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An aeroplane requires for take off a spe...

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 coefficient of friction between aeroplane and ground is 0.2 What is the maximum force required by the engine of the plane for take off ?

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From 3rd equation of motion for take off,
`[80 xx (5)/(18)]^(2) = 0^(2) + 2a xx 100`
i.e., `a = (200//81) m//s^(2)`.....(i)
Now if F is the required force, for take off
`F - f ge ma`
or `F ge ma + mu mg` [as `f = mu mg`]
or `F ge 10^(4) [(200)/(81) + 0.2xx 9.8]`
or `F ge 4.43 xx 10^(4) N`
So, the minimum force required by the engine of plane for take off is `4.43 xx 10^(4) N`.
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