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.
I got the weight=2.4×10^4 N but not the displaced air!!
Find the volume of the displaced air.
Please help
To find the weight of the displaced air, we need to consider the principle of buoyancy. According to Archimedes' principle, the buoyant force exerted on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
In the case of a hot-air balloon that is neither ascending nor descending, the balloon is in equilibrium, so the weight of the displaced air must be equal to the weight of the balloon and its load.
Given that the total weight of the balloon, including its load and the hot air in it, is 24000 N, we can assume that the weight of the displaced air is also 24000 N.
Therefore, the weight of the displaced air is 24000 N.
Now, to find the volume of the displaced air, we need to use the concept that the weight of the displaced air is equal to the weight of an equivalent volume of air at standard atmospheric conditions.
The weight of a substance can be calculated using the formula:
Weight = density × volume × acceleration due to gravity
Since the weight of the displaced air is equal to the weight of the balloon and its load, and we assume the weight of the displaced air is 24000 N, we can rearrange the formula to find the volume:
Volume = Weight / (density × acceleration due to gravity)
The density of air at standard atmospheric conditions is approximately 1.225 kg/m^3, and the acceleration due to gravity is approximately 9.8 m/s^2.
Plugging in the values, we can calculate the volume:
Volume = 24000 N / (1.225 kg/m^3 × 9.8 m/s^2)
Volume ≈ 1973 m^3
Therefore, the volume of the displaced air is approximately 1973 cubic meters.