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42.   Pilots of high-performance fighter
planes can be subjected to large centripetal
accelerations during high-speed turns. Because of these accelerations, the
pilots are subjected to forces that can be much
greater than their body weight, leading to an accumulation of blood in the
abdomen and legs. As a result, the brain becomes starved
for blood, and the pilot can lose consciousness (“black out”). The pilots
wear “anti-G suits” to help keep the blood from draining out of the brain. To
appreciate the forces that a fighter pilot must endure, consider the
magnitude FN of the normal force that the pilot’s seat
exerts on him at the bottom of a dive. The magnitude of the pilot’s weight is
W. The plane is traveling at 230 m/s on a vertical circle of radius
690 m. Determine the ratio FN/W. For comparison,
note that blackout can occur for values of FN/W as
small as 2 if the pilot is not wearing an anti-G suit.
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