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Why is it easier to generate lift when the air is denser?
A place where the air is denser simply means that there is more air in a single place.
This is absolutely fantastic for aircraft: lift is produced from the movement of air passing over and under the wing, with the air passing above being forced to speed up and thus drop in pressure. The high pressure under the wing of the plane will push it up. If you have more air trying to get around the obstacle of the wing, it speeds up more quickly, and the high pressure underneath creates lift faster.
Quite simply, denser air means more lift. This is why it is difficult for plane to fly at higher altitudes, where there isn't much air to produce enough lift.