Final answer:
The upward buoyant force on an airship is proportional to the airship's internal volume and the difference in density between the air outside and the helium gas inside. The correct statement is that the buoyant force depends on the difference between the density of air and that of helium gas.
Step-by-step explanation:
The upward buoyant force on an airship is a key aspect to understand in physics, particularly in the study of fluid dynamics. The buoyant force that allows an airship, such as one filled with helium, to float is due to the principle of buoyancy, which states that the upward buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. This is described by Archimedes' principle.
In the case of an airship, which is filled with helium gas and floats in air, the upward buoyant force is proportional to the difference in the density between the air outside and the helium gas inside, multiplied by the gravitational force and the volume of the airship. Specifically, since the density of helium (0.179 kg/m³) is less than that of air (1.29 kg/m³), the airship is able to float. Thus, the correct statement would be that the buoyant force on the airship is proportional to the airship's internal volume and the difference in density of air and helium gas.
When an airship flies over Western Pennsylvania and stays at a level constant in the air, this buoyant force acts against the gravitational force, thus allowing the airship to float. It's important to note that while the helium provides buoyancy due to being less dense than air, the weight of all passengers combined does not directly affect the buoyant force, although an increased weight would require more helium or a larger volume for the airship to stay afloat. The internal volume of the airship is indeed essential for determining the total buoyant force because the larger the volume, the more air is displaced.