Question

Плотность воздуха 1,3 кг/м3. Груз какой максимальной массы сможет поднять воздушный шар общей массой 50 кг и объѐмом 100 м3?

Answer 1

Дано: m1=50 кг; p=1.3 кг/м3 V=100 м3 m=?
(m1+m)*g=p*g*V
m1+m=p*V
m=p*V-m1=1.3*100-50=80кг.
Ответ 80 кг максимальная масса груза

Answer 2

Calculation of the Maximum Mass the Balloon Can Lift

To calculate the maximum mass that an air balloon can lift, we need to consider the buoyant force acting on the balloon. The buoyant force is equal to the weight of the air displaced by the balloon. The weight of the air displaced can be calculated using the formula:

Buoyant force = Density of air * Volume of the balloon * Acceleration due to gravity.

Given that the density of air is 1.3 kg/m³, the volume of the balloon is 100 m³, and the acceleration due to gravity is approximately 9.8 m/s², we can calculate the buoyant force:

Buoyant force = 1.3 kg/m³ * 100 m³ * 9.8 m/s² = 1274 kg * m/s² = 1274 N.

The buoyant force is equal to the weight of the air displaced, which is also equal to the weight of the balloon and the payload it can lift. Therefore, the maximum mass the balloon can lift is 1274 kg or 1.274 metric tons.

Since the total mass of the balloon and the payload is 50 kg, the maximum mass the balloon can lift is greater than the total mass, so the balloon will be able to lift the payload.

Please note that this calculation assumes ideal conditions and does not take into account factors such as air resistance, the weight of the balloon envelope, or the weight of the gas used to fill the balloon. These factors can affect the actual lifting capacity of the balloon.

Conclusion

The air balloon with a total mass of 50 kg and a volume of 100 m³ will be able to lift a payload of up to 1.274 metric tons.