A hot-air balloon has a volume of 2979 m^3. The density of the air outside the balloon is 1.205

step 1 have a hot balloon having volume v equals to 2979 meter cube and density of the air outside so r

A hot-air balloon has a volume of 2979 m^3. The density of...

A hot-air balloon has a volume of $2979 \mathrm{~m}^{3}$. The density of the air outside the balloon is $1.205 \mathrm{~kg} / \mathrm{m}^{3}$. The density of the hot air inside the balloon is $0.9441 \mathrm{~kg} / \mathrm{m}^{3}$. How much weight can the balloon lift (including its own weight)?

Key Concepts

Archimedes' Principle

Archimedes' Principle states that any object submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces. This principle underlies the operation of hot-air balloons, explaining how the displaced air creates lift.

Buoyant Force

Buoyant force is the net upward force acting on an object immersed in a fluid. It is determined by the difference between the weight of the displaced fluid and the weight of the fluid that fills the object. In the context of a hot-air balloon, this force is key to overcoming gravity and creating lift.

Density

Density, defined as mass per unit volume, helps determine the weight of a given amount of fluid or gas. In buoyancy problems, comparing the density of the external air with that of the internal hot air allows one to compute the net buoyant force, as the difference in densities directly influences the amount of lift.

Volume

Volume is the measure of the space occupied by an object and is crucial in determining the total mass of the displaced fluid. For a hot-air balloon, the volume of the balloon, when combined with the density of the surrounding air, dictates the total weight of air displaced, which is central to calculating the lift.

Net Lift Calculation

The net lift of a buoyant object is calculated by subtracting the weight of the lighter internal medium (inside the balloon) from the weight of the denser external medium (displaced air). This difference provides the effective lifting capacity, indicating how much additional weight the balloon can raise.

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