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.

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 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.

Answer 1

Ac = v^2/R = 230^2/690 = 76.7 meters/ second^2

A = g + 76.7 total at bottom
= 9.8 +76.7 = 86.5 m/s^2
A/g = 86.5 / 9.8 = 8.8
better get that suit on

Answer 2

To determine the ratio FN/W, we need to calculate both the magnitude of the normal force (FN) and the magnitude of the weight (W).

First, let's calculate the magnitude of the weight (W):
The weight of an object is given by the equation W = mg, where m is the mass and g is the acceleration due to gravity. We know that the force of gravity acts downward, so the weight can be written as W = mg.

However, we are not given the mass of the pilot. Instead, we are given the acceleration of gravity (g) as a reference point. The acceleration due to gravity is approximately 9.8 m/s². Therefore, we can rewrite the weight equation as W = (mass of the pilot) × g.

Next, we need to calculate the magnitude of the normal force (FN):
The normal force is the force exerted by a surface to support the weight of an object resting on it. In this case, the seat exerts the normal force on the pilot. At the bottom of a dive, the normal force should be equal to or greater than the weight of the pilot to prevent them from falling off the seat.

To calculate the centripetal acceleration (ac) of the pilot in the circular motion, we use the equation ac = v²/r, where v is the velocity and r is the radius of the circle. In this case, v = 230 m/s and r = 690 m.

Now, let's calculate the centripetal force (Fc) experienced by the pilot using the equation Fc = m × ac, where m is the mass of the pilot.

Since the centripetal force is provided by the normal force, we can write Fc = FN.

Finally, we equate the centripetal force to the weight to calculate the ratio FN/W:

Fc = FN = W

Now, let's put all of this information together to calculate the ratio FN/W.

1. Calculate the weight (W):
W = (mass of the pilot) × g
Note: The question does not give information about the mass of the pilot.

2. Calculate the centripetal acceleration (ac):
ac = v²/r
ac = (230 m/s)² / 690 m

3. Calculate the centripetal force (Fc) using Fc = m × ac:
Fc = (mass of the pilot) × ac

4. Equate the centripetal force to the weight to find FN:
Fc = FN = W

5. Calculate the ratio FN/W:
Ratio FN/W = FN / W

Unfortunately, without knowing the mass of the pilot, we cannot proceed with the calculations to find the ratio FN/W.

Answer 3

To determine the ratio FN/W, we need to find the normal force (FN) exerted by the pilot's seat and the weight (W) of the pilot.

1. Find the weight of the pilot (W):
The weight of an object is given by the formula W = m * g, where m is the mass of the object and g is the acceleration due to gravity (approximated as 9.8 m/s^2). However, the mass of the pilot is not given, so we need additional information.

2. Calculate the centripetal acceleration (a):
The centripetal acceleration is given by the formula a = v^2 / r, where v is the velocity of the plane and r is the radius of the vertical circle. Plugging in the given values, we get:
a = (230 m/s)^2 / 690 m = 76.67 m/s^2

3. Find the net force (F_net) acting on the pilot:
The net force acting on the pilot is given by the equation F_net = m * a, where m is the mass of the pilot. Since the mass is not given, we can cancel it out from the ratio FN/W, so we don't need to determine the mass separately.

4. Determine the force exerted by the pilot's seat (FN):
In a vertical circle, the normal force (FN) exerted by the pilot's seat is equal to the net force (F_net) plus the weight (W). Therefore, FN = F_net + W.

5. Calculate the ratio FN/W:
Finally, we can calculate the desired ratio by dividing FN by W: FN/W = (F_net + W) / W.

Unfortunately, since we do not know the mass of the pilot, we cannot determine the specific value of FN/W in this case.