Question

Two red blood cells each have a mass of 3.55×10−14 kg and carry a negative charge spread uniformly over their surfaces. The repulsion arising from the excess charge prevents the cells from clumping together. Once cell carries −2.60 pC of charge and the other −2.90 pC, and each cell can be modeled as a sphere 7.20 μm

in diameter.

What minimum relative speed ?

would the red blood cells need when very far away from each other to get close enough to just touch? Ignore viscous drag from the surrounding liquid.

?=

What is the magnitude of the maximum acceleration ?max

of each cell?

?max=

Answer 1

by applying conservation of energy at two different locations. One at infinite separation and the other at an instant when the two blood cells touch each other.

At infinite separation, the blood cell has kinetic energy but there is no electrostatic potential energy and when they touch each other, the two blood cells have electrostatic potential energy but not kinetic energy.

; where d is separation between the centres of two blood cells

; => u = 1.63 x 107 m/s

The minimum relative speed of the blood cell is v = 2 u = 3.26 x 107 m/s.

The blood cell will have maximum acceleration when they just touch each other.

The maximum acceleration of the blood cell is

The maximum acceleration of each cell is amax = 368.74 x 1020 m/s2 .