A centrifuge is a device that rotates samples in a test tube at high rpm to sepa

Question

A centrifuge is a device that rotates samples in a test tube at high rpm to separate compounds in a sample. Some ultracentrifuges (like the one in this problem) can reach a centripetal acceleration of 2.0 million g’s.

a) If a sample under investigation is 7.0 cm from the rotational axis of this centrifuge, calculate the tangential velocity of the sample.

b) Your coworker is filling the test tubes with samples to be separated in the centrifuge, when she accidentally adds an extra 1.0 gram of the sample to the tube. When you point this out, she says it’s not a big deal since it’s only a gram. Calculate the increase in force exerted on the mechanism by your soon-to-be-fired coworker.

Explanation / Answer

Given

the acceleration of the centrifuge is a = 2*10^6*g

the sample placed at 7.0 cm from the rotational axis that is radius of r = 7*10^-2 m

a) Tangential velocity of the sample is V =?

we knwo that the centrifugal force is Fc = mv^2/r

acceleration is ma = mv^2/r ==> a = v^2/r

tangential velocity is v = sqrt(a*r)

v = sqrt(2*10^6*9.8*0.07) m/s

v = 1171.324 m/s

b)

As we know that the centrifugal force depends on mass

if one gram of sample added to the tube then increase in force is

initially the force F1 = mv^2/r

added one gram of sample force is F2 = (m+0.001)v^2/r

increased in force is F2-F1 = (v^2/r)(m+0.001-m)

F2-F1 = (v^2/r)(0.001)

= (1171.324^2/0.07)(0.001)

= 19599.998 N

so the increased force due to addition of one gram of sample to the test tube is F = 19599.998 N

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