The ultracentrifuge is an important tool for separating and analyzing proteins. Because of the enormous centripetal accelerations, the centrifuge must be carefully balanced, with each sample matched by a sample of identical mass on the opposite side. Any difference in the masses of opposing samples creates a net force on the shaft of the rotor, potentially leading to a catastrophic failure of the apparatus. Suppose a scientist makes a slight error in sample preparation and one sample has a mass 10 mg larger than the opposing sample.

Complete Question

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The net force is  

Explanation:

Generally the net force is a force that come up due to the unequal centripetal force(A difference in centripetal force ) and it is mathematically represented  as

and the difference in centripetal force   is mathematically represented as

Which the difference in mass multiplied by the centripetal acceleration

  Substituting 10 mg = for , 12 cm = for radius

  and  70,000 rpm =

a and b sometimes have a positive value

resonant frequency