How is the weight of air accounted for when measuring a person, a car or an airship? I'm not sure how to account for the weight of air when measuring different objects.

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*When I weigh myself on a scale am I also weighing all of the air directly above me up to the edge of the atmosphere?

*If I weighed a car am I also weighing the air inside the car?  Because air pressure falls as altitude increases would a car weigh less at higher altitude because the air would weigh less?

*If I could weigh a Zeppelin at 20,000 feet would I also be weighing all of the air inside the Zeppelin?  Or does air not show up on the scale because it is freely floating in and out of the craft?

 A: *

*No, you are actually measuring the weight of the object minus the weight of the air displaced by the object. The weight of the column does not matter, because it makes pressure all around the object, what matters is only is the pressure difference across the object's height, which results in the buoyant force, that only depends on the weight of the displaced air. In general you assume that object's density is much larger than the air, so the buoyant force is too small to affect the weight. This approximation is not valid if the buoyant force is not small relative to the weight.


*You can either consider the air as part of the car or not, that is irrelevant, the reason is that the measured "weight" will not change. The two different choices are equivalent, because you can consider the air as part of the car, thus contributing to its weight, or not part of the car, then contributing to the buoyant force. If you go to a high altitude the measured weight will be less, because the density of the air inside it will be and thus the buoyant force will (I am assuming a constant g here, otherwise I do not know what effect is more important, less gravity or less air density)


*If an object is floating it means that the weight is smaller than the buoyant force, so it does not have any sense to measure the weight with a scale, plus of course this is impossible. If you put the scale upside down, it would be measuring the buoyant force less the weight.(I am assuming you are talking about the passenger's section air, because the zeppelin had Hydrogen inside)
A: The science youtuber Derek Muller made a video about a place where the force exerted by a very large weight needs to be known to a very high degree of accuracy. The vido is titled World's heaviest weight.
From the content of the video:
The US National Institute of Standards and Technology (NIST) has a huge setup to certify force transducers such that a 1,000,000 pounds of force can be exerted. Certification requires measurement accuracy to within five parts per million (.0005%)
The volume of the stack of weights is such that it displaces a volume of air with a weight of 125 pounds. In order to achieve the required level of accuracy this buoyancy must be taken into account.

Of course, in most cases the effect from air buoyancy is far smaller than the accuracy of the weighing scale.
