A centrifuge rotates at 100 rev/s (i.e. ,628 rad/s).If the test tube places the suspension at 8.00 cm from the axis of rotation,by what factor are the terminal speeds of the settling particles increased as compared to sedimentation cause by gravity?
A)3.2E+3
B)3.2E+5
C)3.2E+4
D)5.0E+3
E)4.2E+3

Question

A centrifuge rotates at 100 rev/s (i.e. ,628 rad/s).If the test tube places the suspension at 8.00 cm from the axis of rotation,by what factor are the terminal speeds of the settling particles increased as compared to sedimentation cause by gravity?
A)3.2E+3
B)3.2E+5
C)3.2E+4
D)5.0E+3
E)​4.2E+3

Quizplus · Accepted Answer

The centrifugal force acting on a particle in a centrifuge is given by $F = m\omega^2r$, where $m$ is the mass of the particle, $\omega$ is the angular velocity in rad/s, and $r$ is the radius from the axis of rotation. The force due to gravity acting on the same particle is $F_g = mg$, where $g$ is the acceleration due to gravity ($9.8 m/s^2$). The factor by which the terminal speeds are increased is given by the ratio of the centrifugal force to the gravitational force, which is $\frac{m\omega^2r}{mg} = \frac{\omega^2r}{g}$.Given $\omega = 628 rad/s$ and $r = 8.00 cm = 0.08 m$, we can calculate this factor as follows:$$\frac{\omega^2r}{g} = \frac{(628)^2 \times 0.08}{9.8} \approx 3.2 \times 10^3$$Therefore, the terminal speeds of the settling particles are increased by a factor of approximately 3200 compared to sedimentation caused by gravity.

A Centrifuge Rotates at 100 Rev/s (I