the magnitude of a pilot is w. the plane is travelling at 230m/s on a vertical circle of radius 690m. determine the ratio Fn/w. for comparison,note that black out can occur for values fn/w as small as 2 if the pilot is not wearing an anti-G suit
To determine the ratio Fn/w, we first need to understand the forces acting on the pilot as it moves in a vertical circle.
When the plane is at the top of the circle, the gravitational force (mg) acts downwards, and the normal force (Fn) acts upwards.
At the bottom of the circle, the gravitational force (mg) still acts downwards, but the normal force (Fn) now acts downwards as well, due to the acceleration of the plane in that direction.
Given the information and using Newton's second law (Fnet = ma), we can calculate the net force on the pilot at the top of the circle:
At the top of the circle:
Net Force (Fnet) = Fn - mg = m * (v^2 / r)
Fn - mg = m * (v^2 / r)
Since we're interested in the ratio Fn/w, let's substitute w (magnitude of pilot's weight) for mg in the equation:
Fn - w = m * (v^2 / r)
Now, solving for Fn:
Fn = m * (v^2 / r) + w
Finally, we can find the ratio Fn/w:
Ratio Fn/w = Fn / w = [m * (v^2 / r) + w] / w
Substituting the given values:
v = 230 m/s (velocity of the plane)
r = 690 m (radius of the circle)
w = magnitude of the pilot's weight
We can calculate the ratio Fn/w by substituting these values into the equation above.