The spring constant, denoted as $k$, is generally positive. It represents the stiffness of the spring, and by Hooke's Law, it relates the force applied to a spring to the displacement (stretch or compression) of the spring:

$F = -k \cdot x$

Here:

• $F$ is the force exerted by the spring (in Newtons),
• $k$ is the spring constant (in N/m),
• $x$ is the displacement of the spring from its equilibrium position (in meters).

The negative sign in the equation indicates that the force exerted by the spring is in the opposite direction of the displacement, meaning it resists the deformation (either compression or stretching). However, the spring constant $k$ itself is a positive value because it simply quantifies the stiffness of the spring, and stiffness cannot be negative.

So, in summary:

• The spring constant $k$ is positive.
• The force exerted by the spring, as given by Hooke's Law, is negative when the spring is stretched and positive when the spring is compressed (in terms of the restoring force).

Would you like a deeper explanation or examples of spring-related problems?

Here are 5 related questions to explore:

1. What happens to the spring force if the spring constant is large versus small?
2. How does the potential energy stored in a spring relate to the spring constant?
3. Why does Hooke’s Law only apply to springs that behave elastically?
4. How can we measure the spring constant experimentally?
5. How do different materials affect the spring constant?

Tip: Remember that the spring constant $k$ can vary depending on the material, diameter, and length of the spring!