Hooke's law establishes the relationship between which two physical quantities in elastic materials?

The correct answer is Stress and Strain.

Key Points

• Hooke's law states that, within the elastic limit, the deformation (strain) of an elastic material is proportional to the applied force (stress).
• The law is mathematically expressed as σ = Eε, where σ is stress, ε is strain, and E is the material's modulus of elasticity.
• This principle is fundamental to understanding the behavior of materials under elastic deformation and is crucial in fields like material science and engineering.
• Stress refers to the force per unit area applied to a material, while strain is the relative deformation or change in shape/size of the material.
• Hooke's law applies only within the elastic limit, beyond which permanent deformation occurs.

Additional Information

• Elastic Limit: The maximum stress that a material can withstand without undergoing permanent deformation.
• Young’s Modulus: A measure of the stiffness of a material, defined as the ratio of stress to strain in the linear region of the stress-strain curve.
• Stress Types: Stress can be classified as tensile, compressive, or shear based on the direction of the applied force.
• Applications: Hooke's law is widely applied in designing springs, calculating material properties, and analyzing mechanical systems.
• Limitations: Hooke's law is valid only for elastic materials and does not account for plastic deformation or non-linear stress-strain behavior.