Re: derivation of Newton's 3rd law from 2nd law

On 6/29/25 7:18 AM, Luigi Fortunati wrote:

On 17 Jun 2025 21:03:56 +0100 (BST), "Jonathan Thornburg [remove
-color to reply]" <dr.j.thornburg@gmail-pink.com> wrote:
>

As noted, consider the 1-dimensional motion of 3 (rigid) bodies touching
each other (A on the left, B in the middle, C on the right), with an
external force F_ext pushing right on A.  Because the 3 bodies are
touching each other and are rigid, they all share a common acceleration
(with respect to some inertial reference frame), which by Newton's 2nd
law applied to the entire compound body A+B+C is
>
a = F_ext/(m_A + m_B+ m_C)                                        (1)

>
The hypothesis is not clear.

Sure it is, just READ his post -- the part you quoted above, plus the
assumption that Newton's first two laws are valid (from the context in
this thread).

The masses of the bodies are fine because they are scalar quantities
and, therefore, it is enough to say that they are equal to 10 kg each
(m_A=m_B=m_C=10kg) and nothing else is needed.

His demonstration is more general than that, and holds for ANY masses
m_A, m_B, m_C, not just when they are equal. And there is no need to
assume 10kg either -- ANY three values will do. But rather than assume
specific values, it is MUCH better to calculate in terms of abstract
symbols, as he did.

Instead, it is not enough to say that (for example) the external force
is equal to +100N (F_ext=+100N) because it is not specified *where*
this force acts: it is not said what the point of application is.

Sure it is specified: "an external force F_ext pushing right on A". It
really doesn't matter when on A the F_ext is applied, but the phrasing
("pushing") implies it is applied to the left side of A (remember all
three objects are rigid). And again there is no need to assume 100N --
any value of F_ext will do. But of course the combination of the masses
and the force determine the acceleration a (his eq. 1).

For example, if the external force is electromagnetic or gravitational
it acts on all the particles

But it isn't -- he specified it is "pushing right on A". You seem to
often get lost in your own fantasies, rather than reading the post and
applying just the physical situation it describes.

Your formula (1) a=100/30=3.33 m/s^2 is valid in both cases.

You seem to have difficulty thinking in terms of abstract symbols (m_A,
F_ext, ...), and always seem to replace them with specific numbers. That
is a HUGE limitation in your mental processes. Note that all of the laws
of physics are phrased in terms of abstract symbols, including Newton's
three laws.

Based on your other formulas, are the forces in the upper part of the
scheme correct or those in the lower part or are there others?

His physical situation has no "upper part" or "lower part"; it is
"1-dimensional motion". READ his post.

In the latter case, tell me what these forces are and I will adjust
the scheme to the values ??you will communicate to me.

He COMPUTED all of the forces -- just READ his post. Of course they are
all abstract symbols standing in for ANY values.

This is getting very repetitive, so don't expect me to contribute any more.

Tom Roberts