# Hot air balloon - Archimedes Principle

• Attis
In summary: The total mass would depend on the material and cargo, which is not given.In summary, the conversation discussed the calculation of the total mass of a hot air balloon using Archimedes' Principle. The correct formula for calculating the mass is M = ρV, where ρ is the density of the hot air and V is the volume of the balloon. The attempt at a solution that included the acceleration due to gravity, g, was incorrect as it equated mass with force. The total mass of the balloon would also include the mass of the balloon material and cargo, which was not given in the problem.
Attis

## Homework Statement

A hot air balloon with V = 500 m^3 is floating in the air without moving. The air outside the balloon has a density of 1,20 kg/m^3, and the hot air inside the balloon has a density of 0,75 kg/m^3. Calculate the total mass of the hot air balloon.

## Homework Equations

Archimedes Principle F0 = ρVg

## The Attempt at a Solution

F0 = (1,20 -0,75) * 500 = 225 kg

What I don´t understand is why g wasn´t integrated into this answer? How come the answer isn´t (1,20-0,75)*500 * 9,82 =2210 kg?

Attis said:

## Homework Statement

A hot air balloon with V = 500 m^3 is floating in the air without moving. The air outside the balloon has a density of 1,20 kg/m^3, and the hot air inside the balloon has a density of 0,75 kg/m^3. Calculate the total mass of the hot air balloon.

## Homework Equations

Archimedes Principle F0 = ρVg

## The Attempt at a Solution

F0 = (1,20 -0,75) * 500 = 225 kg

What I don´t understand is why g wasn´t integrated into this answer? How come the answer isn´t (1,20-0,75)*500 * 9,82 =2210 kg?

The buoyant force is ρVg, but you made it equal with mass, which is wrong.

Fo has to be equal to the weight, that is, ρ(outside)Vg=ρ(inside)Vg+Mg where M is the mass of the balloon and cargo, without the air inside the balloon.
You can divide the whole equation with g.

ehild

1 person
I do not think you described the problem as stated. Because as stated, the answer is simply ## m = \rho V##, where ##\rho## is the hot air density, by definition of density.

The answer that you think should be true is not a correct answer to a question about mass, simply because that answer gives some force.

voko said:
I do not think you described the problem as stated. Because as stated, the answer is simply ## m = \rho V##, where ##\rho## is the hot air density, by definition of density.

The total mass of the hot-air balloon was asked. It is not the mass of the air only, but includes both the balloon material and the cargo.

ehild

ehild said:
The total mass of the hot-air balloon was asked. It is not the mass of the air only, but includes both the balloon material and the cargo.

Then the answer is wrong. Just the air in the balloon is 375 kg.

## What is the Archimedes Principle?

The Archimedes Principle states that any object that is partially or fully submerged in a fluid experiences an upward force equal to the weight of the fluid it displaces. This is why objects float in water and why hot air balloons can lift off the ground.

## How does the Archimedes Principle relate to hot air balloons?

The Archimedes Principle is the scientific explanation for how hot air balloons are able to fly. By filling the balloon with hot air, it becomes less dense than the surrounding air and experiences an upward buoyant force, allowing it to lift off the ground.

## What is the role of hot air in a hot air balloon?

Hot air is essential in hot air balloons because it is what makes the balloon less dense than the surrounding air. This creates the upward buoyant force that allows the balloon to lift off the ground and fly.

## How does temperature affect the flight of a hot air balloon?

Temperature plays a crucial role in the flight of a hot air balloon. As the temperature of the air inside the balloon changes, the density of the air also changes, affecting the buoyant force and the altitude of the balloon. Hot air balloons are typically flown in the early morning or late afternoon when the air temperature is more stable.

## What safety measures are taken to ensure a safe hot air balloon flight?

Hot air balloon pilots must undergo rigorous training and certification to ensure the safety of their passengers. Additionally, hot air balloons are regularly inspected and maintained to ensure they are in proper working condition. Weather conditions are also carefully monitored before each flight to ensure safe flying conditions.

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