An aircraft loops a vertical loop of radius R=500 m with a constant velocity $\mathrm{v}=360 {\mathrm{kmh}}^{-1}$. Find the weight of the flier of mass m=70 kg in the lower, upper, and middle points of the loop.

Forces on the flier in the frame of aircraft (non inertial reference frame) is 

i) Normal reaction (N)

(ii) Pseudo force $\left(\frac{{\mathrm{mv}}^2}{\mathrm{R}}\right)$

(iii) Gravitational force  (mg)

According to problem, ${\mathrm{v}}_{\mathrm{T}}={\mathrm{v}}_{\mathrm{b}}={\mathrm{v}}_{\mathrm{m}}=\mathrm{v}$

The net force on flier at every point should be zero in the frame of aircraft. For top point T,

$$\begin{gathered} {\mathrm{N}}_{\mathrm{T}}+\mathrm{mg}=\frac{{{\mathrm{mv}}^2}_{\mathrm{T}}}{\mathrm{R}} \\ \therefore {\mathrm{N}}_{\mathrm{T}}=\frac{{\mathrm{mv}}^2}{\mathrm{R}}-\mathrm{mg}=0.7 \mathrm{kN} \\ \mathrm{For} \mathrm{bottom} \mathrm{point}, \\ {\mathrm{N}}_{\mathrm{B}}=\mathrm{mg}+\frac{{{\mathrm{mv}}^2}_{\mathrm{b}}}{\mathrm{R}}=2.1 \mathrm{kN} \end{gathered}$$

$N_m=\sqrt{{\left(\frac{{\mathrm{mv}}^2}{\mathrm{R}}\right)}^2+{\left(\mathrm{mg}\right)}^2}=1.56 \mathrm{kN}$