How does a large spring constant (k) affect the elasticity of a string?

A large spring constant (k) indicates that the material is stiffer and less prone to stretching under a given load. In physics, the spring constant is a measure of how much force is needed to stretch or compress a spring by a unit distance. According to Hooke's Law, the force (F) applied to a spring is directly proportional to the displacement (x) from its equilibrium position, represented by the formula F = kx.

When the spring constant is large, it means that a greater amount of force is required to produce a small amount of displacement. Thus, a string with a large spring constant will resist deformation more than one with a smaller spring constant. This inherent rigidity translates to the string being harder to stretch, leading to the conclusion that a larger spring constant indeed makes the string less elastic and more challenging to extend.

The other options generally misinterpret the relationship between spring constant and elasticity, but understanding that a large spring constant correlates to reduced extensibility and greater stiffness helps clarify the mechanics of elastic materials.