Question

An aeorplane requires a speed of 72K mph for a take off with 150 m run on the ground. The mass of the plane is 1500 kg and the coefficient of friction between the aeroplane and the ground is 0.4. Assuming that the aeroplane accelerates uniformly during take off, the minimum force exerted by the engine of the plane for take off is 

(1) 2000 N 

(2) 1950 N 

(3) 7880 N 

(4) none

Answer 1

Correct option is (3) 7880 N 

For the aeroplane to take off, it needs 72 Kmph at the end of 150 m. 

\(\therefore\) required uniform acceleration would be 

2 as = v - u

\(\Rightarrow 2 a(150 m) = (72 (\frac {1000}{3600})m/s)^2 - 0 ^2\)

\(\Rightarrow a = 4 /3 \,m/s^2\)

F_f  - F = ma

\(\Rightarrow \mu mg - ma = F _{engine}\)

\(\Rightarrow\) \(F _{engine} =1500 (0.4 \times 10 - 1.33)\)

\(\Rightarrow F_{engine} = 7880 N\)