Re: Newton e Hooke

Jonathan Thornburg [remove color- to reply] il 12/02/2025 09:02:31 ha scritto:

In article <vne5fv$2i6se$1@dont-email.me>, Luigi Fortunati asked:
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It is true that Hooke's law is a special case because it only concerns elastic bodies, but what body is not elastic?

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If you compress an elastic body, and then remove the compression, the
body will rebound (that's part of the definition of the word "elastic"
in physics).  But if if I take a lump of modeling clay and squish it
(e.g., I apply a leftward force to the left side of the lump, and a
rightward force to the right side of the lump), and then remove the
applied forces, the clay won't rebound.  We conclude that mdodeling
clay is not an elastic body.
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In general, the property of being elastic or not being elastic depends
on both the body and the size and time dependence of the forces applied.
For example, if I push on a car's bumper with my hand, I'm probably not
strong enough to deform the bumper non-elasticly.  But if I hit the
bumper with a sledge-hammer, I may well permanently deform the bumper,
i.e., deform it non-elasticly.
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All bodies are compressible because even the most rigid ones have a degree of elasticity other than zero.

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I think you need to restrict this statement to *macroscopic* bodies:
We can certainly apply forces to an electron, but I don't think it's
meaningful to refer to "compressing an electron".  (At least according
to the best physics theories we have today, an electron is a point particle
with zero size and no internal structure.  If/when we have a theory of
quantum gravity this might change, and it might then become meaningful
to talk about compressing an electron.)

My reasoning is independent of the degree of elasticity of a body.

The force acting on a body can generate two consequences: Newton's acceleration or Hooke's compression/elongation (if the body is elastic).

And if the body is not elastic? It deforms, breaks (like a bumper hit by a sledge-hammer) or spreads (like modeling clay).

All these effects are similar to those of Hooke's force because they are due to the contrast between action and reaction (third law), just like the compression or elongation of the spring, where the acting forces are two.

Instead, acceleration does not.

Acceleration arises precisely from the lack of any contrast to the only accelerating force: that of Newton's second law F=ma.

In my animation https://www.geogebra.org/m/ddnzbhjy there is the external force (black) that acts on the point A of the car that is on a frictionless plane and that has nothing on the other side.

The question is: is the black force (of the hand or the sledge-hammer) a "net" force that accelerates or is it also a force that compresses or breaks because it is opposed?

Luigi Fortunati