Question

1. answer all questions. 2. for credit, show your work where necessary. 3. all answers to be done on canvas. 4. do not download the respondus lockdown browser (rlb) when taking the exam. 5. refer all technical problems with rlb to msu dit team @ the main library. 6. if facing technical challenges with your technology - laptop, ipad & wi - fi, plan to take the exam at main library. 7. plan your calendar accordingly because there will be no other make - up! 8. for extra credit, a handwritten \cheat\ sheet, pdf format, can be submitted to a canvas message to the instructor immediately after the exam. question 10 medical technicians use small centrifuges to isolate blood cells. a typical unit holds six (6) test tubes, rotates at 3380 revolutions per minute, and produces a centripetal acceleration of 1600 g. how far are the test tubes from the rotation axis? show your work for credit? 10 pts

Explanation:

Step1: Recall centripetal - acceleration formula

The centripetal - acceleration formula is $a = r\omega^{2}$, where $a$ is the centripetal acceleration, $r$ is the radius (distance from the rotation axis), and $\omega$ is the angular velocity. First, convert the rotational speed from revolutions per minute to radians per second. Given $n = 3380$ revolutions per minute. The angular velocity $\omega$ in radians per second is calculated as $\omega=\frac{2\pi n}{60}$.
$\omega=\frac{2\pi\times3380}{60}\text{ rad/s}\approx 354.1\text{ rad/s}$
The centripetal acceleration $a = 1600g$, and since $g = 9.8\text{ m/s}^2$, then $a=1600\times9.8\text{ m/s}^2 = 15680\text{ m/s}^2$.

Step2: Solve for the radius $r$

From $a = r\omega^{2}$, we can solve for $r$ by the formula $r=\frac{a}{\omega^{2}}$.
Substitute $a = 15680\text{ m/s}^2$ and $\omega\approx354.1\text{ rad/s}$ into the formula:
$r=\frac{15680}{(354.1)^{2}}\text{ m}\approx 0.125\text{ m} = 12.5\text{ cm}$

Answer:

The test - tubes are approximately $12.5$ cm from the rotation axis.