Springs and Elasticity: The load per unit deflection of a spring is called what?

Introduction:
The question tests basic spring terminology in mechanics of materials. When a spring is loaded, it deflects. The proportionality between the applied load and the resulting deflection is a fundamental property used in design and testing of springs.

Given Data / Assumptions:

• Linear elastic behavior holds (Hooke's law regime).
• Deflection is small and recoverable (no plastic deformation).
• We are naming the parameter defined as load per unit deflection.

Concept / Approach:
For a linear spring, load P and deflection δ follow P = k * δ. Here, k is the spring rate, also known as spring stiffness. Therefore, load per unit deflection equals k. Other terms in the options are standard but mean different things in material testing.

Step-by-Step Solution:
Identify definition: load per unit deflection ⇒ P/δ.Relate to Hooke’s law for springs: P = k * δ ⇒ P/δ = k.Therefore, the required term is spring stiffness (spring rate).

Verification / Alternative check:
Units check: If P is in N and δ in m, k is N/m, which is the standard unit of stiffness. This dimensional confirmation verifies the identification.

Why Other Options Are Wrong:
Proof resilience: Energy per unit volume up to elastic limit, not load/deflection.Proof stress: Stress used to define yield-like behavior (e.g., 0.2% offset), unrelated to spring rate.Proof load: A specified test load in quality checks, not a ratio.Spring index: Ratio of mean coil diameter to wire diameter, a geometry parameter.

Common Pitfalls:
Confusing stiffness (k) with strength-related terms (proof stress) or energy terms (proof resilience). Another common error is mixing geometric quality factors (spring index) with mechanical response parameters.

Final Answer:
stiffness.