Question

An aeroplane flies in a loop (a circular path in a vertical plane) of radius 200 m. The pilot's head always points toward the centre of the loop. The speed of the aeroplane is not constant; the aeroplane goes slowest at the top of the loop and fastest at the bottom. At the top of the loop, the pilot feels weightless. What is the speed of the aeroplane at this point?

At the bottom of the loop, the speed of the aeroplane is 280 km/h . What is the apparent weight of the pilot at this point? His true weight is 710 N .

Answer 1

2899.24 N

Step-by-step explanation:

W = Weight of pilot

r = Radius

v = Velocity

g = Acceleration due to gravity = 9.81 m/s²

`mg=m(v^2)/(r)\\\Rightarrow v=√(gr)\\\Rightarrow v=√(9.81* 200)\\\Rightarrow v=44.3\ m/s`

Speed of the aeroplane at the top of the loop is 44.3 m/s

Now, v = 280 km/h = 280/3.6 = 77.78 m/s

Apparent weight

`A=W+(W)/(g)(v^2)/(r)\\\Rightarrow A=710+(710)/(9.81)* (77.78^2)/(200)\\\Rightarrow A=2899.24\ N`

Apparent weight at the bottom of the loop is 2899.24 N