Re: derivation of Newton's 3rd law from 2nd law (was: Re: The experiment)

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.

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.

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.

For example, if the external force is electromagnetic or gravitational
it acts on all the particles of body A spreading uniformly and without
generating thrusts between one particle and another while, if it is a
contact force concentrated on particle A of body A, it pushes *only*
this particle and then the thrust propagates forward, passing from
particle to particle, through an endless series of single molecular
actions and reactions.

Obviously, these are two completely different conditions and I believe
you are referring to the second hypothesis.

The scenario is that of my scheme
https://www.geogebra.org/classic/d2bxrrmg where there are two possible
different manifestations of the propagation of the force F_ext=100N
inside the 3 bodies.

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

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?

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

Hi, Luigi