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Properties of Matter

13 min read

Elasticity and Young’s modulus

A material is elastic if it returns to its original shape when the force is removed. For a wire stretched by a force F, stress is the force per unit cross-sectional area and strain is the extension per unit original length.

Stress σ in pascals, strain ε has no unit, Young modulus E in pascals. Steel: E ≈ 2 × 10¹¹ Pa; copper 1.2 × 10¹¹ Pa; rubber 10⁷ Pa.
  • Young modulus (Pa)
A stress–strain graphA graph of stress against strain for a ductile metal wire. The line is straight up to the limit of proportionality, where Hooke’s law holds and the gradient is the Young modulus. Past the elastic limit the wire is permanently stretched, then it reaches the yield point, the maximum or ultimate tensile stress, and finally breaks.strainstresslimit of proportionalityelastic limit / yieldultimate tensile stressbreaksgradient = Young modulus E
Open the Hooke's law lab
Add masses to a spring and measure the extension.
Try itStretching a wire

Choose the force, the length, the diameter and the material (Young modulus). Find the stress, strain and extension.

Worked exampleYoung modulus of a wire

A steel wire of length 2.0 m and cross-sectional area 1.0 mm² stretches by 1.0 mm under a load of 200 N. Find the Young modulus.

  1. Stress = 200 ÷ (1.0 × 10⁻⁶) = 2.0 × 10⁸ Pa.
  2. Strain = 0.001 ÷ 2.0 = 5.0 × 10⁻⁴.

Answer: 4.0 × 10¹¹ Pa.

The energy stored in a stretched wire or spring equals the area under the force–extension graph.

Surface tension and capillarity

The surface of a liquid behaves like a stretched skin. The surface tension γ is the force acting along a line of unit length in the surface (N/m), or the energy needed to make 1 m² of new surface. It is caused by the unbalanced attraction of molecules at the surface by those below. Water has γ ≈ 0.072 N/m at 20 °C and it decreases when the liquid is heated or when detergent is added.

The rise of a liquid in a capillary tube of radius r, with contact angle θ. The excess pressure inside a small droplet of radius r is 2γ/r.
Try itCapillary rise

Choose the radius of a glass capillary tube. Find how high water rises in it. (γ = 0.072 N/m, θ = 0°, ρ = 1 000 kg/m³)

Steel is about 20 times stiffer than wood and 20 000 times stiffer than rubber.

Density and intermolecular forces

Density ρ = mass ÷ volume. The behaviour of matter comes from forces between its particles. At close range they repel; further apart they attract; the balance gives an equilibrium separation. Stretching a solid pulls atoms apart against the attractive force. When a solid is compressed the repulsive force pushes back.

Solid typeBondingProperties
CrystallineRegular arrangement of atomsSharp melting point; may be anisotropic (properties differ with direction)
Amorphous (glass)No long-range patternSoftens over a range of temperatures
Polymeric (rubber)Long chainsElastic over large strains
Check yourself The Young modulus is the ratio of…
Check yourself Which will make a liquid rise higher in a capillary tube?
Check yourself The area under a force–extension graph gives…

Key terms

Stress
Force per unit cross-sectional area.
Strain
Extension per unit original length.
Young modulus
The ratio of stress to strain in the elastic region.
Surface tension
The force per unit length along the surface of a liquid.

Summary

  • Stress = F/A; strain = ΔL/L; E = stress ÷ strain; energy stored = ½FΔL.
  • Past the elastic limit a material deforms permanently.
  • Surface tension explains droplets and capillary rise h = 2γcosθ ÷ ρgr.
  • Properties of matter arise from intermolecular forces.
Fluid Dynamics Heat