Calculus I

study guides for every class

that actually explain what's on your next test

Hooke’s law

from class:

Calculus I

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.

congrats on reading the definition of Hooke’s law. now let's actually learn it.

ok, let's learn stuff

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?
© 2024 Fiveable Inc. All rights reserved.
AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.
Glossary
Guides