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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.
PhysicsLaws of MotionJEE Main
Options:
  • A 2.1 kN, 0.7 kN, 1.5 kN
  • B 0.7 kN, 1.5 kN, 2.1 kN
  • C 1.5 kN, 2.1 kN, 0.7 kN
  • D none of these
Solution:
2756 Upvotes Verified Answer
The correct answer is: 2.1 kN, 0.7 kN, 1.5 kN
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,

                        vT = vb = vm = 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

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