Question

A rollercoaster is designed with a 10 m tall vertical circular loop. Calculate the minimum speed necessary to get around the loop without falling down.

Answer 1

$$F_g=F_c,$$ $$mg=\dfrac{mv^2}{r},$$ $$v_{min}=\sqrt{gr}=\sqrt{9.8\ \dfrac{m}{s^2}\times10\ m}=9.9\ \dfrac{m}{s}.$$