• Kenosha Kid
    3.1k
    Sure, it's much more useful for more ideal mechanical oscillators like atoms. Not very universal for springs and stuff like Hooke had in mind.
  • SophistiCat
    1.8k
    Sure, it's much more useful for more ideal mechanical oscillators like atoms. Not very universal for springs and stuff like Hooke had in mind.Kenosha Kid

    It's very useful for practical stuff though: from ball bearings to bridges to tectonic plates. Take Hooke's law into 3D (with shear) and you get linear elasticity, the backbone of 90% of engineering mechanics from 19th century through the present day.
  • Cartuna
    176
    . Take Hooke's law into 3D (with shear) and you get linear elasticity, the backbone of 90% of engineering mechanics from 19th century through the present day.SophistiCat

    Where did you get that from? 90%? No way. Hooks law doesn't apply to most materials. Even with shear it can't be applied to most materials. Maybe for very small forces, or tiny displacements. Mostly though, a linear algebra just isn't applicable. For a metal spring in the physics class it will do. For an atomic nucleus inside an electron cloud, a Hooke approximation will do.
  • SophistiCat
    1.8k
    Where did you get that from? 90%? No way. Hooks law doesn't apply to most materials. Even with shear it can't be applied to most materials. Maybe for very small forces, or tiny displacements. Mostly though, a linear algebra just isn't applicable. For a metal spring in the physics class it will do. For an atomic nucleus inside an electron cloud, a Hooke approximation will do.Cartuna

    The 90% figure is rhetorical, but yes, much of engineering mechanics is based on the linear elastic model, with plasticity accounting for most of the rest. Applications of non-linear elasticity, rate-dependence, etc. are much less common.

    (Relatively) tiny displacements characterize the operating range of most buildings and machinery, and linear elasticity works well in that range. (Of course, the fact that it is computation-friendly is also a big factor in its popularity.) Forces don't have to be so tiny, since materials like steel and concrete have a high elastic modulus.
  • Cartuna
    176


    I'm not sure how a number can be rethorical. To which parts of engineering you refer? How materials respond to force when pushed or pulled? If you push or pull a material, like steel, or hit hit with a hammer, it will usually react linearly. A piece of steel will produce soundwaves constituted by harmonic oscillators. But all this behavior is preassumed when constructing buildings or bridges and this is what I meant by applying small forces. But the most interesting things happen above yielding, where non-linearity kicks in. Bridges snap, structures disrupt, crack, or break. Irreversibly. And it's that what matters.
  • Kenosha Kid
    3.1k
    By universal I was meaning ranges of values, not types of system. Your examples all suffer the same problem: for a given system, Hooke's law applies only for a (often very narrow) range of values, therefore isn't general, so has dubious claim to law. There's no problem with having a law that applies only to springs, if the law is general. The problem with Hooke's law is that it relies on something it cannot: the material properties of the system (which then change when you test Hooke's law beyond that narrow range of applicability).
  • TheQuestion
    58
    I recall a paper Hawking gave on how multiverses _restore_ the second law, solving the problem of what happens to information about particles destroyed in black holes. Iirc, it's that over an infinite number of universes, the net loss is zero. But don't trust my ability toKenosha Kid

    I like Stephen Hawking theory of the Multiverse. To sum it up in a nutshell he said the Universe is like a mosaic patter and that each region of our Universe may have its own laws of physics.

    A more reasonable theory to me.
  • Kenosha Kid
    3.1k
    The second law is a statistical law, so yes, it doesn't deliver absolutely certain predictions.SophistiCat

    How timely!

    https://www.nature.com/articles/s42005-021-00759-1
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