Question

Find the "Centrifuge effect" of the centrifuge, which spins at the angular velocity (\(\omega\)=523.6 /sec) at a maximum radius of 10 cm.

• A. 2794.6
• B. 2694.6
• C. 2594.6
• D. 2494.6

Hint:

The formula for centrifugal acceleration is $a_c = \omega^2 r$. To find the G-force, divide this by g (\(\approx\) 9.81 m/s$^2$). Always ensure your units are consistent (meters and radians/sec).

Answer 1

The Correct Option is A

Step 1: Define the "Centrifuge effect": It refers to G-force, the ratio of centrifugal acceleration (\(a_c\)) to gravitational acceleration (g).

Step 2: State the formula for centrifugal acceleration:\[ a_c = \omega^2 r \]Where \(\omega\) is angular velocity (rad/s) and r is the radius (m).

Step 3: Substitute values and convert units:\(\omega\) = 523.6 rad/s r = 10 cm = 0.1 m\[ a_c = (523.6 \text{ rad/s})^2 \times 0.1 \text{ m} = 274156.96 \text{ s}^{-2} \times 0.1 \text{ m} = 27415.7 \text{ m/s}^2 \]
Step 4: Compute the G-force using g \(\approx\) 9.81 m/s$^2$.\[ \text{G-force} = \frac{a_c}{g} = \frac{27415.7 \text{ m/s}^2}{9.81 \text{ m/s}^2} \approx 2794.67 \]This matches option (A).