Question

Какая максимальная масса груза которую сможет поднять шар заполненный гелием если:Объем шара = 1000 м³Масса оболочки = 300 кгПлотность воздуха = 1,29 кг/м³Плотность гелия = 0,18 кг/м³

Answer 1

F=ρ₀gV>=mg+Mg;ρ₀-воздух;ρ-гелий
ρ₀gV>=mg+ρgV
ρ₀V>=m+ρV;
ρ₀V-ρV>=m;
V(ρ₀-ρ)>=m
1000(1,29-0,18)>=1110 кг
1110-300=810

Answer 2

Maximum Cargo Mass for a Helium-Filled Balloon

To calculate the maximum cargo mass a helium-filled balloon can lift, we can use the principle of buoyancy. The buoyant force acting on the balloon is equal to the weight of the air it displaces, minus the weight of the balloon itself. Let's calculate the maximum cargo mass using the given parameters.

Given Parameters:

- Volume of the balloon (V) = 1000 m³ - Mass of the balloon's envelope (m_env) = 300 kg - Density of air (ρ_air) = 1.29 kg/m³ - Density of helium (ρ_helium) = 0.18 kg/m³

Calculation:

The buoyant force (B) acting on the balloon can be calculated using the formula: B = (ρ_air - ρ_helium) * V * g

Where: - ρ_air = Density of air - ρ_helium = Density of helium - V = Volume of the balloon - g = Acceleration due to gravity (approximately 9.81 m/s²)

The maximum cargo mass (m_cargo) the balloon can lift is given by: m_cargo = B - m_env

Let's calculate the maximum cargo mass using the provided values.

Calculation:

1. Buoyant force (B): B = (1.29 kg/m³ - 0.18 kg/m³) * 1000 m³ * 9.81 m/s² B ≈ 10449.3 N

2. Maximum cargo mass (m_cargo): m_cargo = 10449.3 N - 300 kg * 9.81 m/s² m_cargo ≈ 7449.3 kg

Conclusion:

The maximum cargo mass that the helium-filled balloon can lift is approximately 7449.3 kg.