A pilot with a mass of 50 kg comes out of a vertical dive in a circular arc such that at the bottom of the arc her upward acceleration is 3.5g. (a) How does the magnitude of the force exerted by the airplane seat on the pilot at the bottom of the arc compare to her weight? (b) Use Newton’s laws of motion to explain why the pilot might be subject to a blackout. This means that an above normal volume of blood “pools” in her lower limbs. How would an inertial reference frame observer describe the cause of the blood pooling?
A plane has an air speed of 200 m/s due North, and is in a wind of 50.0 m/s to the West. The plane's speed relative to the ground is
206m/s
To answer these questions, we can use Newton's laws of motion and apply the principles of centripetal acceleration and centripetal force.
(a) To determine the magnitude of the force exerted by the airplane seat on the pilot at the bottom of the arc, we need to consider the forces acting on the pilot. At the bottom of the arc, the pilot experiences an upward acceleration of 3.5g, where g is the acceleration due to gravity (approximately 9.8 m/s²). From Newton's second law, F = ma, we can find the net force acting on the pilot.
Net force = mass × acceleration
The mass of the pilot is given as 50 kg, so the net force is:
Net force = 50 kg × (3.5g × 9.8 m/s²)
Simplifying the equation, we find:
Net force = 1715 N
Since the pilot is experiencing an upward acceleration, the net force must be directed upward. Since weight is the force due to gravity, directed downward, we can compare the magnitude of the upward force to the pilot's weight.
Therefore, the magnitude of the force exerted by the airplane seat on the pilot at the bottom of the arc is 1715 N, which is greater than the pilot's weight.
(b) The pilot might experience a blackout due to the high acceleration and forces involved in the circular arc motion. This can cause an above-normal volume of blood to pool in her lower limbs. This phenomenon is known as gravitational pooling or orthostatic intolerance.
In an inertial reference frame, an observer would describe the cause of blood pooling as follows:
As the pilot undergoes the circular arc motion, she experiences a high centripetal acceleration towards the center of the circular path. This acceleration acts as a centripetal force, pulling the pilot towards the center. However, even though this centripetal force is strong enough to keep the pilot moving in a circle, it does not provide the necessary force to push the blood upward, against gravity. This causes blood to accumulate or pool in her lower limbs due to the lack of sufficient upward force to counteract gravity.
This pooling of blood can result in reduced blood flow to the brain and can lead to a temporary reduction in oxygen supply, causing the pilot to potentially experience a blackout or loss of consciousness.