Re: Newton e Hooke

[[Mod. note -- Yes, there are multiple flaws in this reasoning:
>
1. In Newtonian mechanics, the concept of "force" is more general than
   *contact* force.  For example, a magnet can exert a force on an iron
   object without every being in contact.

And so, you say that the first of the multiple flaws in my reasoning is
the generalization of the concept of force.
I don't have to talk only about contact forces but also about other
forces.
Ok, I'll satisfy you right away.
Does a magnet that attracts the iron object (and vice versa) generate
acceleration or compression?
Simple, it generates acceleration without compression as long as they
are far apart and then, when they come into contact, it only generates
compression and no longer acceleration: the force that *before*
accelerated is the same that *after* compresses.
The force of gravity does the same: as long as I'm on the wall it
compresses me and does NOT accelerate me, then, when I jump and I'm in
the air, it accelerates me and does NOT compress me.
Here too, the force that first compressed me is the same as the one
that compresses me afterwards.

2. In Newtonian mechanics, a force applied to an object does not
   *necessarily* result in a contraction/elongation of that object.

In cases where the force determines tension, the outcomes can be
different and depend on the degree of elasticity of the body and the
breaking point, so that there can be elongation, contraction or
deformation.
In any case, the part of the force that determines tension does not
cause acceleration, which is determined only by the excess force, that
is, by the "net" force.
The gravitational force that accelerates the meteorite falling on Earth
generates acceleration only for the part that remains after that used
to counteract the resistance of the air.
If the density of the air were so strong that it reacted on par with
the force of gravity, the meteorite would end up stopping during its
fall, as happens to those that fall on a gas planet.

   A contraction/elongation is the result of *differential* motion
   of different subparts of the object

It is true, the contraction/elongation is the result of the reaction of
the different subparts of the object, that is, it is an "internal"
force.
The spring that lengthens or contracts does so because its internal
subparts react to the external force: the lengthening and the
contraction serve the spring to increase its reactive force that
counteracts the external force.
In fact, the spring progressively increases its reaction force as it
lengthens or contracts.

   if a force
   (such as a uniform Newtonian gravitational field) is applied to
   every part of the object such that F/m has the same value for
   every subpart, then there's no contraction/elongation of the
   object.

That's right: in Newtonian mechanics, this force generates acceleration
without tension.

3. "Is it more correct to say that force is that thing that generates
    acceleration or is it better to say that it is that thing that
    generates tension?"
   Neither of those is quite right as an operational definition for
   force in Newtonian mechanics.

There, exactly!
Neither of the two is entirely correct, the correct definition is:
force generates tension and/or acceleration, with the possibility that
one of the two (but never both) is equal to zero.

 You'd be better off with something
   like "*net* force is the thing that generates acceleration".

This is a partial definition that only works for one type of force but
not all.
"Net" force is simply what is left of the force after it has overcome
the opposing force.
The opposing part of the force compresses (and stops accelerating), the
remaining part of the force accelerates (and stops compressing).

There's
   a very clear, concise, and readable discussion of this in chapter 3
   (particularly section 3.4, "Operational Definition of a Numerical
   Scale of Force") of
       Arnold B. Arons
       "A Guide to Introductory Physics Teaching"
       Wiley, 1990
       ISBN 0-471-51341-5
>
4. Notably, the operational definition and the associated reasoning
   described by Arons do NOT make use of of Hooke's law in any way.
   Hooke's law is a separate logical construct, which may or may not
   hold for any given compressible object in any situation.

It is true that Hooke's law is a special case because it only concerns
elastic bodies, but what body is not elastic?
All bodies are compressible because even the most rigid ones have a
degree of elasticity other than zero.
When I push a car, the first thing that happens (before any
acceleration!) is the compression that occurs at the point of contact.
The acceleration occurs only AFTER my force has overcome the resistance
of the car.

Luigi Fortunati