Dorothy is up on her 17.0m by 12.0m roof enjoying the view of Kansas. Suddenly,

Question

Dorothy is up on her 17.0m by 12.0m roof enjoying the view of Kansas. Suddenly, a strong wind blows down her ladder, leaving her stranded. She knows that a high wind reduces the air pressure on the roof, and that there is a danger that the atmospheric pressure inside the house will blow the roof off. As the wind reaches a speed of 37.5m/s, she calls to her Auntie Em for help. Calculate the force on the roof. Dorothy is up on her 17.0m by 12.0m roof enjoying the view of Kansas. Suddenly, a strong wind blows down her ladder, leaving her stranded. She knows that a high wind reduces the air pressure on the roof, and that there is a danger that the atmospheric pressure inside the house will blow the roof off. As the wind reaches a speed of 37.5m/s, she calls to her Auntie Em for help. Calculate the force on the roof.

Explanation / Answer

We know from the defination of pressure,

Pressure = Force/Area

Force = Pressure x Area

Pressure(P) = 1/2 rho v^2

P = 0.5 x 1.25 x 37.5^2 = 878.91 Pa

A = 17 x 12 = 204 m^2

F = P x A = 878.91 x 204 = 179297.64 N

Hence, F = 179297.64 N = 1.8 x 10^5 N.

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