Question

An aeroplane of mass M requires a speed V for the take off . The length of the Runway is S and the coefficient of the friction between the tires and the ground is mew assuming that the plane accelerates uniformly during the take up the minimum force required by the engine of the plane for the takeoff is given by

Answer 1

Suppose the aeroplane was at rest... (u=0)
by using
v² = u² + 2as,
(v is takeoff speed and, a is the acceleration... which is assumed to be uniform during the run)
a = v²/2s

where, s is the distance of run.


Now, frictional force will have to act in the opposite direction of the run...
and, f = ​μN
Now, N = mg , as there is no vertical acceleration.
=> f =​ μmg

Also, this acceleration(a) that we have calculated is nothing but the net acceleration.
Using Newton's II law,i.e., ma_net =F_net
So, ma = F - μ​mg

This is because, we need the acceleration in the direction of the engine force.

so, F = ma + μ​mg = m(a + μ​g) = m( v²/2s + μ​g)