Question

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?

Short answer

The ratio of the normal force to the gravitational force is $3$.

Step-by-step solution

Given information

Given in the question that, A roller coaster car crosses the top of a circular loop-the-loop at twice the critical speed.

Explanation

From the information we observed that $\frac{m{V}^2}{r}$is the result of $N$and $mg$

Here,

$m-$The mass of the roller coaster

$g-$The acceleration due to gravity

$r-$The radius of the circular loop

$V$- The velocity

Therefore,

$\frac{m{V}^2}{r}+N=mg$

$N=mg-\frac{m{V}^2}{r}$

$V^2=4gr$

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

Therefore,

$N=mg-\frac{m\left(4gr\right)}{r}$

$N=-3mg$

Hence, the ratio of the normal force to the gravitational force is$3$

Final answer

The ratio of the normal force to the gravitational force is $3$.