An airplane pilot is going to demonstrate flying in a tightvertical circle. To e

Question

An airplane pilot is going to demonstrate flying in a tightvertical circle. To ensure that she doesn't black out at thebottom of the circle, the acceleration must not exceed 4.0g. If the speed of the plane is 5.0 m/s at the bottom of the circle,what is the minimum radius of the circle so that the 4.0 g limit isnot exceeded? An airplane pilot is going to demonstrate flying in a tightvertical circle. To ensure that she doesn't black out at thebottom of the circle, the acceleration must not exceed 4.0g. If the speed of the plane is 5.0 m/s at the bottom of the circle,what is the minimum radius of the circle so that the 4.0 g limit isnot exceeded?

Explanation / Answer

A circular path means a constant magnitude of acceleration towardsthe center of the circle. And, the equation for this radialacceleration is: arad = v2/r Therefore, r = v2 / arad Substituting the given velocity and the given maximumacceleration, r = (5.0 m/s)2 / (4.0g)    g = 9.8m/s2 =   0.64m The pilot's circular path should not be lower than 0.64m so thatshe would not black out.

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