Newton e Hooke

Newton's second law (F=ma) says that the greater the force applied to
the mass <m>, the greater the acceleration.
It is quite obvious that this is the case: if a child pushes the car,
the acceleration is minimal; if an adult pushes it, the acceleration is
greater.
Hooke's law says that the greater the force we apply to the body, the
greater its contraction/elongation (tension).
It is quite obvious that this is the case: if a child pushes a car, the
tension at the point of contact is minimal; if an adult pushes it, the
tension is greater.
But then, how can we define force?
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?
If force can generate acceleration and also tension, then it is more
correct to say that force is responsible for acceleration and also
tension.
If we push a car with the handbrake on, our force causes only tension
and no acceleration.
If the handbrake is not on, our force generates tension and also
acceleration.
If instead of pushing a car we push a feather, our force causes (almost
exclusively) acceleration without any tension.
Therefore, both laws are natural, faultless and correct but they are
also partial because one takes into account only acceleration
neglecting tension and the other takes into account only tension
neglecting acceleration.
Is this reasoning correct or is there some flaw?
Luigi Fortunati


[[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.

2. In Newtonian mechanics, a force applied to an object does not
   *necessarily* result in a contraction/elongation of that object.
   A contraction/elongation is the result of *differential* motion
   of different subparts of the object (presumably caused by varying
   values of F/m for different subparts of the object); 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.

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