From Newsgroup: sci.physics.research

In the animation
https://www.geogebra.org/classic/ufckd2jm
the spring forces act like a spring pushing body A to the left and body
B to the right.

The spring's force F4 slows the motion of body A, and the force F3 slows
that of body B.

If force F4 is equal to force F1, body A stops and remains at rest; if
it is greater, body A is pushed back.

Similarly, body B stops if F3 is equal to F2 and pushes back if it is
greater.

You can vary the mass of body A with the appropriate slider.

If you set the mass of A to 1 (mA=1), the force F4 is double that of F1,
so half of the force F4 stops body A and the other half pushes it back
at the same velocity as before, with the sign reversed.

The same happens to body B, stopped and pushed back by the force F3.

If you choose the mass of A equal to 3 (mA=3), the force F4 is exactly
equal and opposite to the force F1, so body A is stopped and its
momentum (along with its kinetic energy) is transferred entirely to body B.

The greater force F1 of the larger body A compared to the force F2 of
the smaller body B is due to the excess mass A2 of A, which reacts
inertially.

The conservation of momentum of the system of bodies A+B is guaranteed
by the sum of the forces F1-F5, which is always equal to zero.

[[Mod. note -- What's F5? It's not shown on your diagram.
And, the diagram doesn't "animate", at least for me.
-- jt]]

All force values are calculated with the formula
F1=-(F2+2F2((mA-mB)/(mA+mB)))
which I have already discussed and which establishes the correct ratio
between the action and reaction forces F1 and F2 in an elastic collision.

Luigi Fortunati
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From Newsgroup: sci.physics.research

Luigi Fortunati il 17/04/2026 ha scritto:

In the animation
https://www.geogebra.org/classic/ufckd2jm
the spring forces act like a spring pushing body A to the left and body
B to the right.
...
[[Mod. note -- What's F5? It's not shown on your diagram.
And, the diagram doesn't "animate", at least for me.
-- jt]]

F5 is a new feature that only exists when the masses of bodies A and B
are not equal to each other and, therefore, is not visible in the
initial screen where the mass of A is equal to that of B.

The diagram animates when the "Body mass A" slider (bottom left) is
greater than 1: do you know how to use a slider?

To describe the force F5, I must first analyze the elastic collision in
the animation using Newton's second law.

I use the mass of body B as the unit of measurement, and therefore, the
mass of B is equal to 1 and the mass of A is also equal to 1.

The unit of measurement for time is the duration of the collision, which
is therefore equal to 1.

The initial velocities of A and B are:
viA=+1 and viB=-1
and the final velocities are:
vfA=-1 and vfB=+1

The acceleration of A is:
aA=delta_vA/delta_t=-1-1=-2
and that of B is:
aB=delta_vB/delta_t=+1-(-1)=+2

The force of A accelerating B (via the spring) is
F3=mB*aB=1*(+2)=+2 (action)
and that of B accelerating A (via the spring) is
F4=mA*aA=1*(-2)=-2 (reaction).

The action and reaction are equal and opposite.

Then, by adjusting the "Body Mass A" slider at the bottom left of the screen
(I hope you all know how to use it), we increase the mass of body A from
1 to 2.

The action F3 increases from +2 to +2.67: with +1 it stops body B and
with +1.67 it accelerates it to the final velocity vfB=+1.67.

The reaction F4 increases from -2 to -2.67 (and not to -2 as in the animation):
with -2 it stops body A and with -0.67 it accelerates it to the left to the final velocity vfA=-0.33.

Again, the action F3=+2.67 and the reaction F4=-2.67 are equal and opposite.

Is everything correct?

Luigi Fortunati
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From Newsgroup: sci.physics.research

On 21/04/2026 06:14, Luigi Fortunati wrote:

Luigi Fortunati il 17/04/2026 ha scritto:
> In the animation
> https://www.geogebra.org/classic/ufckd2jm
> the spring forces act like a spring pushing body A to the left and body
> B to the right.
> ...
> [[Mod. note -- What's F5? It's not shown on your diagram.
> And, the diagram doesn't "animate", at least for me.
> -- jt]]

F5 is a new feature that only exists when the masses of bodies A and B
are not equal to each other and, therefore, is not visible in the
initial screen where the mass of A is equal to that of B.

The problem with a spring is that the force is not constant in time.
Initially the bodies are approching each other and compress the
spring. The force in the spring is proportional to the difference
between the length of the compressed spring and the natural length
of the string (at least as long as the spring is not compressed too
much). The energy in the spring is proportional to the square of
that difference.

If you don't want to care about intermediate states of the interaction
you should use momenta instead of forces. The momentum received or
delivered by the spring is the integral of the force over time. Before
the beginning of the interaction and after the end of the interaction
the force is zero so doesn't contribute to momenta. The spring itself
can be considered to have zero mass and therefore having zero momentum.
--
Mikko

[[Mod. note --
(Mikko likely knows this, but others may not.)
Instead of "zero mass" (which can be tricky for analysis), one can
instead take the spring to have a small (but nonzero) mass which is
much less than the mass of any other bodies of interest.
-- jt]]
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