Lecture Notes: Types of Elasticity and Hooke's Law

Key Concepts

• Elasticity: Relates to how an object can change shape (compress, stretch, bend) under force.
• Deformation: Change in shape of an object due to applied forces.

Types of Deformation

• Elastic Deformation:
  • Object returns to original shape after force removal.
  • Example: Elastic band springs back.
• Inelastic (Plastic) Deformation:
  • Object does not return to original shape completely.
  • Example: Plastic retains shape.

Extension

• Definition: Increase in length of a spring when stretched.
• Natural Length: Length of a spring without applied external force.
• Measurement: Additional length measured as a spring is subjected to force.

Forces in Action

• Always requires more than one force to keep an object stationary.
• Even a single force application uses opposing force (e.g., floor pushes back).

Hooke's Law

• Formula: ( F = k \times e )
  • ( F ): Force applied (Newtons)
  • ( k ): Spring constant (Newtons per meter)
  • ( e ): Extension (meters)
• Explanation:
  • Proportional relationship between force and extension.
  • Spring constant ( k ) determines material stiffness.

Force-Extension Graphs

• Direct Proportionality:
  • Straight line passing through the origin signifies direct proportionality.
• Elastic Limit:
  • Point where line starts to curve.
  • Beyond this, Hooke's Law no longer applies, and deformation becomes inelastic.

Summary

• Understanding elasticity, types of deformation, and Hooke's law aids in comprehending material behavior under force.
• Elastic limit signifies transition from elastic to inelastic deformation.