In animation...
Animation in English
https://www.geogebra.org/m/adsgahwf
In animation https://www.geogebra.org/m/adsgahwf
You are missing the inertial force ("red") of the "rigid" wagon weight against the applied "blue" force.
The "rigid" "red" force would be greater than the corresponding red force on the water wagon.
Is the acceleration of the two vagons the same?
Luigi
...
Is the acceleration of the two vagons the same?
No, not initially. The water wagon will initially accelerate faster as
the effective mass is less (because the water is not moving yet). But
when the water sloshes back, towards the rear, it will slow down. The
exact motion depends on the "impedance" of the tractor pulling the
wagons.
Richard Livingston lunedÃ¬ 10/10/2022 alle ore 05:21:46 ha scritto:
...
The red force that at your suggestion I added to the rigid wagon of my animation
https://www.geogebra.org/m/adsgahwf
in your opinion, is there or is it not?
The water cannot move back and forth because the tank car is totallyIs the acceleration of the two vagons the same?
No, not initially. The water wagon will initially accelerate faster as
the effective mass is less (because the water is not moving yet). But
when the water sloshes back, towards the rear, it will slow down. The
exact motion depends on the "impedance" of the tractor pulling the
wagons.
full and there are no empty spaces.
...
Is the acceleration of the two vagons the same?
No, not initially. The water wagon will initially accelerate faster as
the effective mass is less (because the water is not moving yet). But
when the water sloshes back, towards the rear, it will slow down. The
exact motion depends on the "impedance" of the tractor pulling the
wagons.
The water cannot move back and forth because the tank car is totally full and there are no empty spaces.
In that case the two cars will behave exactly the same.
https://www.geogebra.org/m/eega7se6
A similar situation to my previous animation is the following: https://www.geogebra.org/m/gbqzyba2
In the inertial reference frame of the ground, when bodies are still,
there is no centripetal force and there is no centrifugal force either.
During the rotation, the blue centripetal force is activated which is
the only force acting on body A.
Instead, on body B (full of water but with the same overall mass as
body A), in addition to the blue force, the red force of the water
directed outwards (i.e. in the opposite direction to the centripetal
force) also acts.
In your opinion, is it correct that different forces act on body B than
on body A, only because of their different rigidity?
A similar situation to my previous animation is the following: https://www.geogebra.org/m/gbqzyba2
In the inertial reference frame of the ground, when bodies are still,
there is no centripetal force and there is no centrifugal force either.
During the rotation, the blue centripetal force is activated which is
the only force acting on body A.
Instead, on body B (full of water but with the same overall mass as
body A), in addition to the blue force, the red force of the water
directed outwards (i.e. in the opposite direction to the centripetal
force) also acts.
The net force acting
on the volume element of water due to the pressure gradient is then
the difference between the forces acting on the two opposite flat faces
of the volume element, i.e.,
dF_net = p(r+dr) dA - p(r) dA (6)
Also, by Newton's 2nd law (since this volume element of mass dm is moving with centripetal acceleration $a$), there must be a net force acting on
the volume element of
dF_net = dm a (7)
= dA dr a [here we're using (5)] (8)
Ultimately the only thing exerting forces on the water is B
The net force on B is the algebraic sum of these two forces
A similar situation to my previous animation is the following:
https://www.geogebra.org/m/gbqzyba2
In the inertial reference frame of the ground, when bodies are still,
there is no centripetal force and there is no centrifugal force either.
During the rotation, the blue centripetal force is activated which is
the only force acting on body A.
Instead, on body B (full of water but with the same overall mass as
body A), in addition to the blue force, the red force of the water
directed outwards (i.e. in the opposite direction to the centripetal
force) also acts.
In your opinion, is it correct that different forces act on body B than
on body A, only because of their different rigidity?
No, the weight without water has the same "red" reaction force. There
is no difference.
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