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Glossary
Chapter 1: Measuring, modelling and investigating
- Overview
- 1.1 Physical quantities and SI units
- 1.2 Measuring, accuracy and uncertainty
- 1.3 Scientific models and the Nature of Science
- 1.4 Planning and evaluating an investigation
- 1.5 Graphs, gradients and the language of data
- Review
Chapter 2: Describing motion
- Overview
- 2.1 Displacement, velocity and acceleration
- 2.2 Motion graphs
- 2.3 The equations of motion for constant acceleration
- 2.4 Motion under gravity
- Review
Chapter 3: Forces and Newton's laws
- Overview
- 3.1 Forces and free-body diagrams
- 3.2 Newton's first and second laws
- 3.3 Newton's third law and momentum
- 3.4 Friction and resistive forces
- Review
Chapter 4: Work, energy and power
- Overview
- 4.1 Work and energy
- 4.2 Kinetic and potential energy
- 4.3 Conservation of energy
- 4.4 Power and efficiency
- Review
Chapter 5: Stretching and compressing
- Overview
- 5.1 Hooke's law
- 5.2 The spring constant and combinations of springs
- 5.3 Elastic potential energy
- 5.4 Investigating Hooke's law
- Review
Chapter 6: Gravity and gravitational fields
- Overview
- 6.1 Weight, mass and gravitational field strength
- 6.2 Newton's law of universal gravitation
- 6.4 Orbits and satellites
- Review
Chapter 7: Circular motion
- Overview
- 7.1 Angular velocity and period
- 7.2 Centripetal acceleration
- 7.3 Centripetal force and its sources
- Review
Chapter 8: Heat, temperature and energy transfer
- Overview
- 8.1 Temperature, heat and thermal equilibrium
- 8.2 Specific heat capacity
- 8.3 Latent heat and changes of state
- 8.4 Conduction, convection and radiation
- Review
Chapter 9: Waves
- Overview
- 9.1 What a wave is
- 9.2 Frequency, wavelength and wave speed
- 9.3 Transverse and longitudinal waves
- 9.4 The principle of superposition
- 9.5 Stationary waves and resonance
- Review
Chapter 10: Reflection, refraction and diffraction
- Overview
- 10.1 Reflection of waves
- 10.2 Refraction and Snell's law
- 10.3 Total internal reflection and the critical angle
- 10.4 Diffraction and interference
- Review
Chapter 11: Sound
- Overview
- 11.1 Sound as a wave
- 11.2 The speed of sound and its measurement
- 11.3 Pitch, loudness and quality
- 11.4 The Doppler effect
- Review
Chapter 12: Light and electromagnetic radiation
- Overview
- 12.1 The electromagnetic spectrum
- 12.2 The speed of light
- 12.3 Energy in electromagnetic radiation
- 12.4 Lenses and images
- Review
Chapter 13: Charge and electric fields
- Overview
- 13.1 Electric charge and charging
- 13.2 Coulomb's law
- 13.3 Electric fields and field lines
- Review
Chapter 14: Electric circuits
- Overview
- 14.1 Current, potential difference and resistance
- 14.2 Ohm's law and resistors
- 14.3 Series and parallel circuits
- 14.4 Electrical power and energy
- Review
Chapter 15: Magnetism and the force on a current
- Overview
- 15.1 Magnetic fields and magnetic materials
- 15.2 The magnetic field of a current
- 15.3 The force on a current-carrying conductor
- 15.5 The electric motor
- Review
Chapter 16: Electromagnetic induction
- Overview
- 16.1 Magnetic flux and flux density
- 16.2 Faraday's law of induction
- 16.3 Lenz's law and conservation of energy
- 16.4 A.C. and D.C. generators
- 16.5 Transformers and the transmission of electricity
- Review
Chapter 17: The electron
- Overview
- 17.1 Evidence for the electron
- 17.2 Thermionic emission and the electron gun
- Review
Chapter 18: The photoelectric effect and X-rays
- Overview
- 18.1 The photon and the quantum idea
- 18.2 The photoelectric effect
- 18.3 Einstein's photoelectric equation
- 18.4 X-ray production
- Review
Chapter 19: Models of the atom
- Overview
- 19.1 From Thomson to Rutherford
- 19.2 The Bohr model and energy levels
- 19.3 Emission and absorption spectra
- Review
Chapter 20: Radioactivity
- Overview
- 20.1 Radioactive decay and the three emissions
- 20.2 Half-life and activity
- 20.3 Nuclear equations
- 20.4 Uses and hazards of radiation
- Review
Chapter 21: Mass and energy
- Overview
- 21.1 Mass-energy equivalence
- 21.2 Binding energy and the mass defect
- 21.3 Fission and fusion
- 21.4 Nuclear power and its alternatives
- Review
Chapter 22: The Physics In Practice Investigation
- Overview
- 22.1 Reading the brief and choosing a question
- 22.2 Researching from secondary sources
- 22.3 Designing the investigation and gathering primary data
- 22.4 Processing and evaluating your data
- 22.5 Writing the report
- 22.6 Reviewing the whole course
- Review
About this book

5.3 Elastic potential energy — Practise

Work independently. The questions and answers are shown together at the end.

Write $x^2$ out in full before you substitute. The extension is squared, so a small arithmetic slip changes the answer a great deal.

A spring of spring constant 200 N/m is stretched by 0.10 m. Calculate the energy stored in it.
A spring is stretched by 0.20 m and stores 4.0 J. Calculate the energy stored when it is stretched by 0.40 m.

Answers and concise solutions

1. Energy stored

Answer: $E = \tfrac{1}{2}kx^2 = 0.5 \times 200 \times 0.10^2 = 1.0\,\text{J}$ .

2. Energy stored at double the extension

Answer: $16\,\text{J}$ — four times as much, not twice. The extension is squared in $\tfrac{1}{2}kx^2$ , so doubling $x$ multiplies the energy by $2^2 = 4$ .