Question

the california sea lion is capable of making extremely fast, tight turns while swimming underwater. in one study, scientists observed a sea lion making a circular turn with a radius of 0.31 m while swimming at 4.6 m/s. part a what is the sea lions centripetal acceleration, in units of g? express your answer in units of g. part b what percentage is this acceleration of that of an f - 15 fighter jets maximum centripetal acceleration of 9g? express your answer as a percentage.

Explanation:

Step1: Recall centripetal - acceleration formula

The formula for centripetal acceleration is $a_c=\frac{v^{2}}{r}$, where $v = 4.6\ m/s$ and $r=0.31\ m$.

Step2: Calculate centripetal acceleration

$a_c=\frac{(4.6)^{2}}{0.31}=\frac{21.16}{0.31}\approx68.26\ m/s^{2}$.
Since $g = 9.8\ m/s^{2}$, then $a_c$ in terms of $g$ is $\frac{a_c}{g}=\frac{68.26}{9.8}\approx6.97g$.

Step3: For part B

Let the maximum centripetal acceleration of an F - 15 fighter jet be $9g$.
The percentage is $\frac{6.97g}{9g}\times100\%=\frac{6.97}{9}\times100\%\approx77.4\%$.

Answer:

Part A: $6.97g$
Part B: $77.4\%$