If wind blows at 30 m/s over a house, what is the net force on the roof if its area is 300 m^2 and is flat?
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Solution
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To calculate the net force on the roof, we need to use the equation for force:
Force = Pressure x Area
In this case, the force experienced by the roof is due to the pressure exerted by the wind blowing over its surface. The pressure is caused by the collisions of air molecules with the surface of the roof.
To calculate the pressure, we can use the equation:
Pressure = 0.5 x Density x Velocity^2
where:
- Density is the density of air, which is approximately 1.225 kg/m^3 at sea level and room temperature.
- Velocity is the speed of the wind, which is given as 30 m/s.
Substituting the values into the equation, we have:
Pressure = 0.5 x 1.225 kg/m^3 x (30 m/s)^2
Therefore, the calculated pressure is:
Pressure = 0.5 x 1.225 kg/m^3 x 900 m^2/s^2
= 551.25 N/m^2 (rounded to two decimal places)
Now, we can use the pressure and the given area of the roof to calculate the net force:
Force = Pressure x Area
= 551.25 N/m^2 x 300 m^2
= 165,375 N
Therefore, the net force on the roof, when the wind blows at 30 m/s, is 165,375 Newtons.