What is the weight of a container filled with flying birds?

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The puzzle involves a truck container weighing 10,000 kg filled with 500 birds each weighing 200 g, and it questions the total weight measured when the birds are flying inside. In the trivial case, the birds' volume is negligible, while the non-trivial case introduces a single bird weighing 5,000 kg that remains steady in the center due to its wing movement generating lift. The discussion explores whether the total weight measured by a scale on the floor of the container would be more or less than 10,000 kg. The presence of air at atmospheric pressure inside the container is also a factor in the weight measurement. Ultimately, the puzzle challenges conventional understanding of weight and lift in a closed system.
Clausius2
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I have a little puzzle to share:
There is a container of a truck which mass is 10000 Kg. It is filled with 500 birds of 200 g each one.
What is the total weight measured of the container if birds are all flying inside?.
First I propose you to analyse the trivial case: the volume occuped by the birds is negligible compared with the volume of the container.
Second I propose you to analyse the non-trivial case: there is only one bird of 5000kg weighting inside. It remains steady aproximately at the center of the container, due to the movement of its wings that provide it lifting force. Now, what do you think?. Is the total weight measured by an steady scale at the floor more or less than 10000kg?.
There is air inside of the container with atmospheric pressure.
 
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