Question

A plane is travelling at 200 ms^-1 following the curve of a vertical circle.  

If the passengers experience weightlessness at the top of its flight path, what is the radius of the circle?

Answer 1

Since passengers are weightlessness at the top of the flight path, the weight force

$$P = mg$$

is equal to the centrifugal force

$$F_c = ma$$

where $a$ is the acceleration, that is given as follows:

$$a = \dfrac{v^2}{R}$$

where $v = 200m/s$ is the speed, and $R$ is the radius of the circle. Thus, obtain:

$$mg = ma\\ g = \dfrac{v^2}{R}\\ R = \dfrac{v^2}{g}\\ R = \dfrac{200^2}{9.81} \approx 4077m$$

Answer. 4077 m.