A centrifuge is used in some fields to separate small particles into categories.

Question

A centrifuge is used in some fields to separate small particles into categories. Assume you have a centrifuge which turns at 64.5 entire revolutions every second. Consider three points in the centrifuge at r A = 0 cm, r B = 4.00cm, r C = 9.00cm (a) For each, determine the speed of a particle at that radius. (b) For each radius, determine the force, radially inward, that must be exerted on a particle by all the particles which are farther toward the edge of the centrifuge. (c) Explain why this may lead to a separation of particles of different masses

Explanation / Answer

Here ,

angular speed , w = 65.4 rev/s

w = 64.5 * 2pi rad/s = 405.2 rad/s

a) for the speed of particles

for r = 0 cm

vA = 0 * 405.2

vA = 0 rad/s

for r = 4 cm

vB = 0.04 * 405.2

vB = 16.2 m/s

for rC = 9 cm

vC = 0.09 * 405.2

vC = 36.5 m/s

b)

for each particle of mass m , the force is F

FA = m * vA^2/rA

FA = m * 0/rA = 0 N

FB = m * 16.2^2/0.04

FB = 6561* m N

Fc = 36.5^2 * m /0.09

FC = 14802.8 * m N

c)

as the force on the particle is dependent on the mass of particle ,

the particles will get seperated by the mass of particles .

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