Bulk Properties of Solids

Hooke's Law

Hooke's law is a proportional relationship between the force experienced and the extension observed. The relationship exists up to an elastic limit.

Hooke's law

Hooke's law is the relationship that the force F experienced by an extensible object is proportional to its extension ΔL:
- F α ΔL
The constant of proportionality is labelled k and is called the stiffness constant.
This gives the equation:
- F = kΔL
The force acts to restore the object back to its original shape, so it acts in the opposite direction to that of the extension.

Limit of proportionality

Hooke's law is a relationship between two quantities. But, this relationship does not always hold.
- When a force-extension graph is linear, Hooke's law applies.
- When a force-extension graph is non-linear, Hooke's law does NOT apply.

Elastic limit

An object (e.g. a spring) is elastic if it returns back to zero extension when the load on it is removed.
The elastic limit is the maximum force the spring can sustain and then return to zero extension.

Gradient of force-extension graphs

The gradient of a force-extension graph is the value of the constant of proportionality, k.
For springs, this is the familiar spring constant.

Strain and Stress

Summary values of materials are useful for engineers to compare the qualities of different materials. Two examples of summary values are stress and strain.

Effect of forces

Forces can change an object's shape.
The study of stress and strain is a study of how forces change an object's shape.
- Some forces stretch the object.
  - These forces are called tensile forces.
- Some forces squash the object.
  - These forces are called compressive forces.

Stress

Stress can be defined as:
- Stress = $\frac{force\space along\space the\space axis\space of\space the\space object}{cross-sectional\space area \space of \space the \space object}$
- $\sigma = \frac{F}{A}$
If the force is tensile, then the stress is positive.
If the force is compressive, then the stress is negative.
The units are newtons per metre squared (N/m²) or pascals (Pa).

Strain

Strain can be defined as:
- $strain = \frac{extension}{original\space length}$
- $\epsilon = \frac{\Delta L}{L}$
If the force is tensile, then the strain is positive.
If the force is compressive, then the strain is negative.
There are no units for strain because strain is a ratio.

Elastic strain energy

When an elastic object is stretched, energy needs to be supplied to the object to stretch the object.
The supplied energy is the elastic strain energy.
The elastic strain energy can be determined from the area underneath a force-extension graph.

Breaking stress

Breaking stress is the stress required to break the material.
The maximum tensile stress an object can withstand is called the ultimate tensile stress.
Some materials can undergo some strain beyond the point of ultimate tensile stress before breaking.

Plastic and Brittle Behaviour

Objects respond differently to a wide range of stresses and strains.

Plastic behaviour

An object deforms plastically if it undergoes permanent deformation under stress.
Plastic behaviour occurs after the elastic limit.
Stretching strawberry laces is an example of plastic behaviour.
To identify areas of plastic behaviour on a force-extension graph, look to the right of the elastic limit point.

Brittle behaviour

An object is brittle if it breaks suddenly and cracks. There will be very little plastic behaviour shown.
An example of a brittle food is hard sugar sweets.

Fractures

Fractures happen when the material completely breaks.

1Physical Quantities & Units

1.1Physical Quantities & Units

1.1.1Use of SI Units

1.1.2SI Prefixes, Standard Form & Converting Units

1.1.3End of Topic Test - Units & Prefixes

1.1.4Avogadro's Constant

1.1.5Scalars & Vectors

2Measurement Techniques

2.1Measurement, Errors & Uncertainty

2.1.1Measuring Length, Time & Volume

2.1.2Measuring Temperature

2.1.3Circuit Measurements

2.1.4Limitation of Physical Measurements

2.1.5Uncertainty

2.1.6Estimation

2.1.7Displaying Data

2.1.8End of Topic Test - Measurements & Errors

3Kinematics

3.1Equations of Motion

3.1.1Motion in a Straight Line

3.1.2Graphs of Motion

3.1.3Bouncing Ball Example

3.1.4End of Topic Test - Motion in a Straight Line

3.1.5Acceleration Due to Gravity

4Dynamics

4.1Momentum & Newton's Laws of Motion

4.1.1Mass & Inertia

4.1.2Newton's Laws

4.1.3Momentum

4.1.4End of Topic Test - Newton's Laws & Momentum

4.1.5A-A* (AO3/4) - Newton's Third Law

4.2Non-Uniform Motion

4.2.1Projectile Motion

4.3Linear Momentum & Conservation

4.3.1Conservation of Momentum

4.4Force, Density & Pressure

4.4.1Fields

4.4.2Force in Uniform Fields

4.4.3Friction

4.4.4Buoyancy

4.4.5Terminal Speed

4.4.6End of Topic Test - Acceleration Due to Gravity

4.4.7Centre of Mass

4.4.8Forces & Equilibrium

4.4.9End of Topic Test - Scalars & Vectors

4.4.10Moments

4.4.11End of Topic Test - Moments & Centre of Mass

4.4.12Density

4.4.13Pressure

4.5Work, Energy & Power

4.5.1Work & Energy

4.5.2Power & Efficiency

4.5.3Conservation of Energy

4.5.4End of Topic Test - Work, Energy & Power

4.6Circular Motion

4.6.1Circular Motion

4.6.2Circular Motion 2

4.6.3End of Topic Test - Circular Motion

5Gravitational Fields

5.1Gravitational Fields (A2 only)

5.1.1Newton's Law

5.1.2Gravitational Field Strength

5.1.3Gravitational Potential

6Deformation of Solids

6.1Materials

6.1.1Bulk Properties of Solids

6.1.2Energy in Materials

6.1.3Young Modulus

6.1.4End of Topic Test - Materials

7Thermal Physics

7.1Thermal Physics

7.1.1Temperature

7.1.2Measuring Temperature

7.1.3Ideal Gas Law

7.1.4Ideal Gases

7.1.5Boyle's Law & Charles' Law

7.1.6Molecular Kinetic Theory Model

7.1.7Molecular Kinetic Theory Model 2

7.1.8Thermal Energy Transfer

7.1.9Thermal Energy Transfer Experiments

7.1.10End of Topic Test - Thermal Energy & Ideal Gases

7.1.11First Law of Thermodynamics

8Oscillations

8.1Simple Harmonic Motion

8.1.1Simple Harmonic Motion

8.1.2Simple Harmonic Systems

8.1.3Energy in Simple Harmonic Motion

8.1.4Resonance

8.1.5End of Topic Test - Simple Harmonic Motion

8.1.6A-A* (AO3/4) - Simple Harmonic Motion

8.1.7End of Topic Test - Gravitational Fields

8.2Waves

8.2.1Progressive Waves

8.2.2Intensity of Waves

8.2.3Wave Speed & Phase Difference

8.2.4Longitudinal & Transverse Waves

8.2.5End of Topic Test - Progressive Waves

8.2.6Electromagnetic Waves

8.2.7Doppler Effect

8.2.8Sound Waves

8.2.9Measuring Sound Waves

8.2.10End of Topic Test - Waves

8.2.11Ultrasound Imaging

8.2.12Ultrasound Imaging 2

8.3Superposition

8.3.1Stationary Waves

8.3.2Stationary Waves 2

8.3.3End of Topic Test - Stationary Waves

8.3.4A-A* (AO3/4) - Stationary Waves

8.3.5Interference

8.3.6Interference 2

8.3.7End of Topic Test - Interference

8.3.8Diffraction

8.3.9Diffraction Gratings

8.3.10End of Topic Test - Diffraction

9Communication

9.1Communication Channels

9.1.1Communication Channels

9.1.2Modulation

9.1.3Attenuation

9.2Digital Communication

9.2.1Digital & Analogue Signals

9.2.2Representing Sound

10Electric Fields

10.1Electric Fields

10.1.1Coulomb's Law

10.1.2Electric Field Strength

10.1.3Electric Field Strength 2

10.1.4Electric Potential

10.1.5End of Topic Test - Electric Fields

10.1.6A-A* (AO3/4) - Electric and Gravitational Field

10.2Capacitance

10.2.1Capacitance

10.2.2Parallel Plate Capacitor

10.2.3Energy Stored by a Capacitor

10.2.4Capacitor Discharge

10.2.5Capacitor Charge

11Current Electricity

11.1Current Electricity

11.1.1Basics of Electricity

11.1.2Mean Drift Velocity

11.1.3Current-Voltage Characteristics

11.1.4End of Topic Test - Basics of Electricity

11.1.5Resistivity

11.1.6End of Topic Test - Resistivity & Superconductors

11.1.7Power and Conservation

11.1.8Microphones

11.1.9Components

11.1.10Relays

11.1.11Strain Gauges

11.2DC Circuits

11.2.1Circuits

11.2.2Potential Divider

11.2.3Emf & Internal Resistance

11.2.4End of Topic Test - Power & Potential

12Magnetic Fields

12.1Magnetic Fields

12.1.1Magnetic Flux Density

12.1.2End of Topic Test - Capacitance & Flux Density

12.1.3Moving Charges in a Magnetic Field

12.1.4Magnetic Flux & Flux Linkage

12.1.5Electromagnetic Induction

12.1.6Electromagnetic Induction 2

12.1.7Magnetic Flux Density

12.1.8Magnetic Resonance Scanning

12.2Alternating Currents

12.2.1Alternating Currents

12.2.2Operation of a Transformer

12.2.3End of Topic Test - Electromagnetic Induction & AC

12.2.4Rectification

13Modern Physics

13.1Quantum Physics

13.1.1The Photoelectric Effect

13.1.2The Photoelectric Effect Explanation

13.1.3End of Topic Test - The Photoelectric Effect

13.1.4Collisions of Electrons with Atoms

13.1.5Energy Levels & Photon Emission

13.1.6Wave-Particle Duality

13.1.7End of Topic Test - Absorption & Emission

13.1.8Band Theory

13.1.9Diagnostic X-Rays

13.1.10X-Ray Image Processing

13.1.11Absorption of X-Rays

13.1.12CT Scanners

13.2Nuclear Physics

13.2.1Rutherford Scattering

13.2.2Atomic Model

13.2.3Isotopes

13.2.4Stable & Unstable Nuclei

13.2.5A-A* (AO3/4) - Stable & Unstable Nuclei

13.2.6Alpha & Beta Radiation

13.2.7Gamma Radiation

13.2.8Particles, Antiparticles & Photons

13.2.9Quarks & Antiquarks

13.2.10Particle Interactions

13.2.11Radioactive Decay

13.2.12Half Life

13.2.13End of Topic Test - Radioactivity

13.2.14Nuclear Instability

13.2.15Mass & Energy

13.2.16Binding Energy

13.2.17A-A* (AO3/4) - Nuclear Fusion

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