The radius of the loop is 18.9 km
Explanation:
When the airplane is at the top of the loop, the pilot experiences two forces:
Since the plane is moving in a circular motion, the net force on the pilot must be equal to the centripetal force, therefore we can write:
[tex]mg+N = m\frac{v^2}{r}[/tex]
where
m is the mass of the pilot
[tex]g=9.8 m/s^2[/tex] is the acceleration of gravity
N is the normal reaction
v = 430 m/s is the speed of the plane
r is the radius of the loop
Here we are told that the pilot feel weightless at the top of the loop: this means that the normal reaction is zero,
N = 0
Therefore the equation becomes
[tex]mg=\frac{mv^2}{r}[/tex]
And so we can find the radius of the loop:
[tex]r=\frac{v^2}{g}=\frac{430^2}{9.8}=18.9 \cdot 10^3 m = 18.9 km[/tex]
Learn more about circular motion:
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