much greater than their body weight, leading to an accumulation of blood in the

Question

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 of the normal force that the pilot's seat exerts on him at the bottom of a dive. The plane is traveling at 225 m/s on a vertical circle of radius 689 m. Determine the ratio of the normal force to the magnitude of the pilot's weight. For comparison, note that black-out can occur for ratios as small as 2 if the pilot is not wearing an anti-G suit. 9h

Explanation / Answer

Noting that the direction upward (toward the center of the circular path) is positive in the drawing, we see that the centripetal force is

Fc = Fn - W

Fc = Fn - W = mv^2 / r

The weight is given by W = mg, so we can divide the expression for the centripetal force by the expression for the weight and obtain that

Fc = (Fn - W) / W = mv^2 / mgr

Fn / W - 1 = v^2 / gr

Solving for the ratio Fn / W,

Fn / W = v^2 / gr + 1

Fn / W = 225^2 / (9.81 x 689) + 1

Fn / W = 8.45

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