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A wind with speed 40 m/s blows parallel to the roof of a house. The area of the roof is 250 m². Assuming that the pressure inside the house is atmospheric pressure, the force exerted by the wind on the roof and the direction of the force will be (ρ_air = 1.2 kg/m³):

1. 4.8 × 10⁵ N, upwards
2. 2.4 × 10⁵ N, upwards
3. 2.4 × 10⁵ N, downwards
4. 4.8 × 10⁵ N, downwards

Correct answer: 2.4 × 10⁵ N, upwards

Solution

The pressure difference due to the wind is given by Bernoulli's principle: ΔP = 0.5 * ρ_air * v². Substituting ρ_air = 1.2 kg/m³ and v = 40 m/s, we get ΔP = 0.5 * 1.2 * (40)² = 960 Pa. The force is then F = ΔP * A = 960 * 250 = 2.4 × 10⁵ N. Since the pressure outside is lower than inside, the force acts upwards.

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