What is elastic strain energy?

It is the energy stored in a sample as a result of the work done in deforming it, which is recovered when the load is removed if the deformation is elastic.

State the equation for the elastic strain energy stored in a sample obeying Hooke's law:

ΔEₑₗ = ½FΔx, where F is the final force and Δx the extension it produces.

How can the elastic strain energy of a spring obeying Hooke's law be written in terms of k and Δx?

Substituting F = kΔx into ΔEₑₗ = ½FΔx gives ΔEₑₗ = ½kΔx².

Which region of a force-extension graph represents the elastic strain energy stored?

The area under the graph, measured from the origin up to the extension concerned.

How would you estimate the energy stored when the force-extension graph is a curve rather than a straight line?

Estimate the area under the curve by counting the squares beneath it, or by dividing it into strips and using the trapezium rule, then multiply by the energy represented by one square.

A spring of stiffness 25 N m⁻¹ is stretched by 0.12 m within its elastic limit. How much energy is stored?

ΔEₑₗ = ½kΔx² = ½ × 25 × 0.12² = 0.18 J.

Edexcel A-Level Physics 9PH0

Working as a Physicist

Topic overview SI base units, derived units and homogeneity Unit prefixes, conversion and order-of-magnitude estimates Resolution, random errors and systematic errors Uncertainty and how uncertainties combine Improving measurements, graphs and evaluating results Peer review, publication and scientific integrity Risk, benefit and the role of science in society

Mechanics

Topic overview The equations of uniformly accelerated motion Displacement-time and velocity-time graphs Scalars and vectors Resolving vectors and finding resultants Projectile motion Free-body diagrams and Newton's first and second laws Newton's third law, mass and weight Terminal velocity and measuring g by free fall Linear momentum and its conservation Elastic and inelastic collisions in one dimension The moment of a force Centre of gravity, equilibrium and the principle of moments Work done by a force Kinetic and gravitational potential energy Conservation of energy and dissipation Power, and the equation P = Fv Efficiency and wasted energy

Electric Circuits

Topic overview Current, charge and potential difference Resistance, Ohm's law and ohmic behaviour Electrical power and energy Kirchhoff's laws: the current and potential difference rules Combining resistances in series and parallel Circuit calculations, meters and component failure I-V characteristics of conductors, lamps and diodes Thermistors, light dependent resistors and resistance change Resistivity and determining it experimentally Charge carriers, drift velocity and I = nqvA The potential divider equation and the loading effect Sensing circuits with thermistors and light dependent resistors Electromotive force, internal resistance and lost volts Measuring e.m.f. and internal resistance, and cells in combination

Materials

Topic overview Density and how it is measured Upthrust and Archimedes' principle Floating, sinking and upthrust calculations Viscosity, laminar flow and Stokes' law Terminal velocity of a sphere falling through a liquid Measuring viscosity by the falling-ball method Hooke's law, stress and strain The Young modulus and calculations with it Determining the Young modulus of a wire Force-extension graphs, elastic and plastic deformation Stress-strain graphs, ductile and brittle materials Elastic strain energy

Waves and Particle Nature of Light

Topic overview Describing a progressive wave The wave equation and its use Longitudinal and transverse waves Displacement-distance and displacement-time graphs Measuring the speed of sound with an oscilloscope Wavefronts, superposition and phase Coherence, path difference and phase difference Interference in practice Stationary waves, nodes and antinodes Harmonics on a stretched string Investigating a vibrating string, and air columns Intensity, the inverse square law and refractive index Refraction, wave speed and the critical angle Total internal reflection and measuring refractive index Lenses, ray diagrams and the images they form Lens power and the thin lens equation Lens calculations and magnification Reflection, transmission and the pulse-echo principle Pulse-echo calculations, resolution and ultrasound Polarisation and diffraction Single-slit patterns and the diffraction grating equation Grating spectra and measuring wavelength Electron diffraction and the de Broglie equation de Broglie calculations and wave-particle duality Photons and photon energy Models of light and the electronvolt Line spectra and atomic energy levels The photoelectric effect and Einstein's equation Evidence for the photon model and photoelectric calculations

Further Mechanics

Topic overview Impulse and force-time graphs Conservation of momentum in two dimensions Investigating momentum and analysing collisions on video Elastic and inelastic collisions Kinetic energy, momentum and collision calculations The radian, angular displacement and angular velocity Angular velocity, period and frequency of rotation Centripetal acceleration Centripetal force and what provides it Vertical loops and centripetal force calculations

Electric and Magnetic Fields

Topic overview Electric fields and electric field strength Field strength calculations and field diagrams Coulomb's law and the field of a point charge Inverse-square behaviour and combining fields Electric potential and field strength as a potential gradient Uniform fields between parallel plates, and the potential near a point charge Equipotentials, field diagrams and work done Capacitance and the energy stored in a capacitor Capacitor charge and energy calculations Charging and discharging graphs and the time constant The exponential decay equations and logarithmic graphs Investigating capacitor discharge and time-constant calculations Magnetic flux density, flux and flux linkage Forces on currents and moving charges The conditions for inducing an e.m.f.Faraday's law and Lenz's law Flux linkage graphs and induced e.m.f. calculations Alternating current, peak and r.m.s. values Oscilloscope traces and alternating current calculations

Nuclear and Particle Physics

Topic overview Nuclide notation, isotopes and the alpha scattering experiment Conclusions from alpha scattering and the changing model of the atom Thermionic emission and linear accelerators The cyclotron and the radius of a charged particle's path Particle tracks, conservation laws and why high energies are needed Mass-energy equivalence, pair production and annihilation Particle energy units and relativistic lifetimes Baryons, mesons, leptons and quark composition The six quarks, antiparticles and fundamental particles Conservation of charge, baryon number and lepton number Quark changes in beta decay and testing particle equations

Thermodynamics

Topic overview Specific heat capacity and specific latent heat Measuring specific heat capacity and calibrating a thermistor Measuring specific latent heat Internal energy, temperature and absolute zero Mean kinetic energy and the absolute temperature scale The kinetic theory equation and its derivation The ideal gas equation and molecular kinetic energy Boyle's law and investigating a fixed mass of gas Black body radiation and Wien's law The Stefan-Boltzmann law and stellar calculations

Space

Topic overview Luminosity, intensity and the inverse square law Trigonometric parallax and standard candles The Hertzsprung-Russell diagram The life cycle of stars The Doppler effect and redshift Hubble's law and the age of the universe Dark matter and the fate of the universe

Nuclear Radiation

Topic overview Mass deficit, binding energy and the atomic mass unit Binding energy per nucleon, fission and fusion Background radiation and the three types of nuclear radiation Ionising power, penetration and changes in the nucleus Nuclear equations and investigating gamma absorption Activity, the decay constant and half-life Decay graphs and half-life calculations

Gravitational Fields

Topic overview Gravitational fields and gravitational field strength The field of a point mass and calculations with g Newton's law of universal gravitation Orbital speed, period and geostationary satellites Gravitational potential and potential energy Comparing gravitational and electric fields

Oscillations

Topic overview The conditions for simple harmonic motion Displacement, velocity and acceleration in simple harmonic motion The mass-spring oscillator and the simple pendulum Displacement, velocity and acceleration graphs Reading period, amplitude and speed from oscillation graphs Energy in an undamped oscillation Damping and where the energy goes Free and forced oscillations and resonance Resonance in practice and determining an unknown mass

Materials

Elastic strain energy

1 thing to know
Papers 2 and 3

Overview

Recall questions on the energy stored in a stretched sample, why the factor of a half appears, which area of a graph represents it, and estimating it from a curve.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Key term

Which region of a force-extension graph represents the stored elastic strain energy, and what happens to it if the extension is doubled?

Questions from this subtopic

Each one with the model answer underneath.

1
What is elastic strain energy?
Model answer
It is the energy stored in a sample as a result of the work done in deforming it, which is recovered when the load is removed if the deformation is elastic.
2
State the equation for the elastic strain energy stored in a sample obeying Hooke's law:
Model answer
ΔEₑₗ = ½FΔx, where F is the final force and Δx the extension it produces.
3
How can the elastic strain energy of a spring obeying Hooke's law be written in terms of k and Δx?
Model answer
Substituting F = kΔx into ΔEₑₗ = ½FΔx gives ΔEₑₗ = ½kΔx².
4
Which region of a force-extension graph represents the elastic strain energy stored?
Model answer
The area under the graph, measured from the origin up to the extension concerned.
5
How would you estimate the energy stored when the force-extension graph is a curve rather than a straight line?
Model answer
Estimate the area under the curve by counting the squares beneath it, or by dividing it into strips and using the trapezium rule, then multiply by the energy represented by one square.
6
A spring of stiffness 25 N m⁻¹ is stretched by 0.12 m within its elastic limit. How much energy is stored?
Model answer
ΔEₑₗ = ½kΔx² = ½ × 25 × 0.12² = 0.18 J.

See the rest and revise

Other ways to work this

The same content, four other ways.

What is inside Levo

Six ways to work the same material.

1Closed book

2Open book

3Closed book

The 3-step method, run for you

Answer cold, learn it, then prove it stuck. Levo tracks the jump between your first attempt and your last.

Working as a Physicist

Mechanics

Electric Circuits

Materials

Cram a whole paper in one sitting

Sort every topic into what you know and what you do not, then drill only the weak ones.

The gradient gives the .

accelerationvelocitydisplacement

Blank Blitz makes facts automatic

Rapid timed gap-fills on the terms and numbers you need to recall without thinking.

AThe equation is s = (u + v)t/2.

BThe equation is v = u + at.

CThe equation is s = ut + ½at².

Build It gets the exam shape right

Assemble a full-mark answer from its marking points, in the order an examiner wants them.

Speed means rate of change of distance.

TrueFalse

Test It catches misconceptions

Spot the fault in a statement. The traps are the mistakes students actually make.

721941163128510

Brain Breaks between sessions

Short focus games to reset attention, so the next set lands better than the last.

Every question in Materials, on a schedule.

Attempt a question from memory, write the correct version, then attempt it again. Levo records the jump between your first attempt and your last, and brings each question back on the day you are due to forget it.

Start revising, £5 a month See how the method works

Or £46 a year, about £3.83 a month. Cancel anytime.