Question

question 14 of 25 a centrifuge is used to test space pilots. the centrifuge spins with a centripetal acceleration of 6.55 g. if the length of the centrifuges arm is 18 m, what is the speed of the centrifuge? a. 41 m/s b. 34 m/s c. 31 m/s d. 38 m/s

Explanation:

Step1: Recall centripetal - acceleration formula

The centripetal - acceleration formula is $a_c=\frac{v^{2}}{r}$, where $a_c$ is the centripetal acceleration, $v$ is the speed, and $r$ is the radius (length of the centrifuge's arm). Also, $g = 9.8\ m/s^{2}$, and $a_c=6.55g$.

Step2: Calculate the centripetal acceleration value

First, find the value of $a_c$: $a_c = 6.55\times9.8\ m/s^{2}=64.19\ m/s^{2}$.

Step3: Rearrange the centripetal - acceleration formula to solve for $v$

From $a_c=\frac{v^{2}}{r}$, we can solve for $v$ by multiplying both sides by $r$ and then taking the square - root: $v=\sqrt{a_cr}$.

Step4: Substitute the values of $a_c$ and $r$

Substitute $a_c = 64.19\ m/s^{2}$ and $r = 18\ m$ into the formula: $v=\sqrt{64.19\times18}=\sqrt{1155.42}\approx34\ m/s$.

Answer:

B. 34 m/s