(a) A light balloon is filled with 400 m^3 of helium. At 0...

(a) A light balloon is filled with $400 \mathrm{~m}^{3}$ of helium. At $0{ }^{\circ} \mathrm{C}$, what is the mass of the payload that the balloon can lift? (b) In Table 15.1, note that the density of hydrogen is nearly one-half the density of helium. What load can the balloon lift if it is filled with hydrogen?

Key Concepts

Application of Fluid Statics Concepts

In problems involving gas-filled balloons, principles of fluid statics are applied. This includes using the known properties of gases (such as density at specific temperatures and pressures) along with the volume of the balloon to calculate forces and determine the maximum load that can be lifted.

Archimedes' Principle

This principle states that a body immersed in a fluid is buoyed up by a force equal to the weight of the displaced fluid. In the context of gas-filled balloons, it is used to calculate the upward force provided by the volume of air that is displaced by the balloon’s gas.

Buoyant Force and Net Lift

The buoyant force is the net upward force exerted on the balloon due to the pressure difference in the surrounding fluid (air). To determine the net lifting capability, one must subtract the weight of the gas within the balloon from the total weight of the air displaced, thereby calculating the net lift or payload the balloon can support.

Density Differences Between Gases

The density of a gas affects its weight per unit volume. When a lighter gas is used inside a balloon, the difference in density between the surrounding air and the gas creates a greater buoyant force. Understanding how variations in gas density (such as between helium and hydrogen) impact lift is essential in predicting the payload capacity.

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