a. Two red blood cells each have a mass of 9.05*10^-14 kg and carry a negative c

Question

a. Two red blood cells each have a mass of 9.05*10^-14 kg and carry a negative charge spread uniformly over their surfaces. The repulsion arising from the excess charge prevents the cells from dumping together. One celll carries -2.1 uC and the other -3.1 uC and each cell can be modeled as a sphere 3.75*10^4 m in radius. If the red blood cells store very far apart and move directly toward each other with the same speed what initial speed would each need so that they get close enough to just barely touch?

b. What is the maximum accelereation as they move towards each other and just barely touch?

Explanation / Answer

Here ,

mass , m = 9.05 * 10^-14 Kg

q1 = -2.1 uC

q2 = -3.1 uC

radius ,r = 3.75 *10^-4 m

final distance ,d = 2 * r

d = 7.5 *10^-4 m

let the initial speed is u

Using conservation of energy

2 * 0.5 * m * u^2 = k * q1 * q2/d

9.05 *10^-14 * u^2 = 9*10^9 * 2.1 *10^-6 * 3.1 *10^-6/(7.5 *10^-4)

solving for u

u = 2.938 *10^7 m/s

the initial speed of red blood cells is 2.938 *10^7 m/s

b)

let the maximum acceleraation is a

m * a = k * q1 * q2/d^2

9.05 *10^-14 * a = 9*10^9 * 2.1 *10^-6 * 3.1 *10^-6/(7.5 *10^-4)^2

solving for a

a = 1.15 *10^18 m/s^2

the maximum acceleration is 1.15 *10^18 m/s^2

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