Question

When the air inside a particular hot-air balloon cooled, the balloon and its inside air descended. Based on Student 1 's explanation, the reason the balloon and its inside air descended is most likely that the: F. downward buoyant force acting on the balloon and its inside air was stronger than the upward force of gravity acting on the balloon and its inside air. G. upward buoyant force acting on the balloon and its inside air was stronger than the downward force of gravity acting on the balloon and its inside air. H. downward force of gravity acting on the balloon and its inside air was stronger than the upward buoyant force acting on the balloon and its inside air. J. upward force of gravity acting on the balloon and its inside air was stronger than the downward buoyant force acting on the balloon and its inside air.

Short answer

Short Answer: The hot-air balloon descended when the air inside it cooled because the downward force of gravity acting on the balloon and its inside air became stronger than the upward buoyant force acting on the balloon and its inside air, as cooling caused a decrease in the net buoyant force.

Step-by-step solution

Identify the forces at play

According to Archimedes' principle, the buoyant force acting on a submerged object is equal to the weight of the fluid that it displaces. In this exercise, as the hot-air balloon and its inside air descend, we are comparing the upward buoyant force and the downward force of gravity. The stronger of these two forces will determine if the balloon ascends or descends.

Understand how cooling affects buoyant force

When the air inside the hot-air balloon cools, the volume occupied by that air decreases, making the air denser. As a result of this, the hot-air balloon displaces a smaller amount of air. Since the buoyant force is directly proportional to the volume of air displaced, the net buoyant force acting on the balloon and its inside air decreases.

Compare buoyant force and force of gravity

Now, we need to determine if the downward force of gravity is stronger or weaker than the upward buoyant force, as the hot-air balloon descends. Since the net buoyant force has decreased due to the cooling of air inside the balloon, it will be weaker compared to the downward force of gravity.

Choose the correct option

To answer the exercise, we are looking for the option where the downward force of gravity is stronger than the buoyant force. The correct option is: H. downward force of gravity acting on the balloon and its inside air was stronger than the upward buoyant force acting on the balloon and its inside air.

Key concepts

Archimedes' Principle

Understanding Archimedes' principle is key to grasping how objects like hot-air balloons behave in air or any fluid. This principle states that any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object. For a hot-air balloon, the surrounding air is the fluid. When the balloon is inflated with hot air, it displaces a volume of air whose weight is equivalent to the buoyant force acting upon it.

As the balloon rises, it's because the buoyant force overcomes the weight of the balloon. Conversely, if the hot air inside cools and becomes denser, the balloon will descend because it displaces less air, resulting in a diminished buoyant force. Hence, the balloon's ability to float is governed by this principle and the relationship between the volume of displaced air and the resulting buoyant force.

Buoyant Force

The buoyant force is a concept deeply tied to Archimedes' principle. It's the upward force exerted on an object by the fluid in which it is immersed. For our hot-air balloon, when heated, the air inside expands and becomes less dense than the cooler air outside. This difference in density means that the balloon displaces more air and experiences a greater buoyant force, allowing it to rise.

However, when the balloon cools down, the air inside contracts, leading to a decrease in the displaced air's volume and thus a reduction in the buoyant force. The reduction in buoyant force makes the balloon less able to counteract gravity, which remains constant, and the balloon begins to descend. It's important to note that the buoyant force is not downward as option F incorrectly suggests; it always acts in the opposite direction to gravity.

Gravity

Gravity, a force that attracts two bodies towards each other, is key to understanding why hot-air balloons descend when the air inside cools. The force of gravity acting on the balloon, which includes its mass and the mass of the air inside, is a constant downward force. It doesn't change whether the balloon's air is hot or cold.

When the cooling of the balloon's air leads to the air contracting, the mass of the balloon system doesn't change, but the lift generated by the buoyant force decreases because the balloon displaces less air. Hence, gravity becomes the dominant force, as reflected in option H, and this causes the balloon to descend. Since gravity is always present, its role in the flight of the hot-air balloon is vital to maintaining balance with the buoyant force for controlled flight.