# Density of Air in a Hot Air Balloon: Lift a 50 kg Person and Max Weight with Helium

## How much volume of balloon is needed to lift a 50 kg person?

(a) To lift a 50 kg person, what volume balloon is required?

## What is the maximum weight the balloon can carry if hot air is replaced with helium?

(b) What is the maximum mass the balloon can carry with helium instead of hot air?

## Answer:

(a) To lift a 50 kg person, a balloon with a volume of approximately 61.25 cubic meters is required.

(b) When filled with helium, the maximum mass that the balloon can carry is approximately 120 kg.

To lift a 50 kg person using a hot air balloon, the volume of the balloon needed can be calculated by considering the density of hot air and the weight of the person. The density of hot air is 0.8 kg/m3, and in this case, we have the mass of the person as 50 kg.

By using the formula V = (m*g) / (ρ_v*g), where V is the volume of the balloon, m is the mass of the person, g is the acceleration due to gravity, and ρ_v is the density of hot air, we can determine that a balloon with a volume of approximately 61.25 cubic meters is required to lift a 50 kg person.

When considering replacing the hot air with helium, which has a density of 0.2 kg/m3, we can calculate the maximum weight the balloon can carry. By using the same formula and substituting the density of helium, the maximum mass the balloon can carry is approximately 120 kg.

Therefore, by understanding the density differences and utilizing the buoyant force calculation, we can determine the necessary volume for lifting a specific weight with a hot air balloon and the maximum weight possible with helium as the lifting gas.