On a perfect fall day, you are hovering at low altitude in a hot-air balloon, accelerated neither upward nor downward. The total weight of the balloon, including its load and the hot air in it, is 24000 N.

Find the weight of the displaced air.
Find the volume of the displaced air.

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2400

To find the weight of the displaced air, we need to use Archimedes' principle, which states that the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.

1. We know that the total weight of the balloon, including its load and the hot air in it, is 24000 N.
2. Assuming the balloon is hovering at low altitude with no acceleration, the buoyant force acting on it is equal to its weight.
3. Therefore, the weight of the displaced air is also 24000 N.

To find the volume of the displaced air, we need to use the formula for the buoyant force:

Buoyant force = Density of the fluid * Volume of the fluid displaced * Gravity

1. We already know that the weight of the displaced air is 24000 N, which is the buoyant force.
2. The density of air at sea level is approximately 1.2 kg/m^3.
3. The acceleration due to gravity is approximately 9.8 m/s^2.

Let's substitute these values into the formula and solve for the volume of the displaced air:

24000 N = 1.2 kg/m^3 * Volume * 9.8 m/s^2

Simplifying the equation:

Volume = 24000 N / (1.2 kg/m^3 * 9.8 m/s^2)

Volume = 2020.8333 m^3

Therefore, the volume of the displaced air is approximately 2020.8333 m^3.

To find the weight of the displaced air, you need to understand the concept of buoyancy. Buoyancy is the upward force exerted on an object immersed in a fluid, like air or water. It is equal to the weight of the fluid displaced by the object.

In this case, the hot-air balloon is in equilibrium, which means it is neither accelerating upward nor downward. This implies that the buoyant force acting on the balloon is equal to its weight.

The total weight of the balloon and its load is given as 24000 N. Therefore, the weight of the displaced air is also 24000 N.

To find the volume of the displaced air, you can use Archimedes' principle. According to Archimedes' principle, the buoyant force acting on an object in a fluid is equal to the weight of the fluid displaced by the object.

Since the weight of the displaced air is 24000 N, and the density of air is approximately 1.2 kg/m^3, you can use the equation:

Weight of the displaced air = density of air * volume of the displaced air * acceleration due to gravity

24000 N = 1.2 kg/m^3 * volume of the displaced air * 9.8 m/s^2

To find the volume, rearrange the equation:

volume of the displaced air = 24000 N / (1.2 kg/m^3 * 9.8 m/s^2)

Simplifying the equation, you get:

volume of the displaced air ≈ 2041 m^3

Therefore, the weight of the displaced air is 24000 N, and the volume of the displaced air is approximately 2041 m^3.