spectra

Use band theory to explain why the resistance of an intrinsic semiconductor falls as temperature rises, unlike the resistance of a copper wire.

Energy levels in atoms and line spectra

Define the binding energy of a nucleus.

Mass defect and nuclear binding energy

The first law of thermodynamics may be written as $\Delta U = q + w$. Say what the symbols $+\Delta U$, $+q$ and $+w$ mean in this equation.

The first law of thermodynamics

One end of a uniform beam is clamped in position. A metal block of mass $m$ is attached to the free end, so the beam bends, as illustrated in Fig. 3.1. The block is then given a small vertical displacement and released, after which it oscillates with simple harmonic motion. The acceleration $a$ of the block is described by $a = -\frac{k}{m}x$, where $k$ is a constant for the beam and $x$ is the vertical displacement of the block from its equilibrium position.

Damped and forced oscillations, resonance

Explain the main principles used to generate ultrasound waves for medical applications.

Production and use of ultrasound

State three advantages that an optic fibre has over a metal wire when carrying a signal.

Characteristics of alternating currents

State one shared feature and one difference between the electric field lines and the gravitational field lines around an isolated positively charged metal sphere.

Electric field of a point charge

With a labelled diagram, describe the arrangement of a metal-wire strain gauge.

Electric potential

State what the term magnetic field means.

Force on a moving charge

Fig. 9.1 shows an ideal transformer.

Electromagnetic induction