From Newsgroup: sci.physics.research

In article <10jageu$12sh6$1@dont-email.me> (Sat, 03 Jan 2026 22:22:58 PST) Luigi Fortunati wrote:

And the same resultant force of -10 N also acts on the father's hands, resulting from the external force F_son_vs_father (+600 N) and the
internal force F_father_muscles (-610 N).

This shows that the force F_father_vs_son (-610 N) is greater than, and
not equal to, the force F_son_vs_father (+600 N).

If there's a mistake in all this, where is it?

Sorry for the delayed reply -- I've been sick. Catching up now.....

To respond to Luigi's question properly, we need to analyze the
biomechanics a bit more carefully. In particular, we need to drop my
previous assumption that the father's body stays rigid, and go back and
redo the analysis without that assumption.

Let's now model the father's body the same way we're already modelling
the son's body, namely, as rigid legs/torso with arms pushing on (i.e., applying a force on) on hands.

That is, we now have
* father's feet are assumed to be fixed on the ground
* father's legs/torso are assumed to be rigid
* father's arms push left on father's hands
with a force of magnitude /F_father_arms_on_father_hands/
* father's hands push left on son's hands
with a force of magnitude /F_father_hands_on_son_hands/
* son's feet are assumed to be fixed on the ground
* son's legs/torso are assumed to be rigid
* son's arms push right on son's hands
with a force of magnitude /F_son_arms_on_son_hands/
* son's hands push right on father's hands
with a force of magnitude /F_son_hands_on_father_hands/

Notice that I am *not* assuming that /F_son_hands_on_father_hands/
must necessarily be the same as /F_father_hands_on_son_hands/ (which
is what Newton's 3rd law would say).

One complication in this analysis is that if a person's hands move,
then necessarily their arms must also be in motion, but not all of
their arms have the same acceleration. The easiest way to model this
is to treat the hand-arm system as having an "effective mass" which
includes all of the hands but only a fraction of the arms, and say that
that the effective mass is the only part of their body that accelerates.
I'll do this from now on.

Applying this to the son and father, let's take
* effective mass of son's hands + arms = 5kg
* effective mass of father's hands + arms = 10kg

When the push-of-war is tied, we have
F_son_arms_on_son_hands = 600N
F_son_hands_on_father_hands = 600N
F_father_arms_on_father_hands = 600N
F_father_hands_on_son_hands = 600N
and clearly the net force on the hands is zero.

Now if the father increases /F_father_arms_on_father_hands/ to 630N,
but the son doesn't (can't) increase /F_son_arms_on_son_hands/ above 600N,
what happens? (This is basically the situation Luigi was asking about.)
We have
F_son_arms_on_son_hands = 600N
F_son_hands_on_father_hands = don't know yet
F_father_arms_on_father_hands = 630N
F_father_hands_on_son_hands = don't know yet

If we look at the son's and father's hands (and the moving parts of their arms), their combined effective mass is 15kg, and the net force acting on
them is
F_net_on_combined_hands
= F_son_arms_on_son_hands - F_father_arms_on_father_hands
= -30N
Applying Newton's 2nd law to the two hands together, we see that they accelerate with an acceleration of
a_hands = F_net/m
= -30N / 15kg = -2 m/s^2
(This is to the left, which is what we expect since the father is winning
the push-of-war.)

Now let's apply Newton's 2nd law to the son's hands:
F_net_on_son_hands = m_son_hands a_hands = 5kg (-2 m/s^2) = -10N
= F_son_arms_on_son_hands - F_father_hands_on_son_hands
= 600N - F_father_hands_on_son_hands
so we must have F_father_hands_on_son_hands = 610N.

Now let's apply Newton's 2nd law to the father's hands:
F_net_on_father_hands = m_father_hands a_hands = 10kg (-2 m/s^2) = -20N
= F_son_hands_on_F_father_hands - F_father_arms_on_father_hands
= F_son_hands_on_F_father_hands - 630N
so we must have F_son_hands_on_F_father_hands = 610N.

So, using *only* Newton's 2nd law, we conclude that in fact
F_son_hands_on_F_father_hands = F_father_hands_on_son_hands = 610N
i.e., Newton's 3rd law does indeed hold here.

ciao,
--
-- "Jonathan Thornburg [remove -color to reply]" <dr.j.thornburg@gmail-pink.com>
(he/him; currently on the west coast of Canada)
Alberto Moreira (comp.arch, Jan 1999):
"Cache is, basically, a kluge generated by technological restrictions."
Donald C. Lindsay (also comp.arch, Jan 1999):
"No. It's a kluge generated by deeply fundamental restrictions,
like the speed of light."
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From Newsgroup: sci.physics.research

Il 12/01/2026 04:51, Jonathan Thornburg [remove -color to reply] ha scritto:

In article <10jageu$12sh6$1@dont-email.me> (Sat, 03 Jan 2026 22:22:58 PST) Luigi Fortunati wrote:

And the same resultant force of -10 N also acts on the father's hands,
resulting from the external force F_son_vs_father (+600 N) and the
internal force F_father_muscles (-610 N).

This shows that the force F_father_vs_son (-610 N) is greater than, and
not equal to, the force F_son_vs_father (+600 N).

If there's a mistake in all this, where is it?

Sorry for the delayed reply -- I've been sick. Catching up now.....

To respond to Luigi's question properly, we need to analyze the
biomechanics a bit more carefully. In particular, we need to drop my previous assumption that the father's body stays rigid, and go back and
redo the analysis without that assumption.

Let's now model the father's body the same way we're already modelling
the son's body, namely, as rigid legs/torso with arms pushing on (i.e., applying a force on) on hands.

That is, we now have
* father's feet are assumed to be fixed on the ground
* father's legs/torso are assumed to be rigid
* father's arms push left on father's hands
with a force of magnitude /F_father_arms_on_father_hands/
* father's hands push left on son's hands
with a force of magnitude /F_father_hands_on_son_hands/
* son's feet are assumed to be fixed on the ground
* son's legs/torso are assumed to be rigid
* son's arms push right on son's hands
with a force of magnitude /F_son_arms_on_son_hands/
* son's hands push right on father's hands
with a force of magnitude /F_son_hands_on_father_hands/

Notice that I am *not* assuming that /F_son_hands_on_father_hands/
must necessarily be the same as /F_father_hands_on_son_hands/ (which
is what Newton's 3rd law would say).

One complication in this analysis is that if a person's hands move,
then necessarily their arms must also be in motion, but not all of
their arms have the same acceleration. The easiest way to model this
is to treat the hand-arm system as having an "effective mass" which
includes all of the hands but only a fraction of the arms, and say that
that the effective mass is the only part of their body that accelerates.
I'll do this from now on.

Applying this to the son and father, let's take
* effective mass of son's hands + arms = 5kg
* effective mass of father's hands + arms = 10kg

When the push-of-war is tied, we have
F_son_arms_on_son_hands = 600N
F_son_hands_on_father_hands = 600N
F_father_arms_on_father_hands = 600N
F_father_hands_on_son_hands = 600N
and clearly the net force on the hands is zero.

Now if the father increases /F_father_arms_on_father_hands/ to 630N,
but the son doesn't (can't) increase /F_son_arms_on_son_hands/ above 600N, what happens? (This is basically the situation Luigi was asking about.)
We have
F_son_arms_on_son_hands = 600N
F_son_hands_on_father_hands = don't know yet
F_father_arms_on_father_hands = 630N
F_father_hands_on_son_hands = don't know yet

If we look at the son's and father's hands (and the moving parts of their arms), their combined effective mass is 15kg, and the net force acting on them is
F_net_on_combined_hands
= F_son_arms_on_son_hands - F_father_arms_on_father_hands
= -30N
Applying Newton's 2nd law to the two hands together, we see that they accelerate with an acceleration of
a_hands = F_net/m
= -30N / 15kg = -2 m/s^2
(This is to the left, which is what we expect since the father is winning
the push-of-war.)

Now let's apply Newton's 2nd law to the son's hands:
F_net_on_son_hands = m_son_hands a_hands = 5kg (-2 m/s^2) = -10N
= F_son_arms_on_son_hands - F_father_hands_on_son_hands
= 600N - F_father_hands_on_son_hands
so we must have F_father_hands_on_son_hands = 610N.

Now let's apply Newton's 2nd law to the father's hands:
F_net_on_father_hands = m_father_hands a_hands = 10kg (-2 m/s^2) = -20N
= F_son_hands_on_F_father_hands - F_father_arms_on_father_hands
= F_son_hands_on_F_father_hands - 630N
so we must have F_son_hands_on_F_father_hands = 610N.

How can the son increase his force on his father to +610N if the force
he's exerting (+600N) is already equal to his maximum capacity?

Ciao, Luigi.

[[Mod. note --
The son can't increase /F_son_arms_on_son_hands/. But the son doesn't
directly control /F_son_hands_on_F_father_hands/: the additional 10N by
which /F_son_hands_on_F_father_hands/ exceeds /F_son_arms_on_son_hands/
is essentially due to the inertia of the son's hands (which are accelerating
to the left with an acceleration of /a_hands/).

This is similar to how /F_father_arms_on_father_hands/ is 630N, but /F_father_hands_on_son_hands/ is only 610N -- the 20N difference is due
to the inerta of the father's hands (which are also accelerating to the
left with an acceleration of /a_hands/).
-- jt]]
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