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

`A=25 cm^(2), let v_(1)=180 km//h=50m//s`
`v_(2)=234 km//h =65 ms^(-1), p=1 kg//m^(3)`
Total area of the two wings `=2 xx 25 =50m^(2)`
By Bernoulli.s equation `P_(1)-P_(2)=1/2 p(v_(1)^(2)-v_(2)^(2)) ("h =constant")`
`=1/2 xx 1 xx ((65)^(2)-(50)^(2))`
`=862.5 N//m^(2)`
upward force on plane `=(P_(1)-P_(2)) A=862.5 xx 50`
=43125 N
As the plane is in the level, Therefore `mg=(P_(1)-P_(2))A`
`mg=43125`
m=43125/9.8
=4400 g