A rooler coaster track is desingned so that the car travels

A rooler coaster track is desingned so that the car travels upside down on a certain portion of the tracks as shown in the figure below.

For the cart not to fall the centrifugal force (Fc) must be greater than the weight of the car.

Fc >= W

Fc >= m * g

Fc is m * w^2 * r

and w = v/r

so Fc = m * (v/r)^2 * r

Fc = m * v^2 /r

So m * v^2 /r >= m * g

v^2 /r >= g

v >= sqrt (g * r)

v >= sqrt(9.81 m/s^2 * 36 m)

v >= 18.79 m/s