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?

Answer 1

Answer:

$f=145.29Hz$

Explanation:

The centripetal force is given by:

$F_c=ma_c(1)$

Here m is the body's mass in which the force is acting and $a_c$ is the centripetal acceleration:

$a_c=\frac{v^2}{r}(2)$

Here v is the speed of the body and r its radius. The speed is given by:

$v=2\pi fr(3)$

Replacing (3) in (2):

$a_c=4\pi^2f^2r(4)$

Replacing (4) in (1) and solving for f:

$F_c=m4\pi^2 f^2r\\\\f=\sqrt{\frac{F_c}{4m\pi^2r}}\\f=\sqrt{\frac{4*10^{-11}N}{4(3*10^{-16}kg)\pi^2(16*10^{-2}m)}}\\f=145.29Hz$