diff --git a/content/physics/Forces.md b/content/physics/Forces.md index d1a9bbd..803c7bf 100644 --- a/content/physics/Forces.md +++ b/content/physics/Forces.md @@ -133,6 +133,37 @@ $$ \sum{\vec{F}}=\langle ma+mg;-\tfrac{\pi}{2}\rangle $$ +# Springs + +Springs are explained by something called *Hooke's Law*. It essentially states: + +> Ut tensio sic vic[^2] + +That translates to: + +> As extension, so is force + +$$ +\therefore \Delta x \propto F +$$ +The actual formula looks like: +$$ +\vec{F}_e=-k\Delta x +$$ +The subscript $e$ means 'the elastic force' or the force being exerted *by* the spring. That wording is hyper-specific for a reason, that reason being the slight distinction between the signs of the force vectors while the spring is in different states. As you'll see in the diagram below, a positive $\Delta x$ signifies an extension of the spring, which generates a negative force. The exact opposite is true in any other case. + +![](hooke.png) + +Like in any other problem of proportionality (in math), $k$ is taken to be the *constant* value of the proportion. The SI unit for the **spring constant** is Newtons per meter. Therefore, it is possible using simple algebra to show: + +$$ +k=\frac{||\vec{F}||}{x} +$$ + [^1]: I'm working in radians here. +[^2]: This is latin. + + + #physics diff --git a/content/physics/hooke.png b/content/physics/hooke.png new file mode 100644 index 0000000..d6e5040 Binary files /dev/null and b/content/physics/hooke.png differ