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.

5 Must Know Facts For Your Next Test

1. Hooke's law describes linear elasticity for small deformations.
2. The negative sign in $F = -kx$ indicates that the force exerted by the spring is in the opposite direction of displacement.
3. In calculus, Hooke's law can be integrated to find work done in stretching or compressing a spring: $W = \frac{1}{2} k x^2$.
4. The spring constant $k$ represents stiffness; higher values indicate stiffer springs.
5. Hooke's law only applies within the elastic limit of a material; beyond this limit, permanent deformation occurs.

Review Questions

• What does the negative sign in Hooke's law signify?
• How do you calculate work done using Hooke's law?
• What happens if a material exceeds its elastic limit according to Hooke's law?

Related terms

Elasticity: The property of an object or material that causes it to be restored to its original shape after distortion.

Spring Constant: A parameter that measures the stiffness of a spring, denoted as $k$, and used in Hooke’s Law.

Work: In physics, work refers to energy transfer when an object is moved over a distance by an external force; for springs, it's given by $W = \frac{1}{2} k x^2$.