Pulling out of a dive, the pilot of an airplane guides his plane into a vertical circle. at the bottom of the dive, the speed of the airplane is 320 m/s. what is the smallest radius allowable for the vertical circle if the pilot's apparent weight is not to exceed 7 times his true weight?

Smallest Radius = 1.74 km

Explanation:

When we consider a plane maneuvering in a vertical circle, huge amount of force acts on the pilot when the plane is at the bottom of the circle.  

The equation at the bottom of the circle will be:

FN = FC + FG

FN = m*(V^2/R + g)

Where m is the mass of the pilot, g is gravitational acceleration, V is the velocity, and R is the radius of the circle.

FN = 7g*m

V = 320 m/s

g = 9.81 m/s^2

Plugging the values in the above equation,

7g*m = m*(g+V^2/R)

V^2/R = 6g

(320)^2 / R = 6*(9.81)

R = 1.74 km

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hope this is what you're talking about