A wind with speed 40 m/s blows parallel to the roof ofa house. The area of the roof is 250 m^(2). 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: (rho_("air")=1.2kg//m^(3))

A wind with speed 40 m/s blows parallel to the roof ofa house. The are

1.	A wind with speed 40 m/s blows parallel to the roof ofa house. The area of the roof is 250 m^(2). 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: (rho_("air")=1.2kg//m^(3))
Answer» <P>`2.4xx10^(5)N`, upwards `2.4xx10^(5)N`, downwards `4.8xx10^(5)N`, downwards `4.8xx10^(5)N`, upwards Solution :By Bernoulli's theorem, `UNDERSET("inside")ubrace(P_(1)+(1)/(2)rhov_(1)^(2))=underset("outside")ubrace(P_(2)+(1)/(2)rhov_(2)^(2))` Assuming that the roof width is very small, pressure difference, `P_(1)-P_(2)=(1)/(2)rho(v_(2)^(2)-v_(1)^(2))` Here, `rho=1.2kgm^(-3),v_(2)=40ms^(-1),v_(1)=0,A=250m^(2)` `P_(2)-P_(2)=(1)/(2)xx1.2(40^(2)-0^(2))` `P_(1)-P_(2)=(1)/(2)xx1.2xx1600=960Nm^(-2)` Force acting on the roof `F=(P_(1)-P_(2))xxA` `=960xx250` `=2.4xx10^(5)N` upwards