Lecture on Material Stretching and Young's Modulus

Factors Affecting Object Stretch

• Force:
  • Larger force increases extension.
• Cross-sectional Area:
  • Larger area makes stretching harder because material is thicker.
• Original Length:
  • Longer original length results in more stretch.
• Material's Property:
  • Young’s Modulus (E):
    • Measures how hard or easy it is to stretch a material.
    • Higher Young’s Modulus indicates more difficulty to stretch.

Equation for Stretching

• Extension depends on:
  • Force applied
  • Original length
  • Inversely proportional to area and Young's Modulus
• Young’s Modulus Equation:
  • Young’s Modulus (E) = Stress (σ) / Strain (ε)
  • Stress (σ): Force per unit area (similar to pressure, units in Pascals).
  • Strain (ε): Ratio of extension to original length (unitless).

Experiment to Measure Young’s Modulus

• Setup:
  • Two wires: one with a constant weight, another with varying weights.
  • Use a Vernier scale to measure extension.
• Vernier Scale Reading:
  • Measure how many millimeters zero on the scale has moved.
  • Find which line on the scale aligns best for tenths of a millimeter precision.

Graphical Analysis

• Stress vs. Strain Graph:
  • Straight line indicates proportionality.
  • Gradient gives Young’s Modulus.
• Mass vs. Extension Graph:
  • Straight line used to calculate gradient.
  • Provides information on Young’s Modulus using calculated gradient.

Material Behavior and Graph Interpretation

• Yield Point, Ultimate Tensile Strength, and Breaking Point:
  • Points on a graph indicating material limits.
• Limit of Proportionality and Elastic Limit:
  • Point where stress and strain are no longer proportional.
  • Elastic limit is the threshold beyond which deformation is permanent.

Material Types

• Brittle Materials:
  • High Young’s Modulus, breaks upon reaching limit, e.g., glass.
• Ductile Materials:
  • Can be plastically deformed, e.g., copper.

Loading and Unloading Curves

• Energy put in is area under the loading curve.
• Energy released is area under the unloading curve.
• Energy difference (hysteresis) is lost, often as heat.

Recap

• Understanding of stress, strain, Young’s Modulus, and their measurement.
• Importance of visual aids like graphs in interpreting material properties.