An aeroplane flying in the air dips with a speed of 360 km per hr in a vertical circle of radius is 200m the weight of the pilot sitting in it 75kg calculate the force with which the pilot presses his seat and plane is at lowest point and plane is at highest point
what is 77g + 77*v^2/r
convert for v 360km/hr to m/s
Answer
To calculate the force with which the pilot presses his seat at the lowest and highest point, we need to consider two forces acting on the pilot: the gravitational force and the centrifugal force.
1. At the lowest point of the vertical circle:
At the lowest point, the plane is moving in the horizontal direction, while the pilot is moving in the vertical direction. In this case, the centrifugal force will be maximum and acting downwards, while the gravitational force will be acting downwards as well.
To calculate the centrifugal force:
Centrifugal force = m * (v^2) / r
m = mass of the pilot = 75 kg
v = velocity of the plane = 360 km/hr = 100 m/s (convert km/hr to m/s)
r = radius of the vertical circle = 200 m
Centrifugal force = 75 * (100^2) / 200 = 37,500 N (downwards, towards the seat)
The gravitational force will be the weight of the pilot:
Gravitational force = m * g
m = mass of the pilot = 75 kg
g = acceleration due to gravity = 9.8 m/s^2
Gravitational force = 75 * 9.8 = 735 N (downwards, towards the seat)
Therefore, at the lowest point, the force with which the pilot presses his seat is the sum of the centrifugal force and the gravitational force:
Force at lowest point = Centrifugal force + Gravitational force
Force at lowest point = 37,500 N + 735 N = 38,235 N (downwards, towards the seat)
2. At the highest point of the vertical circle:
At the highest point, the plane is still moving in the horizontal direction, while the pilot is moving in the vertical direction. In this case, the centrifugal force will be minimum and acting upwards, while the gravitational force will be acting downwards.
To calculate the centrifugal force:
Centrifugal force = m * (v^2) / r
Using the same values as before:
Centrifugal force = 37,500 N (upwards, away from the seat)
The gravitational force remains the same as before:
Gravitational force = 735 N (downwards, towards the seat)
Therefore, at the highest point, the force with which the pilot presses his seat is the difference between the gravitational force and the centrifugal force:
Force at highest point = Gravitational force - Centrifugal force
Force at highest point = 735 N - 37,500 N = -36,765 N (downwards, towards the seat)
Note: The negative sign indicates that the force is directed opposite to the positive direction (upwards) in this case.
So, the force with which the pilot presses his seat at the lowest point is 38,235 N downwards, and at the highest point is 36,765 N downwards.