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Edexcel A Level Physics

Revision Notes

Home / A Level / Physics / Edexcel / Revision Notes / 4. Materials / Stretching Materials / 4.5 Hooke's Law


4.5 Hooke's Law


Hooke's Law

  • When a force F is added to the bottom of a vertical metal wire of length L, the wire stretches
  • A material obeys Hooke’s Law if:

The extension of the material is directly proportional to the applied force (load) up to the limit of proportionality

  • This linear relationship is represented by the Hooke’s law equation:

ΔF = kΔx

  • Where:
    • F = applied force (N)
    • k = spring constant (N m–1)
    • Δx = extension (m)

 

  • The spring constant is a property of the material being stretched and measures the stiffness of a material
    • The larger the spring constant, the stiffer the material

  • Hooke's Law applies to both extensions and compressions:
    • The extension of an object is determined by how much it has increased in length
    • The compression of an object is determined by how much it has decreased in length

Load extension and force, downloadable AS & A Level Physics revision notes

Stretching a spring with a load produces a force that leads to an extension

Force–Extension Graphs

  • The way a material responds to a given force can be shown on a force-extension graph
  • A material may obey Hooke's Law up to a point
    • This is shown on its force-extension graph by a straight line through the origin

  • As more force is added, the graph may start to curve slightly

4-5-hookes-law-graph_edexcel-al-physics-rn

The Hooke's Law region of a force-extension graph is a straight line. The spring constant is the gradient of that region

  • The key features of the graph are:
    • The limit of proportionality: The point beyond which Hooke's law is no longer true when stretching a material i.e. the extension is no longer proportional to the applied force
      • The point is identified on the graph where the line starts to curve (flattens out)

    • Elastic limit: The maximum amount a material can be stretched and still return to its original length (above which the material will no longer be elastic). This point is always after the limit of proportionality
      • The gradient of this graph is equal to the spring constant k

Worked Example

A spring was stretched with increasing load.

The graph of the results is shown below.

WE - hookes law question image, downloadable AS & A Level Physics revision notes

What is the spring constant?

Step 1: Rearrange Hooke's Law to make the spring constant the subject

k equals fraction numerator capital delta F over denominator capital delta x end fraction

Step 2: Compare the gradient to the equation in Step 1

    • This graph is length - extension, so the gradient gives:

fraction numerator i n c r e a s e space i n space y over denominator i n c r e a s e space i n space x end fraction equals fraction numerator capital delta x over denominator capital delta F end fraction

    • Therefore k is the reciprocal of the gradient

Step 3:  Find the gradient

4-5-hooke_s-law-we-solution-step-3_edexcel-al-physics-rn

Step 4: Calculate gradient

g r a d i e n t space equals space fraction numerator capital delta x over denominator capital delta F end fraction space equals space fraction numerator left parenthesis 0.145 space minus space 0.10 right parenthesis over denominator 0.36 end fraction space equals space 0.125

Step 5: Calculate the spring constant by finding the reciprocal of the gradient

k space equals space fraction numerator 1 over denominator 0.125 end fraction space equals space 8.0

Step 6: Write the answer, including units

    • Spring constant, k = 8.0 N m−1

Exam Tip

Always double check the axes before finding the spring constant as the gradient of a force-extension graph. Exam questions often swap the force (or load) onto the x-axis and extension (or length) on the y-axis.

In this case, the gradient is not the spring constant, it is 1 ÷ gradient instead.



  • 1. Working as a Physicist
    • Working as a Physicist
      • 1.1 SI Units
        • 1.2 Practical Skills
          • 1.3 Estimating Physical Quantities
            • 1.4 Limitations of Measurements
              • 1.5 Scientific Communication
                • 1.6 Applications of Science
                  • 1.7 The Scientific Community
                    • 1.8 Science & Society
                  • 2. Mechanics
                    • Motion
                      • 2.1 Equations of Motion
                        • 2.2 Motion Graphs
                          • 2.3 Properties of Motion Graphs
                            • 2.4 Scalars & Vectors
                              • 2.5 Resolving Vectors
                                • 2.6 Finding the Resultant Vector
                                  • 2.7 Projectiles
                                    • 2.8 Forces as Vectors
                                    • Forces & Momentum
                                      • 2.9 Force & Acceleration
                                        • 2.10 Mass, Weight & Gravitational Field Strength
                                          • 2.11 Core Practical 1: Investigating the Acceleration of Freefall
                                            • 2.12 Newton's Third Law of Motion
                                              • 2.13 Momentum
                                                • 2.14 Conservation of Linear Momentum
                                                • Moments
                                                  • 2.15 Moments
                                                    • 2.16 Centre of Gravity & The Principle of Moments
                                                    • Work, Energy & Power
                                                      • 2.17 Work
                                                        • 2.18 Kinetic Energy
                                                          • 2.19 Gravitational Potential Energy
                                                            • 2.20 The Principle of Conservation of Energy
                                                              • 2.21 Power
                                                                • 2.22 Efficiency
                                                              • 3. Electric Circuits
                                                                • Current, Potential Difference, Resistance & Power
                                                                  • 3.1 Electric Current
                                                                    • 3.2 Potential Difference
                                                                      • 3.3 Ohm's Law
                                                                        • 3.4 Charge Conservation in Circuits
                                                                          • 3.5 Energy Conservation in Circuits
                                                                            • 3.6 Resistance in Series & Parallel
                                                                              • 3.7 Electrical Power
                                                                                • 3.8 Current-Potential Difference Graphs
                                                                                • Resistance, Resistivity & Potential Dividers
                                                                                  • 3.9 Electrical Resistivity
                                                                                    • 3.10 Core Practical 2: Investigating Resistivity
                                                                                      • 3.11 Current & Drift Velocity
                                                                                        • 3.12 Potential Difference & Conductor Length
                                                                                          • 3.13 Potential Dividers
                                                                                            • 3.14 Potential Dividers & Variable Resistance
                                                                                            • E.M.F & Modelling Resistance
                                                                                              • 3.15 Electromotive Force
                                                                                                • 3.16 Internal Resistance
                                                                                                  • 3.17 E.M.F. vs. Terminal Potential Difference
                                                                                                    • 3.18 Core Practical 3: Investigating E.M.F. & Internal Resistance
                                                                                                      • 3.19 Resistance & Temperature
                                                                                                        • 3.20 Resistance & Illumination
                                                                                                      • 4. Materials
                                                                                                        • Density, Upthrust & Viscous Drag
                                                                                                          • 4.1 Density
                                                                                                            • 4.2 Upthrust
                                                                                                              • 4.3 Viscous Drag
                                                                                                                • 4.4 Core Practical 4: Investigating Viscosity
                                                                                                                • Stretching Materials
                                                                                                                  • 4.5 Hooke's Law
                                                                                                                    • 4.6 Stress, Strain & The Young Modulus
                                                                                                                      • 4.7 Force-Extension Graphs
                                                                                                                        • 4.8 Stress-Strain Graphs
                                                                                                                          • 4.9 Core Practical 5: Investigating Young Modulus
                                                                                                                            • 4.10 Elastic Strain Energy
                                                                                                                          • 5. Waves & Particle Nature of Light
                                                                                                                            • Transverse & Longitudinal Waves
                                                                                                                              • 5.1 Properties of Waves
                                                                                                                                • 5.2 The Wave Equation
                                                                                                                                  • 5.3 Longitudinal Waves
                                                                                                                                    • 5.4 Transverse Waves
                                                                                                                                      • 5.5 Representing Waves on Graphs
                                                                                                                                        • 5.6 Core Practical 6: Investigating the Speed of Sound
                                                                                                                                        • Interference & Stationary Waves
                                                                                                                                          • 5.7 Interference & Superposition of Waves
                                                                                                                                            • 5.8 Phase & Path Difference
                                                                                                                                              • 5.9 Stationary Waves
                                                                                                                                                • 5.10 Wave Speed on a Stretched String
                                                                                                                                                  • 5.11 Core Practical 7: Investigating Stationary Waves
                                                                                                                                                  • Refraction, Reflection & Polarisation
                                                                                                                                                    • 5.12 Equation for the Intensity of Radiation
                                                                                                                                                      • 5.13 Refraction & Refractive Index
                                                                                                                                                        • 5.14 Critical Angle
                                                                                                                                                          • 5.15 Total Internal Reflection
                                                                                                                                                            • 5.16 Measuring Refractive Index
                                                                                                                                                              • 5.17 Converging & Diverging Lenses
                                                                                                                                                                • 5.18 Using Ray Diagrams
                                                                                                                                                                  • 5.19 Power of a Lens
                                                                                                                                                                    • 5.20 Thin Lenses in Combination
                                                                                                                                                                      • 5.21 Real & Virtual Images
                                                                                                                                                                        • 5.22 The Lens Equation
                                                                                                                                                                          • 5.23 Magnification
                                                                                                                                                                            • 5.24 Plane Polarisation
                                                                                                                                                                            • Waves, Electrons & Photons
                                                                                                                                                                              • 5.25 Diffraction
                                                                                                                                                                                • 5.26 The Diffraction Grating Equation
                                                                                                                                                                                  • 5.27 Core Practical 8: Investigating Diffraction Gratings
                                                                                                                                                                                    • 5.28 The Wave Nature of Electrons
                                                                                                                                                                                      • 5.29 The de Broglie Equation
                                                                                                                                                                                        • 5.30 Transmission & Reflection of Waves
                                                                                                                                                                                          • 5.31 Pulse-Echo Technique
                                                                                                                                                                                            • 5.32 Wave-Particle Duality
                                                                                                                                                                                              • 5.33 Energy of a Photon
                                                                                                                                                                                              • The Photoelectric Effect & Atomic Spectra
                                                                                                                                                                                                • 5.34 The Photoelectric Effect
                                                                                                                                                                                                  • 5.35 The Photoelectric Equation
                                                                                                                                                                                                    • 5.36 The Electronvolt
                                                                                                                                                                                                      • 5.37 The Particle Nature of EM Radiation
                                                                                                                                                                                                        • 5.38 Atomic Line Spectra
                                                                                                                                                                                                      • 6. Further Mechanics
                                                                                                                                                                                                        • Momentum & Impulse
                                                                                                                                                                                                          • 6.1 Impulse
                                                                                                                                                                                                            • 6.2 Core Practical 9: Investigating Impulse
                                                                                                                                                                                                              • 6.3 Applying Conservation of Linear Momentum
                                                                                                                                                                                                                • 6.4 Core Practical 10: Investigating Collisions using ICT
                                                                                                                                                                                                                  • 6.5 Elastic & Inelastic Collisions
                                                                                                                                                                                                                    • 6.6 Energy-Momentum Relation
                                                                                                                                                                                                                    • Circular Motion
                                                                                                                                                                                                                      • 6.7 Radians & Angular Displacement
                                                                                                                                                                                                                        • 6.8 Angular Velocity
                                                                                                                                                                                                                          • 6.9 Centripetal Acceleration
                                                                                                                                                                                                                            • 6.10 Maintaining Circular Motion
                                                                                                                                                                                                                              • 6.11 Centripetal Force
                                                                                                                                                                                                                            • 7. Electric & Magnetic Fields
                                                                                                                                                                                                                              • Electric Fields
                                                                                                                                                                                                                                • 7.1 Defining an Electric Field
                                                                                                                                                                                                                                  • 7.2 Electric Field Strength
                                                                                                                                                                                                                                    • 7.3 Electric Force between Two Charges
                                                                                                                                                                                                                                      • 7.4 Electric Field due to a Point Charge
                                                                                                                                                                                                                                        • 7.5 Electric Field & Potential
                                                                                                                                                                                                                                          • 7.6 Electric Field between Parallel Plates
                                                                                                                                                                                                                                            • 7.7 Electric Potential for a Radial Field
                                                                                                                                                                                                                                              • 7.8 Representing Radial & Uniform Electric Fields
                                                                                                                                                                                                                                              • Capacitance
                                                                                                                                                                                                                                                • 7.9 Capacitance
                                                                                                                                                                                                                                                  • 7.10 Energy Stored by a Capacitor
                                                                                                                                                                                                                                                    • 7.11 Charge & Discharge Curves
                                                                                                                                                                                                                                                      • 7.12 Core Practical 11: Investigating Capacitor Charge & Discharge
                                                                                                                                                                                                                                                        • 7.13 Exponential Discharge in a Capacitor
                                                                                                                                                                                                                                                        • Magnetic Fields
                                                                                                                                                                                                                                                          • 7.14 Magnetic Flux Density, Flux & Flux Linkage
                                                                                                                                                                                                                                                            • 7.15 Magnetic Force on a Charged Particle
                                                                                                                                                                                                                                                              • 7.16 Magnetic Force on a Current-Carrying Conductor
                                                                                                                                                                                                                                                              • Electromagnetic Induction & Alternating Currents
                                                                                                                                                                                                                                                                • 7.17 Induced E.M.F in a Moving Coil
                                                                                                                                                                                                                                                                  • 7.18 Induced E.M.F between Linked Coils
                                                                                                                                                                                                                                                                    • 7.19 Lenz's Law
                                                                                                                                                                                                                                                                      • 7.20 Faraday's Law
                                                                                                                                                                                                                                                                        • 7.21 Alternating Currents & Potential Differences
                                                                                                                                                                                                                                                                          • 7.22 Root-Mean-Square Current & Potential Difference
                                                                                                                                                                                                                                                                        • 8. Nuclear & Particle Physics
                                                                                                                                                                                                                                                                          • Exploring the Structure of Matter
                                                                                                                                                                                                                                                                            • 8.1 Nucleon & Proton Number
                                                                                                                                                                                                                                                                              • 8.2 The Nuclear Model of the Atom
                                                                                                                                                                                                                                                                                • 8.3 Thermionic Emission
                                                                                                                                                                                                                                                                                  • 8.4 Particle Accelerators & Detectors
                                                                                                                                                                                                                                                                                    • 8.5 Radius of a Charged Particle in a Magnetic Field
                                                                                                                                                                                                                                                                                      • 8.6 Interpreting Particle Tracks
                                                                                                                                                                                                                                                                                        • 8.7 High Energy Particle Collisions
                                                                                                                                                                                                                                                                                          • 8.8 Annihilation of Matter & Antimatter
                                                                                                                                                                                                                                                                                            • 8.9 Unit Conversions for Energy & Mass
                                                                                                                                                                                                                                                                                              • 8.10 Relativistic Situations
                                                                                                                                                                                                                                                                                              • Particle Interactions & Conservation
                                                                                                                                                                                                                                                                                                • 8.11 The Standard Model
                                                                                                                                                                                                                                                                                                  • 8.12 Antimatter
                                                                                                                                                                                                                                                                                                    • 8.13 Conservation Laws in Particle Physics
                                                                                                                                                                                                                                                                                                      • 8.14 Particle Interaction Equations
                                                                                                                                                                                                                                                                                                    • 9. Thermodynamics
                                                                                                                                                                                                                                                                                                      • Thermal Energy Transfer
                                                                                                                                                                                                                                                                                                        • 9.1 Specific Heat Capacity & Latent Heat
                                                                                                                                                                                                                                                                                                          • 9.2 Core Practical 12: Calibrating a Thermistor
                                                                                                                                                                                                                                                                                                            • 9.3 Core Practical 13: Investigating Specific Latent Heat
                                                                                                                                                                                                                                                                                                            • Kinetic Theory & Ideal Gases
                                                                                                                                                                                                                                                                                                              • 9.4 Internal Energy
                                                                                                                                                                                                                                                                                                                • 9.5 Temperature & Absolute Zero
                                                                                                                                                                                                                                                                                                                  • 9.6 Kinetic Theory of Gases Equation
                                                                                                                                                                                                                                                                                                                    • 9.7 Ideal Gas Equation
                                                                                                                                                                                                                                                                                                                      • 9.8 Core Practical 14: Investigating Gas Pressure & Volume
                                                                                                                                                                                                                                                                                                                        • 9.9 Average Molecular Kinetic Energy
                                                                                                                                                                                                                                                                                                                        • Black Body Radiation
                                                                                                                                                                                                                                                                                                                          • 9.10 Black Body Radiation
                                                                                                                                                                                                                                                                                                                            • 9.11 Stefan-Boltzmann Law
                                                                                                                                                                                                                                                                                                                              • 9.12 Wien’s Law
                                                                                                                                                                                                                                                                                                                            • 10. Space
                                                                                                                                                                                                                                                                                                                              • Astronomy
                                                                                                                                                                                                                                                                                                                                • 10.1 Inverse Square Law of Flux
                                                                                                                                                                                                                                                                                                                                  • 10.2 Parallax
                                                                                                                                                                                                                                                                                                                                    • 10.3 Standard Candles
                                                                                                                                                                                                                                                                                                                                      • 10.4 The Hertzsprung-Russell Diagram
                                                                                                                                                                                                                                                                                                                                        • 10.5 The Life Cycle of Stars
                                                                                                                                                                                                                                                                                                                                        • Cosmology
                                                                                                                                                                                                                                                                                                                                          • 10.6 Doppler Shift
                                                                                                                                                                                                                                                                                                                                            • 10.7 Equations for Cosmology
                                                                                                                                                                                                                                                                                                                                              • 10.8 Cosmology
                                                                                                                                                                                                                                                                                                                                            • 11. Nuclear Radiation
                                                                                                                                                                                                                                                                                                                                              • Nuclear Fusion & Fission
                                                                                                                                                                                                                                                                                                                                                • 11.1 Nuclear Binding Energy & Mass Deficit
                                                                                                                                                                                                                                                                                                                                                  • 11.2 Atomic Mass Unit
                                                                                                                                                                                                                                                                                                                                                    • 11.3 Binding Energy per Nucleon Graph
                                                                                                                                                                                                                                                                                                                                                      • 11.4 Nuclear Fusion
                                                                                                                                                                                                                                                                                                                                                      • Radioactivity Decay
                                                                                                                                                                                                                                                                                                                                                        • 11.5 Background Radiation
                                                                                                                                                                                                                                                                                                                                                          • 11.6 Alpha, Beta & Gamma Radiation
                                                                                                                                                                                                                                                                                                                                                            • 11.7 Nuclear Decay Equations
                                                                                                                                                                                                                                                                                                                                                              • 11.8 Core Practical 15: Investigating Gamma Radiation Absorption
                                                                                                                                                                                                                                                                                                                                                                • 11.9 The Random Nature of Nuclear Decay
                                                                                                                                                                                                                                                                                                                                                                  • 11.10 Equations for Nuclear Physics
                                                                                                                                                                                                                                                                                                                                                                • 12. Gravitational Fields
                                                                                                                                                                                                                                                                                                                                                                  • Gravitational Fields
                                                                                                                                                                                                                                                                                                                                                                    • 12.1 Gravitational Fields
                                                                                                                                                                                                                                                                                                                                                                      • 12.2 Gravitational Field Strength
                                                                                                                                                                                                                                                                                                                                                                        • 12.3 Newton’s Law of Universal Gravitation
                                                                                                                                                                                                                                                                                                                                                                          • 12.4 Gravitational Field due to a Point Mass
                                                                                                                                                                                                                                                                                                                                                                            • 12.5 Gravitational Potential for a Radial Field
                                                                                                                                                                                                                                                                                                                                                                              • 12.6 Comparing Electric & Gravitational Fields
                                                                                                                                                                                                                                                                                                                                                                                • 12.7 Orbital Motion
                                                                                                                                                                                                                                                                                                                                                                              • 13. Oscillations
                                                                                                                                                                                                                                                                                                                                                                                • Simple Harmonic Motion
                                                                                                                                                                                                                                                                                                                                                                                  • 13.1 Conditions for Simple Harmonic Motion
                                                                                                                                                                                                                                                                                                                                                                                    • 13.2 Equations for Simple Harmonic Motion
                                                                                                                                                                                                                                                                                                                                                                                      • 13.3 Period of Simple Harmonic Oscillators
                                                                                                                                                                                                                                                                                                                                                                                        • 13.4 Displacement-Time Graph for an Oscillator
                                                                                                                                                                                                                                                                                                                                                                                          • 13.5 Velocity-Time Graph for an Oscillator
                                                                                                                                                                                                                                                                                                                                                                                          • Resonance
                                                                                                                                                                                                                                                                                                                                                                                            • 13.6 Resonance
                                                                                                                                                                                                                                                                                                                                                                                              • 13.7 Core Practical 16: Investigating Resonance
                                                                                                                                                                                                                                                                                                                                                                                                • 13.8 Damped & Undamped Oscillating Systems
                                                                                                                                                                                                                                                                                                                                                                                                  • 13.9 Free & Forced Oscillations
                                                                                                                                                                                                                                                                                                                                                                                                    • 13.10 Resonance Graphs
                                                                                                                                                                                                                                                                                                                                                                                                      • 13.11 Damping & Plastic Deformation


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                                                                                                                                                                                                                                                                                                                                                                                                    Author: Lindsay

                                                                                                                                                                                                                                                                                                                                                                                                    Lindsay graduated with First Class Honours from the University of Greenwich and earned her Science Communication MSc at Imperial College London. Now with many years’ experience as a Head of Physics and Examiner for A Level and IGCSE Physics (and Biology!), her love of communicating, educating and Physics has brought her to Save My Exams where she hopes to help as many students as possible on their next steps.


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