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Re: Newton e Hooke

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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

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Newton e Hooke Luigi Fortunati <fortunati.luigi@gmail.com> - 2025-01-26 08:51 -0800
  Re: Newton e Hooke Luigi Fortunati <fortunati.luigi@gmail.com> - 2025-01-30 08:42 +0000
    Re: Newton e Hooke Luigi Fortunati <fortunati.luigi@gmail.com> - 2025-02-04 23:47 -0800
      Re: Newton e Hooke Luigi Fortunati <fortunati.luigi@gmail.com> - 2025-02-10 22:25 -0800
  Re: Newton e Hooke "Jonathan Thornburg [remove color- to reply]" <dr.j.thornburg@pink-gmail.com> - 2025-02-12 08:02 +0000
    Re: Newton e Hooke Luigi Fortunati <fortunati.luigi@gmail.com> - 2025-02-14 08:09 +0000
      Re: Newton e Hooke "Jonathan Thornburg [remove -color to reply]" <dr.j.thornburg@gmail-pink.com> - 2025-02-16 08:55 +0000
        Re: Newton e Hooke Luigi Fortunati <fortunati.luigi@gmail.com> - 2025-02-16 10:42 -0800
          Re: Newton e Hooke "Jonathan Thornburg [remove -color to reply]" <dr.j.thornburg@gmail-pink.com> - 2025-02-17 08:19 +0000
            Re: Newton e Hooke Luigi Fortunati <fortunati.luigi@gmail.com> - 2025-02-17 22:45 -0800
          Re: Newton e Hooke Tom Roberts <tjoberts137@sbcglobal.net> - 2025-02-18 08:23 +0000
      Re: Newton e Hooke Luigi Fortunati <fortunati.luigi@gmail.com> - 2025-02-16 10:42 -0800
        Re: Newton e Hooke "Jonathan Thornburg [remove -color to reply]" <dr.j.thornburg@gmail-pink.com> - 2025-02-17 08:19 +0000
          Re: Newton e Hooke "Jonathan Thornburg [remove -color to reply]" <dr.j.thornburg@gmail-pink.com> - 2025-02-18 08:23 +0000
            Re: Newton e Hooke Luigi Fortunati <fortunati.luigi@gmail.com> - 2025-02-20 07:56 +0100
              Re: Newton e Hooke Luigi Fortunati <fortunati.luigi@gmail.com> - 2025-02-22 18:13 +0100
                inelastic collision (was: Re: Newton e Hooke) "Jonathan Thornburg [remove -color to reply]" <dr.j.thornburg@gmail-red.com> - 2025-02-26 08:02 +0000
                Re: inelastic collision (was: Re: Newton e Hooke) Luigi Fortunati <fortunati.luigi@gmail.com> - 2025-02-28 14:44 -0800
                Re: inelastic collision (was: Re: Newton e Hooke) "Jonathan Thornburg [remove -color to reply]" <dr.j.thornburg@gmail-pink.com> - 2025-03-01 09:18 +0000
                Re: inelastic collision (was: Re: Newton e Hooke) Luigi Fortunati <fortunati.luigi@gmail.com> - 2025-03-03 08:09 +0000
                Re: inelastic collision (was: Re: Newton e Hooke) Luigi Fortunati <fortunati.luigi@gmail.com> - 2025-03-12 12:37 +0000
                Re: inelastic collision (was: Re: Newton e Hooke) Luigi Fortunati <fortunati.luigi@gmail.com> - 2025-03-16 09:28 +0000
                Re: inelastic collision (was: Re: Newton e Hooke) Luigi Fortunati <fortunati.luigi@gmail.com> - 2025-03-16 21:28 -0700
                Re: inelastic collision (was: Re: Newton e Hooke) "Jonathan Thornburg [remove -color to reply]" <dr.j.thornburg@gmail-pink.com> - 2025-03-02 09:14 +0000

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