A weather balloon is inflated near Earth's surface with a low-density gas. Explain why the balloon rises when it's released.

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valentin68 | College Teacher | (Level 3) Associate Educator

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It is said that Archimedes discovered this principle while taking a bath and feeling easier that he normally ways: a body submerged into a fluid (a liquid or a gas) is pushed upside by a force equal to the weight of the mass of the fluid it displaces. He later called this force buoyant force.

Thus, a balloon that is inflated and is having a volume V displaces a mass of air having a weight (buoyant force)

`F_b =G_(air) =rho_(air)*V`

Because the balloon is inflated with a gas having a lower density than air (let say Hydrogen) the true weight of the balloon is

`G_("balloon") = rho_(H)*V`

Since `F_b >G¨_("balloon")` ,  `F_b` pushes up and  `G_("balloon")` pushes down ` `there will be a resultant force that pushes up the balloon.

`F = F_b -G_("balloon")`  is directed upwards.

The balloon is rising because the resultant force between the buoyant force and the true weight of the balloon is upwards.

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