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15 April 2018

Fun story of the Hooke’s law

I must confess I always felt like a rebel when it comes to how I think about engineering and teaching. I’m not a complex math junky, but I don’t think it stopped me to understand complex problems. If anything I believe I understand them even better… and lack of “math” simply made stuff more fun and “experimental”!

Since you are reading this I hope you feel this at least a bit as well.

Some time ago Zeus recommended me a book by J.E. Gordon “Structures or why things don’t fall down”. The title itself pulled the string in my soul… and I just got a copy by mail!

I must say that I instantly loved the style and how it is written, and I decided to share some awesome stories from it as I read along : ) As you know stories are so much more fun then equations. Also knowing how people figured things out in the first place will definitely help you to understand those things! After all… scientists added mathematics at a much later stage!

Today, a brief and unexpected story of Hooke’s law!

The Hook(e)

The story starts with the fundamental question that is:

Why stuff resist loads at all?

What happens, that when you press a stone it’s… well “solid”. Why does it resist the load?

This is not a trivial question, and it’s worth mentioning we are somewhere in XVII century. This means that it’s not the only thing we don’t know : ) In fact, it’s so difficult, that Galileo himself didn’t really come up with a good answer to this issue!

First real progress was made by Robert Hooke (1635-1703) who lived almost at the same time as Isaac Newton (1642-1727). They even knew each other, at least to the degree sufficient for Newton to despise Hooke… but more on that later : )

Hooke realized that things can resist load only by pushing back at it with the same force. The simplest example is that when I stand on the ground, the ground is pushing at my feet with the same force as my feet are pushing on the ground. If that wouldn’t be the case I would be in motion! If the ground would be pushing “weaker” (or not pushing at all) I would start to dig into the ground, and if the ground would push harder I would be launched into the air!

The cat

The thing is… why on earth does the ground push on you?! Ok, in case of the ground you could propose various philosophical or even religious arguments. But of course, this is not limited to standing on something by far! There are a lot of examples of this “equilibrium” and the best one comes directly from Gordon’s book (and in style!):

(…) it is generally fairly easy to see why a load pushes or pulls on a structure. The difficulty is to see why the structure should push or pull back at the load. As it happens, quite young children have had some inkling of the problem from time to time.

‘Do stop pulling the cat’s tail, darling.’

‘I’m not pulling, Mummy, Pussy’s pulling”.

If we are talking about living creatures we can imagine that cat uses its muscles trying to yank its tail free. This is why it “generates” force that is opposite to girls pull on its tail. Since both forces are equal there is equilibrium and neither girl nor cat moves (the cat is not happy about that!).

But imagine the same girl pulling a string attached to the wall. She does not move, so it seems that the wall is pulling the string just as the cat did. But walls don’t have muscles! And yet apparently they pull all the same on the string attached to them… provided that you are pulling the string as well!

In its simplicity, this is the core of the problem. Solving it must have taken some serious thinking! Finally, however, Hooke concluded:

The power of any Spring is in the same proportion with the Extension thereof!

From there it was quite easy to sum it into a shorter sentence:

As the extension, so the force

And this is what we now call the Hooke’s law. He published it in 1679.

This was a really neat discovery. The more you pull the more material deforms. Since material does not like to be “deformed” if pulls back at the string to go back to a previous state. Simply put, Hooke discovered elasticity!

Funny thing is that mathematics was not involved. This happened later : ) Now wiki for Hooke’s law shows:

I don’t know what you think, but I prefer the cat!

Deeper into the stuff

Hooke was mostly examining entire structures (or things if you like). He would load beams and measure how much they deform etc. This allowed him to form general conclusions. He also realized that after the load was taken beams got back to their original shape within an accuracy of his measurements (which he wasn’t very good at!).

But Hooke did one more major thing (apart from inventing cool stuff like a universal joint that we use to this day). He observed that the “deformation” and “going back to original shape” is not the property of the structure itself. The conclusion was that it is a property of the material that builds the deforming object.

He reasoned, that everything is made of small particles that are connected by the “springs”. If you press the material the springs get shorter (and push back). This causes the “reaction force” in the material, and is also responsible for deformation. I like to use a table with a load as an example of this:

This is what happens inside the wall the girl is pulling with a string. It deforms ever so slightly, tensioning and compressing some of the “atom springs”. Since it wants to get back to original state it pushes back at the string hence creating equilibrium. A bit like a cat I would say!

Play nice! This will be good for your career!

What I love about this story the most is that Hooke did the engineering I love the most. He was very down to earth, and he used science to further down technology and standard of living for people. Hooke designed a lamp used in many households and carriages even 200 years after his death (the lamp used a spring feed to keep candlelight in the center of optical system systems even if the candle burnt and got shorter!). He helped to build a vacuum pump and figured out a compound microscope.

Sadly, Hooke was also known for his bad temper and huge ego. He was also a ladies’ man and lived for long in an informal relationship with his attractive niece Grece.

Newton (who personally was a snob) couldn’t stand that. He was more into “high-plane” science (apart from the law of motion he did some heavy research on the meaning of the number of the beast for instance)! But Newton also had an entirely different lifestyle and philosophy. Those two developed a bitter enmity, that lasted even after Hooke’s death.

Newton (who lived 20 years longer), did a lot to discredit Hooke, his memory and… the importance of applied science(!). At that time Newton was already a super-famous guy, so this came relatively easy. It is also why applied science didn’t get a lot of attention for the next 100 years (!). Next in the line for discovering something interesting about elasticity was Young and Cauchy… but that it for another story : )

Takeaway

There are few important things one can remember from this history:

• The material is made of atoms that are more or less connected with springs (if you like chemistry don’t yell at me… too much :P)
• If you pull the atoms get further apart, and the strings between them are in tension. They want to shorten to get to the previous shape!
• The same thing happens if you compress the material. Springs between atoms get shorter and want to extend to the original shape (pushing back at the load).
• The above is the basic concept we refer to as elasticity and was discovered by Hooke.
• If you happen to be a genius, and you know another one that has a different lifestyle than you… try to outlive him 😛

That’s all folks!

I hope you enjoyed the story, I know I did! Let me know if you like such posts and if it would be a good idea to write more of those! Also, if you like it share the story with your friends!

This is awesome! I’ve prepared a special free FEA course for my subscribers. You can get it below.

Author:Łukasz Skotny Ph.D.

I have over 10 years of practical FEA experience (I'm running my own Engineering Consultancy), and I've been an academic teacher for a decade. Here, I gladly share my engineering knowledge through courses, and on the blog!

Join the discussion

Yaniv Ben-David - 2019-12-13 12:40:49

Cool story!
I definitely know now what the next book I'm going to read will be...:)

Łukasz Skotny Ph.D. - 2019-12-13 20:12:04

Indeed! And definitely do that - that is an awesome book!

Utkarsh - 2019-02-05 17:49:34

Excellent article

Łukasz Skotny Ph.D. - 2019-02-06 08:22:40

Hey Utkarsh!

I'm really glad that you like it! All the best!

Zeus - 2018-05-01 10:46:53

I never understood the dichotomy between engineering ingenuity and mathematics, a good engineer needs both skills, now, I’m afraid that engineering degrees had been reduced to a series of formulas, not encouraging independent reasoning or the development of mental frameworks, that’s why Lukasz’ blog is so important, in this era of FEA and complex mathematical models, he recovers the essentials of engineering principles.

This is not easy, in fact, is the most difficult skill to acquire as an engineer, and it is of prime relevance when solveing complex problems, to name an example, check Antoni Gaudi (he wasn’t very good at maths) Sagrada Familia ropes model, engineering ingenuity as its best.

Łukasz Skotny Ph.D. - 2018-05-01 11:28:58

Wow... Zeus!

Thank you so much for kind words : ) I do agree a lot with what you just wrote, and also I'm really happy you find meaning in what I do : )

All the best
Ł

jeremy theler - 2018-04-24 14:06:30

I prefer the equations!

Łukasz Skotny Ph.D. - 2018-04-24 15:10:14

Hey Jeremy!

Ha! Each of his own I guess :)
I never liked those (apart from times when those made fun!), but maybe this is just because I know too little about stuff... who could tell!

What I know is that I far more enjoy estimate stuff with simple hand calculations and FEA rather than complex equations. They kind of make me feel as an "accountant" but without the "creative accounting" aspect of it :P

All the best Mate
Ł

jeremy theler - 2018-04-24 18:55:39

sure! but this is my motto: "simple problems usually have simple solutions, but complex problems always have complex solutions"

so if you want to fool around you can do back-of-the-envelope calculations, but if you want to go to mars, you will have to get serious about math...

Łukasz Skotny Ph.D. - 2018-04-25 03:01:19

Hey!

I can't agree here : )

Complex problems require complex analysis - this is for sure: I couldn't agree less! But I still don't know why you connect that with mathematics. I mean someone already did the math. The solvers are made already, and you can buy one. As long as you understand what it does, which parameters are responsible for what, and how to run an analysis (and what outcomes to expect) you're just fine. You can use it as a tool. If you would like to do your own solver - then, by all means, math is super important. But I'm a designer, not a solver-maker :)

On a side note, I would never call back-of-the-envelope calculations "fooling around". I consider this to be an art, that sadly is more and more missing among people. Good quick estimates (and knowing how to make them!) are super important in most complex problems. Otherwise, if you will take a "wrong turn" in the complex analysis... you may never know!

All the best
Ł

ijr - 2018-04-24 12:29:13

Thanks Lucasz.

I read that book many years ago and loved it.
Last year I came across a rebel continuum mechanics professor who is busy removing coordinates from mechanics. He is simply against coordinate systems. His argument is simple: Mechanics is about physical objects and unless you need coordinates to help solve a problem, start with the physics itself. He shows that coordinate systems kill all the intuition and can make mechanics appear complex. The most fundamental items in the physical world are scalars: energy, work, speed, mass etc. His approach makes such a complex subject fun.

Łukasz Skotny Ph.D. - 2018-04-24 15:07:31

Hey!

Wow - thanks for sharing that! Rebel professor sounds like a fun guy! Do you recall his name and where to find him?

I do believe that by the tens if not hundreds of Ph.D. we (as a humanity) managed to complex all the things into almost infinity... it strips all the fun from the engineering - which in my opinion is fun "by nature"!

Let's bring this fun back!
Ł

Cormac - 2018-04-24 09:20:50

That book and the follow on (The New Science of Strong Materials) by the same author are excellent for for engineers and non-engineers interested in how materials and structures work. I particularly liked the way he noted that while Greek architecture was beautiful, from a structural engineer's point of view it was very poor. The Greeks didn't use arches, which meant a lot of their buildings such as the lintel pieces in the parthenon loaded stone in tension. His explanation of the crack growth process as a surface tension analogue is the best I've seen anywhere.

If you want another book to make you think, look for Don Norman's Design of Everyday Things. Not about structures, but for anyone who has ever tried to design anything, it will guide your thinking towards good design. Last time I looked the PDF of the revised version was online. The revised version writes less about VCRs - probably the most consistently badly designed human interfaces of all consumer products - as there are plenty of people reading the book now who've never had to rewind a video tape in their lives.

Łukasz Skotny Ph.D. - 2018-04-24 12:22:42

Hey Mate!

I do have the Gordon book about materials (I ordered both at the same time... I haven't started it yet.

The other one I haven't seen - but I will look it up. + I know how to rewind a VCR tape :)

All the best, and thank's for suggestions!
Ł

barmin - 2018-04-17 09:56:15

And if you push strong enough, you can even get a nuclear fusion going on ;)

Neat article and it seems there is another good book to be read during the waiting for FEM results!

Łukasz Skotny Ph.D. - 2018-04-17 10:06:56

Lol!

Definitely a good read - I can't wait to read more, so there is something to this book :)

All the best
Ł