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

$$F=ma_c=m\dfrac{v^2}{r}=m\omega^2r,$$ $$\omega=\sqrt{\dfrac{F}{mr}},$$ $$\omega=\sqrt{\dfrac{4.0\cdot10^{-11}\ N}{3.0\cdot10^{-16}\ kg\cdot0.16\ m}}=913\ \dfrac{rad}{s},$$ $$\omega=913\ \dfrac{rad}{s}\cdot\dfrac{1\ rev}{2\pi\ rad}=145\ \dfrac{rev}{s}.$$

Answer:

$\omega=145\ \dfrac{rev}{s}.$