A wind with speed 45 m/s blows across a roof 20 m long and 12 m wide.The pressure inside the room is 1 atm.What is the net force on this roof due to the pressure difference inside and outside the roof? (The density of air is equal to 1.3 kg/m³.) A)3.2 $\times$ 10⁵ N B)2.4 $\times$ 10⁷ N C)6.3 $\times$ 10⁵ N D)7.0 $\times$ 10³ N E)3.2 $\times$ 10⁸ N

Question

Quizplus · Accepted Answer

The net force on the roof due to the pressure difference can be calculated using Bernoulli's principle, which relates the speed of a fluid to the pressure exerted by that fluid. The pressure difference ($\Delta P$) caused by the wind can be found using the equation $\Delta P = \frac{1}{2} \rho v^2$, where $\rho$ is the density of air (1.3 kg/m$^3$) and $v$ is the speed of the wind (45 m/s). The area ($A$) of the roof is $20 m \times 12 m = 240 m^2$. The force ($F$) is given by $F = \Delta P \times A$. Substituting the values, we get $\Delta P = \frac{1}{2} \times 1.3 \times (45)^2 = 1316.25 Pa$, and $F = 1316.25 Pa \times 240 m^2 = 316,200 N$, which is $3.2 \times 10^5 N$.

A Wind with Speed 45 M/s Blows Across a Roof ×\times×

A Wind with Speed 45 M/s Blows Across a Roof $\times$