To solve this problem it is necessary to apply the concepts of the Centripetal Force and the force caused by gravity. The centripetal force can be described as
[tex]F_c = \frac{mv^2}{r}[/tex]
Where,
m = Mass
v = Velocity
r = Radius
At the same time the force caused by the weight can be described as
[tex]F_g = mg \rightarrow m = \frac{F_g}{g}[/tex]
Where,
m = mass
g = Gravity
If we make a sum of Forces, the forces that act vertically on the body, both in the upward and downward direction must be equivalent to the centripetal Force, therefore
[tex]F_f - F_g = F_c[/tex]
Here [tex]F_f[/tex] represents the force from Plane, then:
[tex]F_f - F_g =\frac{mv^2}{r}[/tex]
If we put the mass of the body according to the weight we would have to:
[tex]F_f - F_g = \frac{(\frac{F_g}{g})v^2}{r}[/tex]
[tex]F_f -7kN = \frac{(\frac{7kN}{9.8})(0.2)^2}{0.8}[/tex]
Converting to SI:
[tex]F_f - 7000 =\frac{(\frac{7000N}{9.8})(200)^2}{800}[/tex]
[tex]F_f = 4271N[/tex]
Therefore the forces that the plane exert on the pilot is 4271N
