Are you hooked on….Hooke’s Law?

Ever wonder what puts the spring in a spring’s step? Ever wonder why some are red, green, yellow, or blue? Why some are super light and others impossibly heavy?

Well, it’s all about Physics! It’s all about Hooke’s Law!  Wait? What? Were you surprised?  After all you are reading the blog of an Aerospace Engineer Pilates Instructor!

From the moment I started Pilates I was hooked! Yes, my pun is intended.  I had the distinct pleasure of suffering though….um I mean learning, yeah learning, Hooke’s Law very early on in my schooling.

What’s Hooke’s Law you say? Well, if you’ll allow me to step up onto my soap box for a moment…

Hooke’s Laws is what makes Pilates, well, Pilates! 

Hooke’s Law is what defines the springs we use every day to change bodies and put the spring in the steps of our clients! (yes, my puns are always intended!) So if we as Pilates teachers want to understand how the springs in Pilates work we must understand Hooke’s Law.

Hooke’s Law, states that the Force (F)  needed to pull a spring over a certain distance (x) is directly proportional to that distance, or simply put as F = k * x. So if we wanted to find out how much force a client needs to push the carriage of a Reformer out a certain distance, how would we do that?  If we are trying to find the Force (F), and we are given the distance (x), we first must know ‘k’. 

Dammit, what the letter ‘k’ is?!? 

‘k” is the “spring constant”, and it depends on the spring, but once you find it you’ll always know it because it’s like the spring’s fingerprint – it never changes. So great, more thinking.  We’ll get back to our example in a minute, but first more Physics!! 

Let’s start with a chart, everyone loves a chart right? The have bright colors, and pretty pictures!? How bad can it be?  

Have you ever seen something like this before?  It’s the chart a certain Pilates equipment manufacturer (see my note on manufacturers below) has on their website (click on it and it will bring you there):

What the hell does that mean, you might be saying? 

The vertical axis says “pounds” and the horizontal axis says “inches of extension”.  Correlating those to Hooke’s Law, F = k * x. Pounds is a Force so that is F, and inches of extension is a distance or x. 

Let’s look at the red line (we shall call this the “red spring”).  If you look at the red spring it crosses a whole bunch of black lines and those black lines have numbers by them.  Take a look at the red spring at 12 inches of extension follow the line across to read the number on the left of the chart and it reads 20 pounds. 

So what does this say?  It says that when 20 pounds is applied to the red spring it will stretch 12 inches. 

What does this mean?  It means that if you were to hang this red spring on a nail in the wall, attach a 20 pound weight at the end the spring would move 12 inches. 

It also means that we have F and now we have x, so we can find ‘k’! Yippee!  OH crap wait, that means we have to do math.  I tried to avoid it I really did!  I just couldn’t help myself!

F = k * x  if F = 20 and x = 12, what’s ‘k’?
20 = k *12
k = 1.6667

Knowing ‘k’ means that we know the fingerprint, the basic fundamental characteristic of that red spring. All the red springs from this manufacturer will always have a ‘k’ = 1.6667 (see my note on manufacturers below).

But, why should you care? as a Pilates teacher, of course? I mean, you care because it’s Physics and you LOVE Physics! Because it tells you what your Pilates equipment is doing! It tells you what your clients are doing on your Pilates equipment! And, what’s better, we can now continue with our example!  

Think about it, let’s say you have 4 of these red springs on your reformer, and just for the hell of it you have a smallish woman who only pushes the carriage out 12 inches when her legs are straight, that means that she’s pushing with 80 pounds of force to keep the carriage there! 

That’s hard work! (Not to be confused with the scientific definition of work which I explain here).

And to think there are people still out there that Pilates is easy!  They’ve clearly never tried it before, or ever taken a Physics lesson from yours truly!

**A short note on Pilates equipment manufacturer springs:  

Every manufacturer’s springs are different.  Some reformers have 5 springs, others only 4, some are all the same others have different colors, but the one thing they are all consistent on is that they make sure that all of their springs of each type/color are all roughly the same. So if you buy red springs from one company, they’ll probably be different than the red ones from another, but rest assured that if you buy 4 red springs from the same company they will all have roughly the same Spring constant (k).  

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4 comments on “Are you hooked on….Hooke’s Law?

  1. I was just discussing this during my last session. I found your posting by looking for the spring constants for the various colored springs. One question: Why don’t the lines in the chart start at zero force for zero extension?

    1. Hi Jim,

      Thank you so much for your question, and it is a great one! Each spring needs a bit of force, called initial force, to make the spring coils separate (inches of extension). It is at that instant that Hooke’s Law takes over (Hooke’s Law is not valid for forces less than 1 Newton).

      So as an example, if you look at the graph in the post above, you’ll notice that the blue line crosses the ‘y’ axis (pounds) at about 5 pounds. This means that it takes 5 pounds of force to get the coils of the blue spring to separate even the littlest bit.

      I hope this helps! Thank you for your question! Keep em’ coming!


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