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

Step-by-step solution

Forces on the flier in the frame of aircaraft (non inertial reference frame) is: (i) Normal reaction (N) (ii)Pseudo force m v ⁡ 2 R ⁡ (iii) Gravitational force d(mg) According to problem, v T = v b = v m = v The net force on flier at every point should be zero in the frame of aircraft. For top point T, N T + mg = mv ⁡ T 2 R ⁡ ∴ N T = mv ⁡ 2 R ⁡ - mg = 0.7 kN For bottom point, N ⁡ B ⁡ = mg + mv ⁡ b 2 R ⁡ = mg + mv ⁡ 2 R ⁡ = 2.1 kN. For middle point, N m = mv 2 R 2 + mg 2 = 1 . 5 k N ⁡