during a thunderstorm,wind with a speed of 47.7 m/s blows across a flat roof with an area of 688m/^2 .Find the magnitude of force exerted on the roof by the wind
Well, it seems like the wind is having quite the blast! Let's calculate the magnitude of force exerted on the roof.
To find the force, we can use the formula:
Force = Pressure × Area
But first, we need to find the pressure. The pressure due to the wind can be calculated using the formula:
Pressure = (1/2) × density × velocity²,
where density is the air density and velocity is the wind speed.
Now, let's plug in the numbers. Since air density may vary, on average it is about 1.225 kg/m³:
Pressure = (1/2) × 1.225 kg/m³ × (47.7 m/s)²
Calculating that, we find:
Pressure ≈ 1392.420 kg/m·s²
Now, let's find the force by multiplying the pressure by the roof's area:
Force = 1392.420 kg/m·s² × 688 m²
After crunching those numbers, we get:
Force ≈ 958,568.96 kg·m/s²
Therefore, the magnitude of force exerted on the roof by the wind is approximately 958,568.96 Newtons. That's quite a punch!
To find the magnitude of force exerted on the roof by the wind, you can use the formula:
Force = Pressure × Area
First, we need to find the pressure exerted by the wind on the roof.
To calculate the pressure, we use the formula:
Pressure = 0.5 × ρ × V^2
Where:
ρ is the density of air (approximately 1.225 kg/m^3 at sea level)
V is the velocity of the wind (47.7 m/s in this case)
We'll assume the density of air is 1.225 kg/m^3 as per sea-level conditions:
Pressure = 0.5 × 1.225 × (47.7)^2
Next, substitute the pressure value we just calculated and the area of the roof into the force formula:
Force = Pressure × Area
Force = (0.5 × 1.225 × (47.7)^2) × 688
Now, calculate this equation:
Force = (0.5 × 1.225 × (47.7)^2) × 688
The magnitude of force exerted on the roof by the wind is the value you get from this calculation.
To find the magnitude of force exerted on the roof by the wind during a thunderstorm, we can use the formula:
Force = Pressure × Area
1. First, we need to find the pressure exerted by the wind on the roof. Pressure is defined as force per unit area, and can be calculated using the formula:
Pressure = (1/2) × density × velocity^2
Where:
- density is the density of air (approximately 1.2 kg/m^3)
- velocity is the speed of the wind (47.7 m/s in this case)
2. Next, we can substitute the calculated pressure into the formula for force to get the magnitude of the force:
Force = Pressure × Area
Where:
- Area is the area of the roof (688 m^2 in this case)
Let's perform the calculations:
1. Calculate pressure:
Pressure = (1/2) × 1.2 kg/m^3 × (47.7 m/s)^2
2. Calculate force:
Force = Pressure × Area
Substitute the values:
Force = Pressure × 688 m^2
Perform the calculations to find the magnitude of the force exerted on the roof by the wind.