An airplane in a wide sweeping "outside" loop can create zero gees inside the aircraft cabin.What must be the radius of curvature of the flight path for an aircraft moving at 150 m/s to create a condition of "weightlessness" inside the aircraft?
A)1 150 m
B)1 800 m
C)2 300 m
D)3 600 m

Question

Quizplus · Accepted Answer

In order to create a condition of weightlessness inside the aircraft, the centrifugal force acting on the aircraft must be equal and opposite to the force of gravity. This can be achieved when the aircraft is in a state of freefall.

When an aircraft is in a wide sweeping "outside" loop, it follows a circular path with a centripetal acceleration given by:

a = v^2 / r

where v is the velocity of the aircraft and r is the radius of curvature of the flight path.

In order to create zero gees, the centripetal acceleration a must be equal and opposite to the acceleration due to gravity g, so:

a = g

v^2 / r = g

r = v^2 / g

Substituting v = 150 m/s and g = 9.81 m/s^2:

r = (150 m/s)^2 / 9.81 m/s^2

r = 2 304 m

Therefore, the radius of curvature of the flight path must be 2 300 m, which corresponds to choice C.

An Airplane in a Wide Sweeping "Outside" Loop Can Create