If an insect is inside of a container, but flying, is it adding weight to the container?

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If an insect is inside of a container, but flying, is it adding weight to the container?

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While an insect hovering in a closed box, presumably filled with air, would be displacing air (and therefore applying its displaced weight downwards), wouldn’t the measured weight still be less than on account that you’d be increasing air pressure in the closed system, which would press equally on all sides of the container? Its mass would be the same as if it were sitting, but actually weighing it would give a middling value.

Am I right?

Maybe that depends more on whether the container itself can flex, or is completely rigid.

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