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 this: it is 2.4×10^4 N
I cannot get the volume please help!!
Find the volume of the displaced air.
never mind......took another 50 % ran out of time, Got the 1st part but not the 2nd ughhhh
For the volume of displaced air, divide the mass (W/g = 2446 kg) by the density of air, which is about 1.3*10^-3 kg/m^3, depending upon P and T.
To find the volume of the displaced air, you 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.
1. Begin by determining the weight of the displaced air. You correctly calculated it as 2.4 × 10^4 N.
2. Next, use the formula for the buoyant force: Buoyant force = weight of displaced fluid.
3. Since the volume of the displaced air is unknown, let's represent it as V.
4. Use the formula for weight: Weight = density × volume × gravitational acceleration.
5. The weight of the air is equal to the buoyant force, so we have:
Weight of air = density of air × V × gravitational acceleration.
6. Equating the buoyant force and the weight, we get:
2.4 × 10^4 N = density of air × V × gravitational acceleration.
7. Rearrange the equation to solve for V:
V = (2.4 × 10^4 N) / (density of air × gravitational acceleration).
8. Now, you need to find the density of air at the given conditions. The air density typically varies with altitude, pressure, and temperature. Assuming standard conditions, the density of air is approximately 1.225 kg/m^3.
9. Plug in the values to calculate V:
V = (2.4 × 10^4 N) / (1.225 kg/m^3 × 9.8 m/s^2).
10. After performing the calculation, you will obtain the volume of the displaced air.
To find the volume of the displaced air, we will 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.
In this case, the hot-air balloon is floating at low altitude, meaning it is displacing a volume of air equal to its own weight. Since the weight of the balloon is given as 24000 N, we can assume that the volume of air displaced is also 24000 N.
However, it is important to note that weight and volume are not equivalent, as weight is a measure of force, while volume is a measure of space. So, we need to convert the weight of the displaced air to its volume.
To find the volume of the displaced air, we can use the density of air. The density of air is approximately 1.225 kg/m³ at sea level and room temperature. We can convert the weight of the displaced air from Newtons to kilograms by dividing by the gravitational acceleration (9.8 m/s²):
Weight of displaced air = 24000 N
Mass of displaced air = Weight of displaced air / Gravity = 24000 N / 9.8 m/s² ≈ 2448.98 kg
Now, to find the volume, we can use the following formula:
Volume = Mass / Density
Volume = 2448.98 kg / 1.225 kg/m³ ≈ 2002.63 m³
Therefore, the volume of the displaced air is approximately 2002.63 m³.