a rollercoaster travels through a loop at 14.2 m/s, and has a centripetal acceleration of 13.6 m/s². what is…

a rollercoaster travels through a loop at 14.2 m/s, and has a centripetal acceleration of 13.6 m/s². what is the radius of the loop? r = ? m

a rollercoaster travels through a loop at 14.2 m/s, and has a centripetal acceleration of 13.6 m/s². what is the radius of the loop? r = ? m

Answer

Explanation:

Step1: Recall centripetal - acceleration formula

The formula for centripetal acceleration is $a_c=\frac{v^{2}}{r}$, where $a_c$ is centripetal acceleration, $v$ is velocity, and $r$ is the radius.

Step2: Rearrange the formula to solve for $r$

We can rewrite the formula as $r = \frac{v^{2}}{a_c}$.

Step3: Substitute given values

Given $v = 14.2$ m/s and $a_c=13.6$ m/s², we substitute these values into the formula: $r=\frac{(14.2)^{2}}{13.6}$. First, calculate $(14.2)^{2}=14.2\times14.2 = 201.64$. Then, $r=\frac{201.64}{13.6}\approx14.8$ m.

Answer:

$14.8$