Two red blood cells each have a mass of 8.0 10-14 kg and carry a negative charge

Question

Two red blood cells each have a mass of 8.0 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 2.50 pC of charge and the other 3.10 pC, and each cell can be modeled as a sphere 7.5 m in diameter.

(a) What speed would they need when very far away from each other to get close enough to just touch? Assume that there is no viscous drag from any of the surrounding liquid. 474.34 Incorrect: Your answer is incorrect. m/s

(b) What is the maximum acceleration of the cells in part (a)?

Explanation / Answer

r = distance between the center = 2 x radius of each spehere = diameter = 7.5 um = 7.5 x 10-6 m

q1 = charge on first sphere = 2.5 x 10-12 C

q2 = charge on second sphere = 3.10 x 10-12 C

V = speed

m = mass of each = 8 x 10-14 kg

using conservation of energy

Kinetic energy of the system, = Electric Potential energy

(0.5) m V2 + (0.5) m V2 = k q1 q2 /r

m V2 = k q1 q2 /r

(8 x 10-14) V2 = (9 x 109) (2.5 x 10-12 ) (3.10 x 10-12 ) / (7.5 x 10-6 )

V = 341 m/s

b)

F = maximum electric Force between the spheres

r = distance

using the force formula

ma = F

ma = k q1 q2 /r2

(8 x 10-14) a = (9 x 109) (2.5 x 10-12 ) (3.10 x 10-12 ) / (7.5 x 10-6 )2

a = 1.55 x 1010 m/s2

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