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 equilibrium.

5 Must Know Facts For Your Next Test

1. The spring constant $k$ is a measure of the stiffness of the spring.
2. Hooke's law can be integrated to find the work done in stretching or compressing a spring: $$W = \int_0^x kx \, dx = \frac{1}{2}kx^2$$.
3. The graph of Hooke's law is a straight line passing through the origin with slope equal to $k$.
4. Hooke's law applies only within the elastic limit of the material; beyond this limit, permanent deformation occurs.
5. In problems involving Hooke's law, integration techniques are often used to calculate potential energy stored in a spring.

Review Questions

• What does the constant $k$ represent in Hooke's law?
• How do you calculate the work done on a spring using integration?
• What happens when a material exceeds its elastic limit according to Hooke's law?

Related terms

Elastic Potential Energy: The energy stored in an elastic object, such as a spring, when it is stretched or compressed. It is given by $$U = \frac{1}{2}kx^2$$.

Spring Constant: A parameter that measures how stiff and resistant to deformation a spring is. Represented by $k$ in Hooke’s Law.

Elastic Limit: The maximum extent to which a material can be stretched or compressed without undergoing permanent deformation.