If a spring is easily extended, what does this imply about its spring constant?

When a spring is easily extended, it indicates that less force is needed to achieve a significant stretch. This relationship between the force applied to the spring and the distance it stretches is described by Hooke's Law, which states that the force ( F ) exerted by a spring is proportional to the extension ( x ), formulated as ( F = kx ), where ( k ) is the spring constant.

A small spring constant signifies that the spring is relatively flexible or weak and requires less force to produce a certain amount of extension. This is consistent with the observation that the spring can be easily extended. Thus, when the spring extends easily, it is indicative of a small spring constant, as less force is needed for greater extensions.

The other answers do not hold true in this context. For instance, a large spring constant would suggest that the spring is stiff, requiring more force for a given extension, thereby contradicting the premise of the spring being easily extendable. A zero spring constant would imply that there is no restorative force, meaning the spring does not behave like a spring at all, which does not align with the question’s scenario. A negative spring constant is not physically meaningful in this context as it does not accurately describe