The stiffness of a spring is determined by the balance of intermolecular forces, specifically the electrostatic attraction between electrons and protons, and the repulsion due to the exclusion principle. Atoms in a solid are spaced at an equilibrium distance, which represents the lowest-energy configuration, requiring energy to stretch or compress the spring. The modulus of elasticity, particularly the Young's modulus for materials like iron, quantifies stiffness, with stiffer materials exhibiting lower extension under a given force. Stiffness can be categorized into various types, including axial, bending, and torsional stiffness, each defined by specific formulas. Understanding these principles is essential for grasping the physics behind spring stiffness.