Question

base your answers to questions 7 - 12 on the information below and on your knowledge of physics.
centrifuge technology in medicine
medical centrifuges are devices that spin samples at high speeds to separate components based on density. blood samples, for example, can be separated into plasma, white blood cells, and red blood cells. understanding circular motion principles is essential for designing centrifuges that operate safely and effectively.
a medical centrifuge rotates test tubes in a horizontal circular path. a test tube holder with a combined mass of 0.150 kilograms (including the sample) travels at a constant speed of 35.0 meters per second along a circular path with a radius of 0.180 meters. diagram 1 shows a top view of the centrifuge with the test tube at position p.
diagram 1: medical centrifuge (top view)
table 1: centrifuge data

property	value
speed	35.0 m/s
radius of path	0.180 m

1. at the instant shown, the test tube is at position p and the centripetal force is directed toward the east. in which direction is the test tube’s velocity at this instant? 1

a) east
b) west
c) north
d) south
8 - 9) develop a mathematical model to calculate the magnitude of the centripetal acceleration of the test tube. show all work, including an equation and substitution with units. 2

Explanation:

Question 7

In circular motion, the velocity of an object moving in a circle is tangent to the circular path at the object's position. Centripetal force is directed toward the center of the circle. If the centripetal force is directed East (toward the center), the velocity at position P (on the circular path) must be tangent to the circle. For a top - view of circular motion, if the center is to the East of P, the tangent direction (velocity direction) at P would be North (perpendicular to the centripetal force direction, as velocity is tangent and centripetal force is radial).

Step 1: Recall the formula for centripetal acceleration

The formula for centripetal acceleration \(a_{c}\) is \(a_{c}=\frac{v^{2}}{r}\), where \(v\) is the speed of the object moving in circular motion and \(r\) is the radius of the circular path.

Step 2: Substitute the given values

We are given that \(v = 35.0\space m/s\) and \(r=0.180\space m\). Substituting these values into the formula:
\(a_{c}=\frac{(35.0\space m/s)^{2}}{0.180\space m}\)
First, calculate \((35.0\space m/s)^{2}=35.0\times35.0\space m^{2}/s^{2} = 1225\space m^{2}/s^{2}\)
Then, divide by the radius: \(a_{c}=\frac{1225\space m^{2}/s^{2}}{0.180\space m}\approx6805.56\space m/s^{2}\) (we can also keep more precise or round as needed, for example, if we calculate \(\frac{35^{2}}{0.18}=\frac{1225}{0.18}\approx6806\space m/s^{2}\))

Answer:

C) North

Question 8 - 9