Final answer:
The force applied to stretch a Hooke's law spring is directly proportional to the displacement of the spring, corresponding to Hooke's law (F = -kx), where F indicates force and x represents displacement.
Step-by-step explanation:
The relationship between force applied and the displacement of a spring, as described by Hooke's law, is directly proportional. This means that the force necessary to stretch or compress a spring varies linearly with the distance the spring is stretched or compressed, provided the deformation stays within the spring's elastic limit. Hooke's law can be expressed as F = -kx, where F is the force exerted by the spring, x is the displacement, and k is the spring's force constant. The minus sign indicates that the force is in the opposite direction of the displacement.
Given the choices presented in the question, the correct relationship is b) Directly proportional because as the spring is stretched from 0 N to 44.9 N, the displacement also increases accordingly, maintaining this proportionality. Hooke's law is a fundamental concept in physics and provides insight into the elastic properties of materials.