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?
To answer question (a), we need to analyze the forces acting on the pilot at the bottom of the arc.
1. Calculate the weight of the pilot:
The weight of an object is given by the equation: weight = mass * gravitational acceleration. Since the mass of the pilot is given as 50 kg, and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the weight as follows:
Weight = 50 kg * 9.8 m/s^2 = 490 N.
2. Determine the net force acting on the pilot:
At the bottom of the arc, the pilot experiences an upward acceleration of 3.5g, where g is the gravitational acceleration. This means the net force acting on the pilot is the sum of the upward force and the downward force.
Since force = mass * acceleration, the upward force acting on the pilot can be determined as:
Upward Force = mass * upward acceleration = 50 kg * (3.5 * 9.8 m/s^2).
3. Compare the upward force to the weight:
To compare the magnitude of the force exerted by the airplane seat on the pilot to her weight, we need to compare the upward force to the weight. If the force exerted by the seat is greater than the weight, then the magnitude of the force is larger.
Comparing the two forces, if the upward force is greater than the weight (490 N), then the magnitude of the force exerted by the seat on the pilot is larger. If the upward force is equal to the weight, then the magnitude of the force exerted by the seat on the pilot is the same. And if the upward force is less than the weight, then the magnitude of the force exerted by the seat on the pilot is smaller.
Now, moving on to question (b):
According to Newton's laws of motion, when an object undergoes acceleration, there is a force acting on it. In the case of the pilot in the vertical dive, the upward acceleration causes increased blood flow to the lower limbs due to the gravitational force on the blood. This increased blood flow can lead to an above normal volume of blood "pooling" in the lower limbs.
From an inertial reference frame observer's perspective, they would describe the cause of the blood pooling as the gravitational force acting on the blood in the pilot's body. Since the pilot is experiencing an upward acceleration at the bottom of the arc, the observer would attribute the pooling of blood to the gravitational force pulling the blood downward, away from the upper body. This can result in a lower blood pressure and decreased oxygen supply to the brain, which may lead to a blackout.