Question

An aeroplane requires a speed of $108$ $kmph$ to take off, to achieve that plane runs on the runway of $100$ $m$. Mass of the plane is $10400$ $kg$ and the coefficient of friction between the plane and the ground is $0.2$. Assuming the plane accelerates uniformly, the minimum force required is (Take $g=9.81m/s^2$)

• A. $2\times {10}^{4}N$
• B. $2.43\times {10}^{4}N$
• C. $6.72\times {10}^{4}N$
• D. $8.86\times {10}^{4}N$

Answer 1

Answer: (C)

$6.72\times {10}^{4}N$

Required take off speed is $108$ $kmph$ i.e $30$ $m/s$ over a run of $100$ $m$.
$v^2-u^2=2as$
$v^2-0=2as$
$a=\frac{v^2}{2s}$

Force that should be developed by the engine is given by:
$F-\mu mg=ma$
$F=0.2\left(10400\right)\left(9.81\right)+10400\left(\frac{{30}^2}{2\left(100\right)}\right)=6.72\times {10}^{4}N$