Re: Newton e Hooke

In article <m1dng8FkasU1@mid.dfncis.de>, I wrote that if we push on
one end of a spring,

the spring's center-of-mass
acceleration is determined by *all* of the applied force, while at the
same time the spring compresses.

and I worked this out in detail for a simple model system.

I neglected to point out that there's actually a much simpler way of
coming to this same conclusion: simply apply conservation of momentum
to the spring.

That is, consider the spring's total (horizontal) linear momentum p.
Since there's an external force F pushing the spring to the right, p
must change according to Newton's 2nd law (dp/dt = F), i.e., the spring's
center of mass must be accelerating to the right at an acceleration
a = F/m_total.

The fact that the spring also has a bunch of internal dynamics isn't
relevant here -- we ony consider the spring's total linear momentum,
and the (horizontal) external force acting on the spring.

In fact, this argument is still true if there's no spring at all, just a
pair of (unconnected) point masses at the ends of the "spring".  That is,
if we apply a force F to one mass, leaving the other mass stationary
(i.e., F is applied to mass #1, and there is no force applied to mass #2),
the center-of-mass of the two masses (at position xc = (x1 + x2)/2)
accelerates with an acceleration
  ac = (a1 + a2)/2
     = (F/m + 0)/2
     = F/(2m)
     = F/m_total
even though there the force is only pushing on one of the two masses.

In article <vot1s2$lj72$1@dont-email.me>, Luigi Fortunati wrote

The acceleration of the center of mass cannot be determined by *all*
the applied force because that force does NOT act on the center of
mass!

For the momentum argument I gave above, it doesn't matter where the
applied force acts.  We only care that it's an external force applied
to *somewhere* in the system of interest (the spring).

Luigi also wrote

If you refuse to watch my animation https://www.geogebra.org/m/mrjtyuwk
you cannot notice that the applied force Fa (black) acts on point A"
and, before it can reach C, it must confront the opposing blue force.

Forces don't "reach" points or "confront" other forces.  Forces (only)
act on, or are applied to, or push/pull on, objects or points on those
objects.

The question is simple: does the opposing blue force in my animation
exist or not?

Yes, there is a reaction force of magnitude F pushing left on the hand.
This force is pushing on the hand, not on the car, so it doesn't affect
the car's motion.

--
-- "Jonathan Thornburg [remove -color to reply]" <dr.j.thornburg@gmail-pink.com>
   (he/him; currently on the west coast of Canada)
      "Every young man is prone to be misled by the suggestions of his
       own ill-founded ambition which he mistakes for the promptings
       of a secret genius, and thence dreams of unrivaled greatness."
                                                   -- Ralph Waldo Emerson