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.

Question

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. (A) 2.1kN,0.7kN,1.5kN (B) 0.7kN,1.5kN,2.1kN (C) 1.5kN,2.1kN,0.7kN (D) none of these

Tardigrade Admin · Accepted Answer

Forces on the flier in the frame of aircaraft (non inertial reference frame) is:
(i) Normal reaction (N)
(ii)Pseudo force

(\frac{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 = \frac{m v _{T}^{2}}{R} ∴ N_{T} = \frac{m v ^{2}}{R} - mg

= 0.7 kN
For bottom point,

N_{B} = mg + \frac{m v _{b}^{2}}{R} = mg + \frac{m v ^{2}}{R}

= 2.1 kN.

For middle point,

N_{m} = (\frac{mv _{2}}{R})^{2} + (mg)^{2} = 1.5 k N

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

$2.1 k N, 0.7 k N, 1.5 k N$

$0.7 k N, 1.5 k N, 2.1 k N$

$1.5 k N, 2.1 k N, 0.7 k N$

none of these

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

2.1kN,0.7kN,1.5kN

0.7kN,1.5kN,2.1kN

1.5kN,2.1kN,0.7kN

none of these

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

$2.1 k N, 0.7 k N, 1.5 k N$

$0.7 k N, 1.5 k N, 2.1 k N$

$1.5 k N, 2.1 k N, 0.7 k N$