Spring Force, Hooke's Law

Hooke's law

In physics, Hooke's law is an empirical law quantifying the force needed to extend or compress a spring with respect to the changed length:

$$F_s=k\Delta x$$

where $F_s$ is the spring force, $\Delta x$ is the changed length of the spring, $k$ is a constant with a unit of $N/m=kg/s^2$. Specifically, $\Delta x=x-x_0$, where $x$ is the current length of the spring, and $x_0$ is the original/natural length of the spring.

Spring constant

Spring constant is usually determined by the material and its shape. As you can see, the higher the spring constant $k$, the more force is required to deform the material, and the stiffer the material is.

This equation also largely holds for the deformation (change in both the shape and the size) of other elastic bodies, such as muscles reflexing, wind blowing on a tall building, car pressing on a long bridge, plucking a string of a guitar, propagating of waves during an earthquake. An elastic body is called to be Hookean if Hooke's law applies to it.

Elastic limit

Why, when we compress a spring and let it go, it comes back to the original shape? Why, when we compress a banana and let it go, it does not come back to the original shape? What is special about a memory foam mattress or a memory foam pillow?

Deformation can be elastic or plastic, or in between. Every object has a certain capacity of elastic restoration. When the deformation is too strong, it reaches the elastic limit and becomes plastic. This limit sometimes is called the limit of proportionality, because Hooke's law fits a linear relationship.

The lesson is that, do not abuse a spring or a spring scale by exerting an overwhelming amount of force.