On a perfect fall day, you are hovering at low altitude in a hot-air balloon, accelerated neither upward nor downward. The total weight of the balloon, including its load and the hot air in it, is 20,000 N. (a) What is the weight ofthe displaced air? (b) What is the vol - ume ofthe displaced air?

Since is at test, the buoyancy force, Fb is equal to the weight of the air, W.

W = 20000 N

B.

Density of air = 1.2 kg/m3

Force = mass * Acceleration

= density * volume * acceleration

20000 = 1.2 * Vol * 9.8

Vol = 1700.7 m3.

weight of air displaced by the balloon is 20,000 N

vol - ume ofthe displaced air is 1700 m³

Explanation:

If the balloon is not accelerating, the net force on it is zero.

There are two forces acting on the balloon: the weight (downward) and the buoyant force of the air (upward). These must be equal. The buoyant force is then 20,000 N. The buoyant force equals the weight of air displaced by the balloon, also 20,000 N

The weight of the air displaced is the densty of air times the volume.

The density of air at 1 atm and 20º C is 1.2 kg/m³

V = 20,000 / (1.2*9.8)

= 1700 m³

weight of air displaced by the balloon is 20,000 N

vol - ume ofthe displaced air is 1700 m³