Hot-Air Balloon Buoyant Force Calculation

What is the buoyant force exerted by the surrounding cold air on a hot-air balloon with a volume of 440 x 10^3 m³?

Given the density of the surrounding air is 2.58 kg/m³.

Answer:

The buoyant force exerted by the surrounding cold air on the hot-air balloon is 1.1 x 10^7 N.

When calculating the buoyant force on the hot-air balloon, we first need to determine the volume of the balloon, which is 440 x 10^3 m³. The next step is to consider the density of the surrounding air, which is given as 2.58 kg/m³.

The buoyant force is the weight of the air displaced by the balloon, and it can be calculated using the formula F_b = ρVg, where F_b is the buoyant force, ρ is the density of the surrounding air, V is the volume of the balloon, and g is the acceleration due to gravity.

Plugging in the values, we get:

F_b = 2.58 * 440 x 10^3 * 9.81

F_b = 1.1 x 10^7 N

Therefore, the buoyant force exerted by the surrounding cold air on the hot-air balloon is 1.1 x 10^7 N.