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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
- 2.5 Deriving the equations of motion from a graph
- 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
- 3.5 Connected objects and systems
- 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
- 4.5 Solving problems with the work-energy model
- 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
- 6.3 Gravitational potential energy in a field
- 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
- 7.4 Circular motion problems
- 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
- 10.5 The diffraction grating
- 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
- 11.5 Calculating with 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
- 13.4 Electric field strength and potential
- 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
- 14.5 Internal resistance and emf
- 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
- 15.4 The force on a moving charge
- 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
- 16.6 R.M.S. values of alternating current
- Review
Chapter 17: The electron
- Overview
- 17.1 Evidence for the electron
- 17.2 Thermionic emission and the electron gun
- 17.3 The charge-to-mass ratio of the electron
- 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

5.1 Hooke's law — Practise

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

Give every answer with its unit, and to the number of significant figures the data justify. Before you use $F = kx$ , check that the spring is within its limit of proportionality.

A spring has a spring constant of 40 N/m. Calculate the force needed to stretch it by 0.15 m.
A force of 12 N stretches a spring by 0.04 m. Calculate its spring constant.
A spring of spring constant 250 N/m is pulled with a force of 8.0 N. Calculate its extension.
State what is meant by the limit of proportionality of a spring, and describe what is observed beyond it.

Answers and concise solutions

1. Force needed

Answer: $F = kx = 40 \times 0.15 = 6\,\text{N}$ .

2. Spring constant

Answer: $k = \dfrac{F}{x} = \dfrac{12}{0.04} = 300\,\text{N/m}$ .

3. Extension

Answer: $x = \dfrac{F}{k} = \dfrac{8.0}{250} = 0.032\,\text{m}$ , which is 32 mm.

4. Limit of proportionality

the point beyond which the force-extension graph is no longer a straight line through the origin
below it, force is directly proportional to extension, so doubling the force doubles the extension
beyond it the graph curves, and each extra newton gives a larger extension than the one before

Answer: The limit of proportionality is the point beyond which the graph of force against extension is no longer a straight line through the origin. Below it, force is directly proportional to extension, so doubling the force doubles the extension. Beyond it the graph curves, and each extra newton produces a larger extension than the one before.