@maxdancona,
With respect. Read again.
1) Even at rest, Gravity applies a force.
F(gravity) =! 0;
ergo: mass*acceration(gravity) =! 0;
egro: neither term can have a value of zero.
It is not a circular argument. Newton's law is not "kind of appropriate," it is very much the law here. Mass is constant, weight is not. Weight, as a defined physically is only one component of the net forces acting on a body.
Net Force =! Weight;
2) Both the air jar and the vacuum jar displace the same amount of atmospheric air. Since the vacuum jar has zero additional mass, the ratio of air-mass it displaces is even higher, hence a greater buoyancy.
What is inside the jar absolutely matters. Buoyancy is a matter of volume and density, and so even if a fluid has a specific volume, the density will determine the force of buoyancy. The lower the density inside, and the greater the density outside will create a greater buoyant force.
E.g. - Fill two balloons to equal volume in a room filled with air. Fill one with air from the room, and fill the other with helium. The helium balloon will rise due to buoyancy. It is because the helium balloon's contents are less dense (mass/volume).
The net force acting on an object at rest (velocity==0) by gravity and buoyancy:
What is inside does matter.
In fact, nothing inside matters! If you could make a lightweight rigid structure and create a perfect vacuum inside, it would float!
At sea level:
1L of air= 1.25 grams
1L of helium = 0.18 grams
1L of vacuum = 0 grams
Same volume, different mass, ergo different density. The greater the difference in density, the greater the force of buoyancy. A vacuum would float better than helium.
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