Does this mean, yes, I have understood you correctly on this point?
Please note that this is an example where conventional physics gives a different result. According to the model of physics I hold, a 2ft by 2ft sheet of cardboard or metal will experience the same force from the wind when held out the window and so I will feel the same push either way. No difference. So if you claim the metal will experience much more force and I will feel a harder push, proportional to the greater weight of the metal, then this helps me identify a testable difference.
The force you're talking about is an adage to the actual force that is more or less a (to us) static force of pressure. As in wind or movement into resistance by acceleration.
Basically ask yourself with the cardboard and metal out of the window, which one bends back more than the other?
Naturally you will know that the cardboard will, so that tells you that the cardboard is not resisting the pressure as much as the metal, so more force is naturally felt whilst holding the metal sheet.
However, this is veering off the path because we are talking about the actual density of both materials in displacing the atmospheric pressure upon them without acceleration or wind being involved.
Scales work by compressing a spring (or something spring-like). The harder you push, the more the spring compresses. That's how we get the measurement of "weight" to begin with - it's about compression of the spring. You are claiming (please confirm) that the air is pushing harder on the metal and the metal in turn is pushing harder on the scale, and that's why the metal compresses more.
Try and picture this. Try it if you want to.
Get a bike pump and put your finger over the hole whilst you pump down on the handle. You feel the pressure of the compressed air, right?
I'll leave that with you.
So please explain what happens. In a given wind, for a sheet of material with a given size, does the wind push denser objects with more force (as I understand your model would predict) or with the same force (as my model predicts)?
The wind doesn't push denser objects with more force. The densewr objects resist the force better than less dense objects.
I use a hair dryer or a fan and blow upwards on a sheet of cardboard such that it hovers there.
It is hovering because it is experiencing the same air pressure from below it as from above. Correct? The two forces cancel out because they are pushing on it from opposite directions.
If I replace the sheet of cardboard with a sheet of metal, will it also hover there?
If not, then it seems like it reacts differently to the air below it than to the air above it. The sheet of cardboard doesn't, but the sheet of metal does. This is the next thing I don't understand.
You would have to increase the force below for the metal to match its density.
Imagine you are laid under those sheets. Cardboard first and then the metal sheet. You push up the cardboard and you immediately feel how light it is but also you feel the resistance above is quite easy to overcome because your cardboard
bends as the atmospheric pressure is pushed into.
With your metal sheet it will bend much less meaning the resistance on it is much larger.
Also the cardboard and metal sheet (although the same shape and size) are repelling much different amount of atmosphere due to the cardboard already being ,mostly atmosphere within it. It's much more porous than the metal sheet, so is repelling much less atmosphere overall.