A 135 kg balloon has a capacity of 1272 m³. If it is filled with helium (0.180 kg/m³), what is the maximum mass of goods it can carry when floating in air (1.30 kg/m³)?

Question

26-11-2024
Physics

High School

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A 135 kg balloon has a capacity of 1272 m³. If it is filled with helium (0.180 kg/m³), what is the maximum mass of goods it can carry when floating in air (1.30 kg/m³)?

Answer :

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shobhnahs shobhnahs · Answer 1 · 2024-09-03T03:15:49-04:00

Final answer:

The maximum mass of goods the balloon can carry when floating in the air is determined by the buoyant force, which is equal to the weight of the displaced air minus the weight of the balloon. To calculate the buoyant force, we need to find the weight of the displaced air and the weight of the balloon. Given the volume of the balloon and the density of air, we can calculate the weight of the displaced air.

Explanation:

To calculate the maximum mass of goods the balloon can carry when floating in the air, we need to determine the buoyant force acting on the balloon. The buoyant force is equal to the weight of the displaced air.

First, we need to calculate the volume of air displaced by the balloon. The density of air is 1.30 kg/m³. Given that the balloon has a capacity of 1272 m³, the volume of air displaced by the balloon is also 1272 m³.

Next, we can calculate the weight of the displaced air using the formula: weight = mass x gravity. The mass of the displaced air is calculated by multiplying the density of air (1.30 kg/m³) by the volume of air displaced (1272 m³). Assuming the acceleration due to gravity is 9.8 m/s², the weight of the displaced air is: weight = 1.30 kg/m³ x 1272 m³ x 9.8 m/s² = 16,065.6 N.

The maximum mass of goods the balloon can carry is equal to the buoyant force. We can calculate the buoyant force using the formula: buoyant force = weight of the displaced air - weight of the balloon. Given that the mass of the balloon is 135 kg and the density of helium is 0.180 kg/m³, the weight of the balloon is: weight of balloon = mass of balloon x gravity = 135 kg x 9.8 m/s² = 1323 N. Substitute the values into the buoyant force formula: buoyant force = 16,065.6 N - 1323 N = 14,742.6 N. Therefore, the maximum mass of goods the balloon can carry when floating in air is 14,742.6 N.