# Spring Forces --- We often study springs using a simplified model. An **ideal spring** will: - be massless - be unable to bend - always obeys Hooke’s Law These requirements results in any ideal spring only being able to *exert forces parallel* to the string. ## Hooke’s Law **Hooke’s Law** states that the force needed to extend or compress a spring by some distance ($x$) *scales linearly* with respect to the distance ![[Spring Forces-1.png|650]] > [!NOTE] **Hooke’s Law** > > $F_\text{spring}=-k \Delta s$ > or > $F_\text{spring}=-k(s-s_0)$ > > where: > - $F_\text{spring}$ is the *restoring force* exerted by a spring > - $k$ is the *spring constant* (stiffness of the spring) > - $\Delta s$ is the *displacement from the relaxed position* (i.e. how much the spring is stretched or compressed) > - $s_0$ is the *relaxed length* of the spring ## Direction of Spring Force The **spring force** ($F_\text{spring}$) is called the *restoring force* because it always acts in the direction that would restore the spring to its relaxed length. If we were to consider this directionality, we can create a *vector form of Hooke’s Law*: $\vec{F}_\text{spring} = -k(s-s_0)\hat{s}$