Answer to Question #246141 in Molecular Physics | Thermodynamics for Kelani

Question

A sample of blood is placed in a centrifuge of radius 16.0 cm. The mass of a red blood cell is 3.0 ✕ 10⁻¹⁶ kg, and the magnitude of the force acting on it as it settles out of the plasma is 4.0 ✕ 10⁻¹¹ N. At how many revolutions per second should the centrifuge be operated?

__ rev/s

Answer 1

We use the relation between angular velocity, the force of the circular motion, and the acceleration to find the angular velocity $\omega$ expressed in rev/s:

$F_c=ma_c=\cfrac{mv^2}{r}=m\omega^2r \\ \text{ } \\ \omega= \cfrac{2\pi}{T}=\sqrt{\cfrac{F_c}{mr}} \\ \implies \omega=\sqrt{\cfrac{4\times10^{-11}\,N}{(3\times10^{-16}\,kg)(0.16\,m)}} \\ \therefore \omega=912.87\frac{rad}{s}(\frac{1\,rev}{2\pi \,rad})=145.288\frac{rev}{s}$

After substitution, we were able to find that the centrifuge should be operated at least with $\omega =$ 145.3 revolutions per second.

Reference:

• Sears, F. W., & Zemansky, M. W. (1973). University physics.