# Problem: A roller coaster car crosses the top of a circular loop-the-loop at twice the critical speed.What is the ratio of the normal force to the gravitational force?

###### FREE Expert Solution

Centripetal force, FC:

$\overline{){{\mathbf{F}}}_{{\mathbf{C}}}{\mathbf{=}}\frac{\mathbf{m}{\mathbf{v}}^{\mathbf{2}}}{\mathbf{r}}}$

At critical speed, gravitational force and centripetal forces are equal:

$\begin{array}{rcl}{\mathbf{F}}_{\mathbf{G}}& \mathbf{=}& {\mathbf{F}}_{\mathbf{C}}\\ \mathbf{m}\mathbf{g}& \mathbf{=}& \frac{\mathbf{m}{\mathbf{v}}^{\mathbf{2}}}{\mathbf{r}}\\ \mathbf{v}& \mathbf{=}& \sqrt{\mathbf{r}\mathbf{g}}\end{array}$

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###### Problem Details

A roller coaster car crosses the top of a circular loop-the-loop at twice the critical speed.

What is the ratio of the normal force to the gravitational force?