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 can use Archimedes' principle, which states that the buoyant force acting on an object immersed in a fluid is equal to the weight of the fluid displaced by the object. In this case, the fluid is air.
Let's assume that the density of air is constant and equal to the average density of air at sea level, which is approximately 1.225 kg/m^3.
The weight of the displaced air can be calculated using the formula: weight = density * volume * gravitational acceleration.
Given that the weight of the balloon is 24000 N (or kg*m/s^2), we can rearrange the formula to solve for the volume of the displaced air.
weight = density * volume * gravitational acceleration
24000 N = 1.225 kg/m^3 * volume * 9.8 m/s^2
Solving for volume:
volume = 24000 N / (1.225 kg/m^3 * 9.8 m/s^2)
volume = 1964.2 m^3
Therefore, the volume of the displaced air is approximately 1964.2 cubic meters.
To summarize:
- The weight of the displaced air is 24000 N.
- The volume of the displaced air is 1964.2 cubic meters.