Engineering and Science Admissions Test (ESAT) Physics Module Syllabus

State the equations for kinetic energy and gravitational potential energy.

Kinetic energy: $E_{k} = \frac{1}{2}mv^{2}$. Gravitational potential energy: $E_{p} = mgh$.

Define work done by a force and give its formula.

Work done is energy transferred when a force moves its point of application: $W = Fs\cos\theta$, where $\theta$ is the angle between force and displacement. Units: joules (J).

State the principle of conservation of energy.

Energy cannot be created or destroyed, only transferred or transformed from one form to another; the total energy of a closed system remains constant.

Using energy conservation, derive the speed of an object that falls freely through height $h$ from rest.

$mgh = \frac{1}{2}mv^{2} \Rightarrow v = \sqrt{2gh}$.

Define power and give two formulas for it.

Power is the rate of energy transfer (work done per unit time): $P = \frac{W}{t} = \frac{E}{t}$. For motion at constant velocity: $P = Fv$. Units: watts (W).

Define efficiency and give its formula.

Efficiency is the fraction of input energy usefully transferred: $\text{efficiency} = \frac{\text{useful energy (or power) output}}{\text{total energy (or power) input}} \times 100\%$. It is always $< 100\%$ for real machines.

Define density and give its formula and SI units.

Density is mass per unit volume: $\rho = \frac{m}{V}$. SI units: $\mathrm{kg\,m^{-3}}$.

Define pressure and give its formula and SI unit.

Pressure is force per unit area acting perpendicular to a surface: $P = \frac{F}{A}$. SI unit: the pascal, $1\ \mathrm{Pa} = 1\ \mathrm{N\,m^{-2}}$.

Give the equation for pressure due to a column of fluid of height $h$.

$P = \rho g h$, where $\rho$ is fluid density, $g$ gravitational field strength and $h$ the depth below the surface.

Define electric current and state its formula and unit.

Current is the rate of flow of charge: $I = \frac{Q}{t}$. Unit: the ampere (A), where $1\ \mathrm{A} = 1\ \mathrm{C\,s^{-1}}$.

Define potential difference (voltage) and state its formula.

Potential difference is the energy transferred per unit charge between two points: $V = \frac{W}{Q}$. Unit: the volt, $1\ \mathrm{V} = 1\ \mathrm{J\,C^{-1}}$.

What is the elementary charge, and how is charge related to a number of electrons?

The elementary charge is $e = 1.6 \times 10^{-19}\ \mathrm{C}$. Total charge $Q = ne$, where $n$ is the number of electrons.

State Ohm's law and the equation linking voltage, current and resistance.

For an ohmic conductor at constant temperature, current is proportional to potential difference: $V = IR$, where $R$ is resistance in ohms ($\Omega$).

Give the formula for the resistance of a wire in terms of resistivity.

$R = \frac{\rho L}{A}$, where $\rho$ is resistivity ($\Omega\,\mathrm{m}$), $L$ is length and $A$ is cross-sectional area.

Write the formulas for total resistance of resistors in series and in parallel.

Series: $R_{\text{total}} = R_{1} + R_{2} + \dots$. Parallel: $\frac{1}{R_{\text{total}}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \dots$.

State three equations for electrical power dissipated in a component.

$P = IV = I^{2}R = \frac{V^{2}}{R}$. Electrical energy is then $E = Pt = IVt$.

State Kirchhoff's two circuit laws.

Current law: the sum of currents into a junction equals the sum out (conservation of charge). Voltage law: the sum of e.m.f.s around any loop equals the sum of potential differences (conservation of energy).

How do current and potential difference behave in series and parallel circuits?

Series: current is the same everywhere; voltage is shared (adds up) across components. Parallel: voltage is the same across each branch; current is shared (splits) between branches.

Describe the I-V characteristic of a filament lamp and why it is non-ohmic.

The graph is an S-shaped curve: as current increases the filament heats up, raising its resistance, so the gradient decreases. It is non-ohmic because resistance changes with temperature.

State the wave equation linking speed, frequency and wavelength.

$v = f\lambda$, where $v$ is wave speed ($\mathrm{m\,s^{-1}}$), $f$ is frequency (Hz) and $\lambda$ is wavelength (m). Also $f = \frac{1}{T}$ where $T$ is the period.

Distinguish transverse and longitudinal waves, giving an example of each.

Transverse: oscillations are perpendicular to the direction of energy transfer (e.g. light, water waves). Longitudinal: oscillations are parallel to energy transfer, with compressions and rarefactions (e.g. sound).

Define amplitude, wavelength and frequency of a wave.

Amplitude: maximum displacement from the rest position. Wavelength: distance between two adjacent points in phase (e.g. crest to crest). Frequency: number of complete waves passing a point per second (Hz).

Name the four wave behaviours and briefly define each.

Reflection: bouncing off a boundary. Refraction: change of direction due to a change in speed entering a new medium. Diffraction: spreading of waves through a gap or around an obstacle. Interference: superposition of two waves giving reinforcement or cancellation.

State the law of reflection.

The angle of incidence equals the angle of reflection ($\theta_{i} = \theta_{r}$), both measured from the normal, and the incident ray, reflected ray and normal lie in the same plane.

List the regions of the electromagnetic spectrum in order of increasing frequency.

Radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, gamma rays (increasing frequency and energy, decreasing wavelength).

What do all electromagnetic waves have in common, including their speed in a vacuum?

They are transverse, transfer energy, can travel through a vacuum, and all travel at the same speed in vacuum: $c = 3.0 \times 10^{8}\ \mathrm{m\,s^{-1}}$.

What is the audible frequency range for humans, and how does the speed of sound in air compare to its speed in solids?

Humans hear roughly $20\ \mathrm{Hz}$ to $20\,000\ \mathrm{Hz}$. Sound travels faster in solids than in liquids, and faster in liquids than in gases (it needs a medium and cannot travel through a vacuum).

Define specific heat capacity and give its equation.

Specific heat capacity is the energy needed to raise the temperature of $1\ \mathrm{kg}$ of a substance by $1\ \mathrm{K}$. Equation: $Q = mc\Delta\theta$, with units of $c$ being $\mathrm{J\,kg^{-1}\,K^{-1}}$.

Define specific latent heat and give its equation.

Specific latent heat is the energy needed to change the state of $1\ \mathrm{kg}$ of a substance with no temperature change: $Q = mL$. Units of $L$: $\mathrm{J\,kg^{-1}}$ (fusion for melting, vaporisation for boiling).

State the three combined gas laws (Boyle's, Charles's, Pressure law) and the ideal gas relation.

Boyle: $PV = \text{const}$ (constant $T$). Charles: $\frac{V}{T} = \text{const}$ (constant $P$). Pressure law: $\frac{P}{T} = \text{const}$ (constant $V$). Combined: $\frac{PV}{T} = \text{const}$, with $T$ in kelvin.

Name the three types of nuclear radiation and rank their penetrating and ionising power.

Alpha ($\alpha$): most ionising, least penetrating (stopped by paper). Beta ($\beta$): medium (stopped by a few mm of aluminium). Gamma ($\gamma$): least ionising, most penetrating (reduced by thick lead/concrete).

Define half-life of a radioactive isotope.

The half-life is the average time taken for half the radioactive nuclei in a sample to decay, or equivalently for the activity (count rate) to fall to half its initial value.

Write the changes in an alpha decay and a beta-minus decay.

Alpha: $^{A}_{Z}X \rightarrow\ ^{A-4}_{Z-2}Y +\ ^{4}_{2}\alpha$. Beta-minus: $^{A}_{Z}X \rightarrow\ ^{\;A}_{Z+1}Y +\ ^{\;\;0}_{-1}\beta$ (a neutron becomes a proton plus an electron).

Describe the basic structure of the nuclear atom (constituents and their relative charges).

A small dense nucleus of protons (charge $+1$) and neutrons (charge $0$) surrounded by orbiting electrons (charge $-1$). Atomic number $Z$ = number of protons; mass number $A$ = protons + neutrons.

Sketch the field pattern and force direction for magnetic fields, and state the motor-effect rule.

Magnetic field lines run from north to south pole outside a magnet. A current-carrying wire in a field experiences a force given by Fleming's left-hand rule (thumb = force/motion, first finger = field, second finger = current).

What does electromagnetic induction require, and what is its consequence (Faraday/Lenz)?

A change in magnetic flux linking a conductor induces an e.m.f. The induced e.m.f. is proportional to the rate of change of flux (Faraday), and it opposes the change producing it (Lenz's law).

Give the equation for gravitational field strength near Earth and its meaning.

$g = \frac{F}{m}$ (force per unit mass on a test mass). Near Earth's surface $g \approx 9.81\ \mathrm{N\,kg^{-1}}$, numerically equal to the free-fall acceleration.

List the SI base quantities and their units for mass, length, time, current and temperature.

Mass: kilogram (kg); length: metre (m); time: second (s); electric current: ampere (A); thermodynamic temperature: kelvin (K). (Also amount: mole; luminous intensity: candela.)

Distinguish a scalar from a vector and give two examples of each.

A scalar has magnitude only (e.g. mass, energy, speed, temperature). A vector has magnitude and direction (e.g. force, velocity, acceleration, momentum).

Give the SI prefixes and powers of ten for nano, micro, milli, kilo, mega and giga.

nano $= 10^{-9}$, micro $= 10^{-6}$, milli $= 10^{-3}$, kilo $= 10^{3}$, mega $= 10^{6}$, giga $= 10^{9}$.