Why does a hot air balloon rise in the atmosphere?

• A. Because the heated air inside the balloon becomes heavier than the surrounding air, causing the balloon to rise.
• B. Because the balloon material repels gravity when heated.
• C. Because the pressure inside the balloon is lower than the pressure outside, which pushes the balloon upward.
• D. Because the air inside the balloon is heated, making it less dense than the cooler air outside, so the upward buoyant force $F\_b$ exceeds the weight $W$ of the balloon.

Answer: (D)

Verified step by step guidance

1. Understand that a hot air balloon rises due to the principle of buoyancy, which depends on the difference in density between the air inside the balloon and the surrounding air.
2. Recall that when air is heated, its molecules move faster and spread apart, causing the air to become less dense compared to the cooler air outside the balloon.
3. Apply Archimedes' principle, which states that the buoyant force \(F_b\) on an object immersed in a fluid is equal to the weight of the fluid displaced by the object. In this case, the fluid is the surrounding cooler air.
4. Express the buoyant force as \(F_b = \rho_{\text{outside}} \cdot V \cdot g\), where \(\rho_{\text{outside}}\) is the density of the cooler outside air, \(V\) is the volume of the balloon, and \(g\) is the acceleration due to gravity.
5. Compare the buoyant force \(F_b\) to the weight of the balloon \(W = m_{\text{balloon}} \cdot g\), where \(m_{\text{balloon}}\) includes the mass of the balloon material and the heated air inside. The balloon rises when \(F_b > W\) because the less dense heated air inside reduces the overall weight, allowing the upward buoyant force to lift the balloon.