From f321130183270b3090b41bf60e01ea3202efa4e1 Mon Sep 17 00:00:00 2001 From: Krishna Date: Thu, 19 Sep 2024 00:01:30 -0500 Subject: [PATCH] springs --- content/physics/Forces.md | 31 +++++++++++++++++++++++++++++++ content/physics/hooke.png | Bin 0 -> 373720 bytes 2 files changed, 31 insertions(+) create mode 100644 content/physics/hooke.png 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 0000000000000000000000000000000000000000..d6e5040679d086d5b72937a73dfadcc20d10f0ec GIT binary patch literal 373720 zcmeAS@N?(olHy`uVBq!ia0y~yU{_{fV6Eq1VqjpH_~qI%1_lPs0*}aI1_r((Aj~*b zn@^g7L4m>3#WAEJ?#^~UKS|)vQi3+cl%EF@A9Rk~uk~c;t9^Pc0_l>Rl z>)HOT-`GwsdjD>^*z7BMYj3M+w&-~63SGI)TFd#n`4toMvvcmtU$;6pXJ=-~s+(!^ z&)Zkc`CM6lZs)q4>x$=Q#$A72;}<5;#>fByns27%fM|vX*^{<_oXN06HIo%2;^BP> zszF+1c6VIX5Qcv|4#x;&PCkIDfu<*_#`Yo6}Ue85kULZ)`|B{CfRA~(O=_xqiovYSrqE|bXST^=CQ0s{gb>{0>Q z(>+vz??&LOtE|W5yE$%nlY;E%KzPVPVUe_2H8s_G`y|q*Rry*o|L-c3RdQC_cP_qjg6br&-;Nx zaKilg_LZNW9PJj@ho=@$E*c`aY=v@BQBhHGv9x*K932J*hOLU~>dONcyM29ib#?sy zx=n1Qfn}Q*8OnUwYbU#n*`FdXm; zkBZurd3l)u&up{YS!*0)Q+%`;N?q#e{@vJ^oPKuJRB$*XUR@Qs*sWK}wyMO@(Qy-7 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