an airplane has a volume of 124 m^3. how much buoyant force does the air exert on it? assume the air density remains 1.29 kg/m^3.

Answer 1

Let

V = 124 m³ the be volume of the plane,

r = 1.29 kg/m³ be air density,

g = 9.81 m/s² be gravitational acceleration.

The buoyant force, F, is the weight of the air displaced by the plane:

F = g r V = 9.81 m/s² × 1.29 kg/m³ × 124 m³ = 1569.2 N

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Solution to your question in your comment

Let

V = 2210 m³ the be volume of the balloon,

m = 216 kg be the weight of the balloon and basket,

r = 1.29 kg/m³ be ambient air density,

q (to be calculated) be density of air hot enough to make the balloon float,

g = 9.81 m/s² be gravitational acceleration.

The buoyant force (upward), F_up is the weight of the ambient air displaced by the balloon:

F_up = grV

The balloon will float when F_up equals the downward force F_down of gravity,

due to the weight of the balloon, basket, and hot air inside.

F_down = g(m + qV)

Now set the two forces equal and solve for q:

F_up = F_down

grV = g(m + qV)

q = r - m/V

In other word, the air inside must have its density reduced by the fraction m/V

Substituting actual numbers

q = 1.29 kg/m³ - 216 kg / 2210 m³ = 1.19 kg/m³