Question

Pilot of high-performance fighter planes can be subjected tolarge centripetal acceleration during high-speed turns. Because ofthese accelerations, the pilots are subjected to forces that can bemuch greater than their body weight, leading to an accumulation ofblood in the abdomen and legs. As a result, the brain becomesstarved for blood, and the pilot can lose consciousness ("blackout"). The pilots wear "anti-G suits" to help keep the blood fromdraining out of the brain. To appreciate the forces that a fighterpilot must endure, consider the magnitude FN of thenormal force that the pilot's seat exerts on him at the bottom of adive. The magnitude of the pilot's weight is W. The plane istraveling at 230 m/s on a vertical circle of radius 690 m.

Determine the ration FN/W. For comparison, note thatblack-out can occur for values of FN/W as small as 2 if the pilot is not wearing an anti-G suit.

Answer 1

The ratio of the normal force to the weight of a fighter pilot at the bottom of a dive can be calculated using centripetal force and weight formulas. With a plane speed of 230 m/s and a radius of 690 m, the ratio FN/W is found to be approximately 7.7, which is above the blackout threshold of 2 without an anti-G suit.

Step-by-step explanation:

To calculate the ratio FN/W, where FN is the normal force (centripetal force in this context) that the pilot's seat exerts on him, and W is the weight of the pilot, we can use the formula for centripetal force, which is Fc = mv2/r. In the scenario provided, the fighter plane is traveling at a speed v = 230 m/s on a vertical circle with radius r = 690 m. The weight of the pilot can be represented by W = mg where g is the acceleration due to gravity (9.80 m/s2). The pilot's actual weight is irrelevant as it will cancel out in the ratio calculation.

Now, let's substitute the given values into the centripetal force formula:

FN = mv2/r = m(230 m/s)2/(690 m),

and for weight:

W = mg = m(9.80 m/s2).

To find the ratio FN/W, we simply divide the expression for FN by the expression for W:

FN/W = (m(230 m/s)2/(690 m))/(m(9.80 m/s2)).

After canceling out the mass m, we have:

FN/W = (2302)/(690*9.80) which simplifies to approximately 7.7, which is much higher than the blackout threshold of 2 without an anti-G suit.