Question

The radius of a centrifuge bowl is 0.1 m and is rotating at 850 revolutions per minute. The centrifugal force developed in terms of gravity force (g-force) is _________ (round off to two decimal places). Given: Acceleration of gravity (g) = 9.81 m/s$^2$ and $\pi = 3.14$

Hint:

Centrifugal force can be calculated as \( F_c = m \omega^2 r \), and to express it in terms of g-force, divide by the gravitational force \( mg \).

Answer 1

Correct Answer: 79.5

First, convert the rotational speed from revolutions per minute (RPM) to radians per second: \[ \omega = \text{RPM} \times \frac{2\pi}{60} \] \[ \omega = 850 \times \frac{2 \times 3.14}{60} = 89.04 \ \text{radians/second} \] Now, calculate the centrifugal force: \[ F_c = m \cdot \omega^2 \cdot r \] Where: - \( m = 1 \) kg (since we are comparing to gravity force) - \( \omega = 89.04\ \text{radians/s} \) - \( r = 0.1 \ \text{m} \) \[ F_c = 1 \times (89.04)^2 \times 0.1 = 1 \times 7923.39 \times 0.1 = 792.34~\text{N} \] To express this in terms of g-force: \[ \text{g-force} = \frac{F_c}{m \cdot g} = \frac{792.34}{9.81} = 80.8~\text{g-force} \] Thus, the centrifugal force in terms of g-force is: \[ \boxed{81.0~\text{g-force}} \]