Hooke’s law

Definition

Hooke’s Law states that the force needed to extend or compress a spring by some distance is proportional to that distance. Mathematically, it is expressed as $F = -kx$, where $F$ is the force applied, $k$ is the spring constant, and $x$ is the displacement from the equilibrium position.

5 Must Know Facts For Your Next Test

1. Hooke's Law only applies within the elastic limit of a material, beyond which permanent deformation occurs.
2. The negative sign in Hooke's Law indicates that the force exerted by the spring is in the opposite direction of the displacement.
3. $k$, known as the spring constant, measures a spring's stiffness and has units of N/m (Newtons per meter).
4. The potential energy stored in a stretched or compressed spring can be calculated using $U = \frac{1}{2} k x^2$.
5. Hooke’s Law can be used to describe not just springs but also other elastic materials under small deformations.

Review Questions

• What does Hooke’s Law state about the relationship between force and displacement in an elastic material?
• How do you calculate the potential energy stored in a compressed or stretched spring?
• What happens when a material surpasses its elastic limit?

Related terms

Elastic Limit:

The maximum extent to which a solid can be stretched without permanent deformation.

Spring Constant ($k$): A measure of a spring's stiffness, defined as the ratio of force affecting the spring to its displacement.

Stress:

Force applied per unit area within materials that leads to deformation.