An aeroplane requires for take off a speed of `80 km//h` the run on the ground being 100 m The mass of aeroplane is `10^(4)` kg and ground is 0.2 What is the maximum force required by the engine of the plane for take off ?

Explanation

Here ,` upsilon = (80 xx 1000)/(60 xx 60) = (200)/(9) m//s `
` s = 100 m , u = 0 , mu = 0.2 , m = 10^(4) kg F = ? `
From ` upsilon^(2) - u^(2) = 2 as `
` ((200)/(9))^(2) - 0 = 2 xx a xx 100 `
` a = (200 xx 200 )/(9 xx 9 ) xx (1)/(200) = (200)/(81) m//s^(2) `
Force required to produce acceleration
`F_(1) = ma = 10^(4) xx (200)/(81) = 1.96 xx 10^(4) N`
Force required to overcome friction
`F_(2) = mu R = mu ng = 0.2 xx 10^(4) xx 9.8 = 1.96 xx 10^(4) N`
`:.` maximum force required by the engine to take off `= F_(1) + F_(2)`
`=2.47 xx 10^(4)+1.96 xx 10^(4) = 4.43 xx 10^(4) N`.