Talk:Hooke's law

Thank you for this Article you guys really saved my ass. —Preceding unsigned comment added by 74.232.151.240 (talk) 04:13, 10 September 2007 (UTC)

I think the comment about hashing would be better placed on the anagram page.

Charles Matthews 12:13, 20 Mar 2004 (UTC)

Would it be appropriate to mention here that Hooke's Law is only a linear approximation (albeit one that is very good up to the elastic limit)? CyborgTosser 01:04, 23 Aug 2004 (UTC)

I agree, plus I think the use of stress/strain should be toned down. It's not the main idea behind Hooke's Law. --Dan 15:02, 3 August 2006 (UTC)

The picture shows a compression spring so the text under the picture should surely say Hooke's law accurately models the physical properties of common mechanical springs at small extensions or compressions. As a newbie I don't know how to edit the text myself. (cuddlyable3)84.210.139.189 11:07, 12 December 2006 (UTC)

I've changed it to Hooke's law accurately models the physical properties of common mechanical springs for small changes in length. - EndingPop 13:01, 12 December 2006 (UTC)

Tensor notation

Hi,

Does anyone know whether in the generalized form, some indices are covariant and some other are contravariant? So should we write something like

$\sigma _{ij}=C_{kl}^{ij}\cdot \varepsilon ^{kl}$

(random proposition)?

I never saw something like this in my books, nobody cares in continuum mechanics, but if we want to be strict and stick to the math conventions...

Cdang 15:34, 26 Nov 2004 (UTC)

Probably more like

$\sigma _{ij}=C_{ij}^{kl}\cdot \varepsilon _{kl}$

actually.

(PS There is something suspicious about the strain tensor, though, as I read in another encyclopedia.)

Charles Matthews 16:37, 26 Nov 2004 (UTC)

I got another answer from fr:, someone proposes σ_jⁱ because it should be covariant in j (number of the face) and contravariant in i (axes of the force). Any other opinion ?

other opinion: the force is of same type than the conjugate momentum and thus of opposite type than the coordinate; the faces are also "dual" to the coordinates (via the completely antisymmetric tensor of rank 3), thus both indices should be of the same type. (But maybe I made an error in my reasoning...). But without considering opinions, one could just check its transformation properties under rotations...— MFH: Talk 18:12, 20 Jun 2005 (UTC)

Concerning your suspicion about the strain tensor, pleasewrite them down at the talk page.

Cdang 13:44, 6 Dec 2004 (UTC)

As it is written currently on strain tensor, the latter should have one upper and one lower index (but maybe rather x^j is meant to be there instead of x_j, and idem for u).

Next, upper and lower indices are different only if the metric is different from δ_ij, else this tensor and its inverse allow to raise and lower indices. However, in 3 dimensions people usually consider x^j and x_j the same. Without fixing a convention about the index position of coordinated and derivatives, it is quite useless to ask this question for more complicated derived tensors (imho). — MFH: Talk 17:38, 20 Jun 2005 (UTC)

Microscopic Interpretation of Hooke's Law

I am missing any reference to the microscopic interpretation of Hooke's law in the article, and in particular to the fact that it starts to fail already at about 1% of the value that should be expected if molecular forces are responsible. I have discussed this issue on my page http://www.physicsmyths.org.uk/hooke.htm and suggested there that in fact plasma polarization fields due to free electrons in the material might actually be responsible for the linear stress/strain curve in the Hooke-region.

Thomas

Hooke's law is an observation expressed in simplistic linear math. You are trying to derive it from atomic-level analysis and have a hypothesis. Good luck, that is research.Cuddlyable3 19:16, 12 February 2007 (UTC)

citation

i don't know why this was added to the end of the article:

Bibliography citation (MLA style): Various Authors. “Hooke’s Law.” Wikipedia. 18/08/2005. Wikipedia, 19/08/2005 <http://en.wikipedia.org/wiki/Hooke's_law>

. — Omegatron 13:35, 22 September 2005 (UTC)

Series spring derivation

Shouldn't the line;

$F_{b}=-k_{2}\left(x_{2}-x_{1}\right).\quad \quad \quad (1)\,$

Read;

$F_{b}=-k_{eq}\left(x_{2}-x_{1}\right).\quad \quad \quad (1)\,$

k_1 and k_2 haven't been introduced yet

Please sign your posts. Stovetopcookies 02:06, 18 November 2006 (UTC)

Why talk about a prismatic rod?

"For many applications, a prismatic rod, with length L and cross sectional area A, can be treated as a linear spring."

Under the heading "Details" the above sentence with its reference to an unfamiliar "prismatic rod" confused me. The term "prismatic rod" just links to "bar" which has a lot of meanings. Apart from that obscure word "prismatic" I think the unclarity is because the writer has a diagram in his head that we can't see. That diagram would show that the discussion has changed from a coiled spring like in the picture to an elemental block of material, and that this is being extended (or compressed) in the direction of its length L, which is not obvious. (cuddlyable3) 84.210.139.189 15:00, 11 December 2006 (UTC)

In structural analysis a prismatic rod usually refers to a rectangular prism. Regardless, this statement about the linearity of the stress-strain curve is true for any bar of constant cross-section. I've made this change in the article. -EndingPop 18:07, 11 December 2006 (UTC)

As you see my objection is to using the word "prismatic" which can send an ordinary reader (equipped with an ordinary dictionary and not privy to the jargon of structural analysis) into a spin. In the real world the statement is NOT "true for any bar of constant cross-section". Uniform cross-section is not even a requirement for Hooke's law, only for the elemental analysis to follow. I also dislike the introduction words "For many applications..." which smack of pedantic vagueness.

As a friendlier alternative I suggest:

We may view a small rod of any elastic material as a linear spring. The rod has length L and cross-sectional area A. (cuddlyable3)84.210.139.189 10:57, 12 December 2006 (UTC)

Treatment of zero-length springs

The discussion of zero-length springs seems confused, and badly obscures the simple definition of a zero-length spring, namely a spring for which L0 is zero in the expression force = (spring constant) * ( length - L0 ). The article also misleadingly asserts that zero-length springs do not obey Hooke's law: in a typical zero-length spring's operating range, the force is indeed a linear function of the length, and that is Hooke's Law. One might wonder whether Hooke's Law requires that the linear relationship extend all the way to zero force, but even if one asserts that there is such a requirement (which is not stated in the current article, by the way), it does not rule out Hooke's-Law behavior of zero-length springs, since a zero-length spring can be constructed to encompass the zero-force region within its linear regime. Thus, non-Hooke's-Law behavior is not an essential attribute of zero-length springs.

I would propose that the discussion of zero-length springs adds nothing to the discussion of Hooke's Law, and should appear as a standalone Wikipedia entry. Since the only discussion of zero-length springs that I've ever seen relates to gravimetry, the web page at http://jclahr.com/science/psn/zero/winding/gravity_sensor.html would make an excellent starting point.

Peter 22:06, 11 January 2007 (UTC)

There was an article on zero-length springs, but as it was a stub and said nothing that was not already stated in this article, I deleted it and replaced it with a redirect here. Heliomance 12:53, 12 January 2007 (UTC)

The discussion on zero-length springs is not confused, it is incorrect. As can be found from the references, the zls is designed to be linear, but have an (apparent) length of zero. The constant-force element comes from the way it is used in the LaCoste suspension, which is a particular geometry. Pedant543 06:41, 5 November 2007 (UTC)

Relationship to Harmonic oscillator

This page should link to Harmonic oscillator at some point and discuss the relationship. —The preceding unsigned comment was added by 132.206.14.212 (talk) 20:51, 25 January 2007 (UTC).

As long as the oscillation stays within the range where the spring obeys Hooke's law, the oscillation is so-called Simple Harmonic Motion. That means it follows a sinusoidal function of time in the ideal case (always modified in practice by friction and/or transient disturbance, i.e. we can't make it a perpetual motion device). Be wary of HagermanBot's proposal because of the following nemenclature tangle: "harmonics" in music and electronics are overtones (multiples) of the fundamental frequency. From that viewpoint, the Simple harmonic motion of the ideal Hookean spring oscillator means Without harmonics. I hope there is a less confusing way to explain the above.Cuddlyable3 16:56, 8 February 2007 (UTC)

IP edit, can somebody verify

Referring to this recent edit, can this (no edit summary) be verified or should it be reverted because no verification was given? --Berland 11:10, 18 May 2007 (UTC)

Ok, I had a look at it myself, and the change made the formula consistent with the preceding, so the edit is hereby verified. --Berland 11:14, 18 May 2007 (UTC)

Tensor notation part perhaps a bit unprecise?

Am I the only one who thinks, that the last part of the article is, from a physical point of wiev, a bit wierd? The point of writing up Hookes Law in tensor notation is not just so the eggheads can use their fancy math, but it is needed to make a precise description of the elastic properties in 3D (what the derivation shows). Since the page already use expressions from Landau & Lifshitz, why not go overboard and use a thermodynamic derivation like theirs? That would 1. Show the importance of the 3D expression 2. Give some useful connections to thermodynamics via. the identity: $\left({\frac {dU}{d\varepsilon _{ij}}}\right)_{S}=\sigma _{ij}$ I would gladly write it, if someone else would correct my wiki-errors. I suspect I'd make quite a few...