Re: Inertia and third principle

Mikko il 04/08/2024 02:53:54 ha scritto:

The law of conservation of momentum is equivalent to lawes of inertia
and reaction together. If conseervation of momentum is violated without
interaction the law of inertia is violated. If conservation of momentum
is violated in an interaction the law of reaction is violated.

This is not the case and my animation
https://www.geogebra.org/m/qterew9m proves it.

Is it true or not that the momentum of the 15 particles is transformed
(in the collision) into 15 blue impulsive forces directed towards the
right which (inside body A) accumulate in the 3 particles of the first
row and discharge their action on the B body?

Is it true or not that body B does the same thing with its 9 particles
and its 9 red impulsive forces directed towards the left?

It is true or not that the two bodies react (inertially) to external
forces with their internal forces.

Is it true or not that the action and reaction forces would not be
activated if there were not the opposite inertia of the two bodies?

Is it true or not that *mathematically* the action of body A against
body B is +15 and the reaction of body B against body A is -12.75? If
not, how much are they worth?

Luigi Fortunati

[[Mod. note --
Your questions are in some sense ill-posed: they use words which don't
have well-defined meanings in physics.  Notably, it's not clear what
it means to say that impulsive forces do or don't "accumulate"; it's
not clear what it means to say that action-reaction forces are or are
not "activated"; and it's certainly not clear what it means to ask
how much an action-reaction force "is worth".

To analyze a collision at the level of granularity you're trying to
achieve (i.e., forces acting on the individual mass particles which
make up bodies A and B, you need to include the inter-particle forces
between the particles which make up each body.  That is, if we label the
columns of particles in your animations from left to right as A5, A4,
A3, A2, A1 (comprising body A) and B1, B2, B3 (comprising body B),
then we need to take into account that the actual structure is
effectively
   A5 <--> A4 <--> A3 <--> A2 <--> A1    B1 <--> B2 <--> B3
where each '<-->' denotes a spring with some energy dissipation
(we need the dissipation in order for the collision to be inelastic).
If, for example, we push B1 to the right relative to B2 and B3), that
will compress the B1 <--> B2 spring, but B3 won't be (immediately)
affected.  However, the compressed B1 <--> B2 spring will then
accelerate B2 to the right, compressing the B2 <--> B3 spring,
which will then accelerate B3 to the right.

To analyze the collision, we really need to write out Newton's 2nd
law for all the particles, taking into account all the forces.  It's
a bit of a mess, but it will give a precise answer.
-- jt]]