On a perfect fall day, you are hovering at a 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 12000 N.
What is the volume of the displaced air in units of m3? (Use 1.2 kgm3 for the density of air)
Ah, the joys of being a balloon in the autumn sky! Let's calculate that volume for you.
Since the balloon is hovering at a low altitude and not accelerating, we know that the force of the displaced air is equal to the weight of the balloon. So, the weight of the displaced air is also 12000 N.
Now, to find the volume of the displaced air, we can use Archimedes' principle. According to "Mr. A": "The buoyant force experienced by an object submerged in a fluid is equal to the weight of the fluid displaced by the object." Sounds fancy, right?
The buoyant force is equal to the weight of the displaced air, which we've determined to be 12000 N. And we can determine the density of the air as 1.2 kg/m³. So, let's plug those values into our trusty formula:
Buoyant force = density of air × volume of displaced air × acceleration due to gravity
12000 N = 1.2 kg/m³ × volume of displaced air × 9.8 m/s²
Now, we can solve for the volume of the displaced air, or V:
V = 12000 N / (1.2 kg/m³ × 9.8 m/s²)
V ≈ 1000 m³
So, the volume of the displaced air is around 1000 cubic meters. Just imagine all the clown noses that could fill that space!
To find the volume of the displaced air, we can use Archimedes' principle, which states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. In this case, the buoyant force on the hot-air balloon is equal to its weight, since it is neither accelerating upward nor downward.
The weight of the hot-air balloon, including its load and the hot air in it, is 12000 N. This is equivalent to the buoyant force acting on the balloon.
Using the formula for the buoyant force, we have:
Buoyant force = (density of air) * (volume of displaced air) * (gravitational acceleration)
12000 N = (1.2 kg/m^3) * V * (9.8 m/s^2)
Simplifying the equation, we can solve for the volume (V):
V = 12000 N / ((1.2 kg/m^3) * (9.8 m/s^2))
V = 12000 N / (11.76 kg*m/s^2)
V ≈ 1020.41 m^3
Therefore, the volume of the displaced air is approximately 1020.41 m^3.
To find the volume of the displaced air, we can 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.
In this case, the balloon is hovering at a low altitude, which means it is not submerged in the air but displaced by it. The buoyant force acting on the balloon is equal to the weight of the air it displaces.
Given that the total weight of the balloon, including its load and the hot air in it, is 12000 N, we can assume that this weight is equal to the buoyant force.
Let's denote the volume of the displaced air as V.
Using the formula for the weight of a substance (weight = density * volume * gravity), we can express the weight of the displaced air as:
12000 N = (1.2 kg/m^3) * V * 9.8 m/s^2
Dividing both sides of the equation by (1.2 kg/m^3 * 9.8 m/s^2), we can solve for V:
V = 12000 N / (1.2 kg/m^3 * 9.8 m/s^2)
Calculating this expression gives us the volume of the displaced air in units of cubic meters (m^3).