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What physics principle makes a balloon fly?

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Balloon ride in Spain with Siempre en las nubes

Balloon ride in Spain with Siempre en las nubes

The principle behind hot air balloon physics is the Archimedes Principle which states that the buoyant force on a submerged object is equal to the weight of the fluid that is displaced by the object.
For a hot air balloon, the upward buoyant force acting on it is equal to the weight of air displaced. The density of air is 1.2 kg per cubic meter; therefore to lift a balloon is going to be necessary to displace a great volume of air so its weight exceeds the weight of the envelope, plus the weight of passengers, and the upward force is greater than the downward force of gravity.
In helium balloons the buoyant force is created because helium is less dense and lighter than the air surrounding them. In hot air balloons the lifting force is created by modifying the temperature of the air inside of the envelope, reducing its density.

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