Re: Newton e Hooke

In article <vos7hr$gpqq$1@dont-email.me>, Luigi Fortunati writes

In my animation https://www.geogebra.org/m/mrjtyuwk there is the force
F of the hand that presses against the car and accelerates it according
to Newton's second law (F=ma).
 

[[...]]

 
And then I ask myself (and I ask you): At point A" *of the car* does
only one force arrive (the black force F of the hand) or does the blue
reaction force of the car also arrive?

I'm not sure precisely what it means to say that a force "arrives" at
a point; I think it's more useful to say that forces are *applied to*
or *push on* or *act on* an object or a point.

Now to Luigi's question:
At the moment when we first apply the force F to the car, F (shown in
black in Luigi's diagram) is the only (horizontal) force pushing on point
A" of the car.  (The car's reaction force on the hand, shown in blue in
Luigi's diagram, isn't pushing on A" or any other part of the car, and so
isn't involved in determining the car's motion.)

However, very quickly after we first start pushing on the car, an
additional force comes into play.  That's because the car isn't a point
mass -- the car is an extended body which will (slightly) deform under
the influence of the force F which continues to be pushing on A".  As
soon as the car starts compressing there are *two* horizontal forces
pushing on the point A": the rightward force F applied by the hand, AND
a leftward force applied by the compressed metal making up the car's
body.

Analyzing this is complicated, but earlier in this thread I suggested a
simple model of "pushing on a spring" which I think captures the key parts
of the physics but is still relatively easy to analyze:  we model the car
as two point masses (the left and right ends of the car), interconnected
with a (massless) spring-with-friction.  (Note that we need to have some
friction somewhere in our model or order for the initial transients to
damp out.)  This model looks like this:

                            -------> * /\/\/\/\/\ *
                            F        m1           m2

If you run the simulation program I posted earlier in this thread, it
will print out the positions of the two masses as a function of time;
you can use your favorite graphics program to plot this data, and see
how the two ends of the car move and the length of the "car's body"
(the separation x2-x1) changes with time.


Luigi also asked:

And at point A' *of the hand* does only one force arrive (the blue
reaction force of the car) or does the black force F of the hand also
arrive?

To answer this we'd have to dig into the the internal structure and
compressability of the hand (which is also an extended body), and where
the musles are that are applying the forces.  The issues involved would
be similar to the ones I just described for forces acting on the car
point A", but I'm not going to go through this in detail.

ciao,
--
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