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 of the normal force that the pilot's seat exerts on him at the bottom of a dive. The plane is traveling at 229 m/s on a vertical circle of radius 642 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.

Question

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 of the normal force that the pilot's seat exerts on him at the bottom of a dive. The plane is traveling at 229 m/s on a vertical circle of radius 642 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.

Answer 1

To determine the ratio of the normal force to the magnitude of the pilot's weight, we need to first find the net force acting on the pilot and then compare it to the weight of the pilot.

In this scenario, the net force acting on the pilot is the centripetal force required to keep the pilot moving in a circular path.

We can calculate the centripetal force using the formula:

F_c = m * (v^2 / r)

where
F_c is the centripetal force,
m is the mass of the pilot,
v is the speed of the plane,
and r is the radius of the circular path.

In this case, the speed of the plane is given as 229 m/s, and the radius of the vertical circle is 642 m.

Next, we need to calculate the weight of the pilot. The weight of an object is given by the formula:

Weight = m * g

where
m is the mass of the pilot,
and g is the acceleration due to gravity.

For this calculation, we can assume the acceleration due to gravity is 9.8 m/s^2.

Now, we can find the ratio of the normal force to the magnitude of the pilot's weight using the formula:

Ratio = Normal Force / Weight

Let's calculate it step by step.

1. Calculate the centripetal force:
F_c = m * (v^2 / r)

Substituting the given values:
F_c = m * (229^2 / 642)

2. Calculate the weight of the pilot:
Weight = m * g

Assuming the mass of the pilot is 70 kg:
Weight = 70 kg * 9.8 m/s^2

3. Calculate the ratio:
Ratio = F_c / Weight