Two red blood cells each have a mass of 9.05 × 10-14 kg and carry a negative cha

Question

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 clumping together. One cell carries -2.70 pC and the other -3.10 pC, and each cell can be modeled as a sphere 3.75 × 10-6 m in radius. If the red blood cells start 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? Assume that there is no viscous drag from any of the surrounding liquid. What is the maximum acceleration of the cells as they move toward each other and just barely touch?

Explanation / Answer

electric PE at infinite = 0

KE =2 m v^2 /2

when they comes in contact. KE= 0

EPE = (kq1q2)/(d) = (9x 10^9 x 2.70 x 10^-12 x 3.10 x 10^-12 ) / (2 x 3.75 x 10^-6)

EPE = 1.0044 x 10^-8 J

using energy conservation,

0 + mv^2 = 1.0044 x 10^-8 + 0

(9.05 x 10^-14 x v^2 ) = 1.0044 x 10^-8

v = 333.14 m/s ,..........Ans

Force at final position,

F = kq1q2/d^2 = (9x 10^9 x 2.70 x 10^-12 x 3.10 x 10^-12 ) / (2 x 3.75 x 10^-6)^2

F = 1.3392 x 10^-3 N

a = F/ m = 1.48 x 10^10 m/s^2

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