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Old Feb 20th 2018, 11:06 AM   #1
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Hook's Law Graph Orientation

Hook's law is commonly represented with F along the vertical Y axis and extension along the horizontal. This is what the text books stipulate, at l;east in the UK. I've seen an Asian video which has it the other way around, but elsewhere it's as stated.

Yet this commonly-accepted orientation reverses the convention of placing the dependent variable on Y.

So why does convention require the counter-intuitive orientation?
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Old Feb 20th 2018, 11:11 AM   #2
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The strain energy is the area under the graph in the conventional presentation.

The area between the graph and the vertical axis is called the complementary energy and is not equal to the strain energy in the general case.

So beware presentation the other way round.

https://www.google.co.uk/search?sour....0.sxR4stKTIVg
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Old Feb 20th 2018, 11:29 AM   #3
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Studiot, thanks for making time to help me. I accept your point about strain energy. If we reverse the graph we'd have to reverse the strain energy definition or gt the wrong answer. So don't do it - I get that. But it doesn't explain why the common convention of presenting the dependent variable on Y is abandoned here. In my saner world (he said) Force would be on X - the thing you change, extension would be along Y - the thing which arises from the change you made, and strain energy would be defined the other way.

So. Anyone?

It's a bit like Ohm's law = V = IR. That always seemed counter-causal to me. It's ont that the voltage dropped is equal to the current flowing time the resistance. It's that IF YOU APPLY a voltage V, then a current I WILL FLOW through a resistance R. Clearly, mathematically, they are re-arrangements of the same thing, but in terms of an understanding of reality - one is helpful, and the other is confounding.
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Old Feb 20th 2018, 11:55 AM   #4
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But which force?
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Old Feb 20th 2018, 12:23 PM   #5
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My thought also. E=IR is called a Law. With this relation, E,I and R exist together.
What is a Law? Stress as E times strain. Law? Again E, stress and strain happen in
combo. Another law? So what is a constituitive relation? A definition?

F = mA ... another law? Has meaning with A = 0. Has meaning with Sum of F = 0
This is a Law.
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Old Feb 20th 2018, 12:46 PM   #6
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I am glad to see someone take a deeper interest.

I asked 'what force' because there are actually two forces.

The load and the restoring force or the (reaction from the loaded object).

Note that you can also regard force as the dependent variable.

So the force required to stretch a spring a given amount = spring constant x the given amount

Note that the spring constant is a characteristic of the spring, the Force is not.

BBC - GCSE Bitesize: Hooke's Law
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Old Feb 21st 2018, 02:35 AM   #7
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Interesting stuff for sure, but ultimately, for me, un-satisfying.
You apply the force, and the sprint stretches. Force is the controlled variable and is usually on the X axis. Extension is what happens when you apply the force - it is the dependent variable and belongs on the Y axis.

Studiot I take your point about reaction force. It's a clever point, and it's undeniably true, but it doesn't really address the common sense "obvious" real-world application of Hooke's law - which is that you hang the (swear) wight, and then you measure the (swear) extension. " (swear)ed" in this case, is a scientific term.

[Struts off stage right muttering "(swear)ed straight"]

Last edited by topsquark; Feb 21st 2018 at 03:04 AM.
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Old Feb 21st 2018, 08:05 AM   #8
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Studiot I take your point about reaction force. It's a clever point, and it's undeniably true, but it doesn't really address the common sense "obvious" real-world application of Hooke's law - which is that you hang the (swear) wight, and then you measure the (swear) extension. " (swear)ed" in this case, is a scientific term.

That's a bit strong.

Take a close look at these graphs.

In the first one I have plotted Load against Extension in the conventional manner.

Note that this is a well behaved mathematical function, with the load being a single value for any given value of extension.

Thus the function described by this graph can be substituted into all sorts of mathematical formulae and procedures without problem.


Now look at the graph drawn the other way round.

I have indicated that points 1 and 2 on the graph have the same value of load, but have different values of extension.

This is the real world that you were so flippant about.

This means that extension as a function of load is not a single valued function and cannot be used in formulae associated with the mechanics of the situation. The example I have already offered you is the work done by the load or the energy stored in the spring.

All real world elastic objects act like this.
Attached Thumbnails
Hook's Law Graph Orientation-load_ext.jpg  
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