Overview
This lecture reviews key concepts related to materials in physics, including forces, Hooke’s Law, stress and strain, Young’s modulus, and the behavior of different types of materials.
Tensile and Compressive Forces
- Tensile forces stretch (extend) a material.
- Compressive forces shorten (compress) a material.
Hooke’s Law
- Hooke’s Law: Force applied is proportional to extension (F = kx).
- F = applied force (Newtons), x = extension, k = spring constant (Newtons/meter).
- Extension = final length − initial length.
- The spring constant k = F/x, with units N/m.
- Force vs. extension graph: gradient = spring constant k, area under curve = elastic potential energy (work done).
Experiments for Hooke’s Law
- Suspend masses from a spring, measure extension for each mass.
- Use F = mg for force, plot force against extension.
- Accurate readings require eye-level measurement to reduce parallax error.
- Straight line through origin confirms Hooke's Law.
Elastic Potential Energy
- Elastic potential energy = ½ F x or ½ k x² (from area under force-extension graph).
- Units are Joules (N·m).
Stress and Strain
- Stress (σ) = force/cross-sectional area (N/m² or Pascals).
- Strain (ε) = extension/original length; unitless or as a percentage.
Ultimate Tensile Strength and Young’s Modulus
- Ultimate tensile strength: maximum stress a material withstands before breaking.
- Young's modulus (E) = stress/strain = (F/A) / (x/L) = (F × L) / (A × x).
Young’s Modulus Experiment
- Clamp wire horizontally, add varying masses and measure extension.
- Measure diameter with micrometer, area = π(d²)/4.
- Plot force vs. extension; gradient gives E via E = (gradient × original length)/area.
Deformation and Material Properties
- Ductile: can be drawn into wires.
- Elastic deformation: returns to original shape when force removed.
- Plastic deformation: does not return to original shape after force removed.
Stress-Strain Graphs for Different Materials
- Ductile materials: obey Hooke’s Law up to the limit of proportionality; elastic limit marks onset of permanent deformation; ultimate tensile strength is max stress before breaking.
- Brittle materials (e.g., glass): straight stress-strain line until breaking point; only elastic deformation.
- Polymeric materials (e.g., rubber, polythene): distinctive stress-strain curves, not straight; may show elastic or plastic behavior; Hooke’s Law not always obeyed; some energy lost as heat.
Key Terms & Definitions
- Tensile Force — force that stretches a material.
- Compressive Force — force that compresses or shortens a material.
- Hooke’s Law — force is proportional to extension within the elastic limit.
- Spring Constant (k) — stiffness of a spring, N/m.
- Stress (σ) — force per unit area, N/m² or Pascals.
- Strain (ε) — extension per unit original length, unitless.
- Ultimate Tensile Strength — maximum stress before breaking.
- Young’s Modulus (E) — ratio of stress to strain, measures stiffness.
- Elastic Deformation — material returns to original shape after force is removed.
- Plastic Deformation — permanent change in shape after force is removed.
- Ductile — can be drawn into wires; exhibits both elastic and plastic deformation.
- Brittle — breaks without significant plastic deformation.
Action Items / Next Steps
- Review stress, strain, and Hooke’s Law equations.
- Practice calculations for elastic potential energy and Young’s modulus.
- Revisit experimental setups for measuring spring constant and Young's modulus.