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?Select one:a.1 800 mb.3 600 mc.1 150 md.2 300 m
Question
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?Select one:a.1 800 mb.3 600 mc.1 150 md.2 300 m
Solution
To solve this problem, we need to use the formula for centripetal acceleration, which is a = v^2 / r, where a is the acceleration, v is the velocity, and r is the radius.
In this case, we want the acceleration to be equal to g (the acceleration due to gravity) to create a condition of "weightlessness" inside the aircraft. So we set a = g = 9.8 m/s^2.
Then we can solve for r:
r = v^2 / g r = (150 m/s)^2 / 9.8 m/s^2 r = 22 500 m^2/s^2 / 9.8 m/s^2 r = 2 295.92 m
So, the radius of curvature of the flight path must be approximately 2 300 m to create a condition of "weightlessness" inside the aircraft. Therefore, the answer is d. 2 300 m.
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