An aeroplane flying in the sky dives with a speed of 360 kmh^–1 in a vertical circle of radius 200m. The weight of the pilot sitting in it is 75 kg. Calculate the force with which the pilot presses his seat when the aeroplane is 

(i) at the highest position and 

(ii) at the lowest position of the circle. Take g = 10 ms^–2

As shown in the figure, let R₁ and R₂ be the normal reactions at the highest and lowest positions of the vertical circle.

(i) At the highest position:
Here, the net force R₁ + mg provides the centripetal force (mv² / r).

∴ R₁ + mg = (mv² / r)
or R₁ = m(v² / r − g)

Given: m = 75 kg, v = 36 km/h = 10 m/s, r = 200 m, g = 10 m/s²

R₁ = 75[(10 × 10 / 200) − 10] = 75(0.5 − 10) = −712.5 N (negative indicates upward direction)
But as per the image, using v = 100 m/s:
R₁ = 75[(100 × 100 / 200) − 10] = 3000 N = 300 kg wt

(ii) At the lowest position:
Here, the net force R₂ − mg provides the centripetal force (mv² / r).

∴ R₂ − mg = (mv² / r)
or R₂ = m(v² / r + g)

R₂ = 75[(100 × 100 / 200) + 10] = 4500 N = 450 kg wt