A plane is in level flight at constant speed and each of its wings has an area of `25m^(2)`. If the speed of the air is `180km//h` over the upper wing surface, determine the plane's mass . (Take air density to be `1 kg//m^(3)`). `g=9.8m//s^(2)`.

Explanation

Here speed of air over lower wing `v_(1)=180km//h=180xx(5)/(18)=50ms^(-1)`
speed over the upper wing `v_(2)=234km//h=234xx(5)/(18)=65ms^(-1)`
`therefore` pressure difference `P_(1)-P_(2)=(1)/(2)rho(v_(2)^(2)-v_(1)^(2))=(1)/(2)xx1(65^(2)-50^(2))=862.5Pa`
`therefore` Net upward force, `F=(P_(1)-P_(2))A`
this upward force balances the weight of the plane
`thereforemg=F=(P_(1)-P_(2))A` [`A=25xx2=50m^(2)`]
`thereforem=((P_(1)-P_(2))A)/(g)=(862.5xx50)/(9.8)=4400N`