The ultracentrifuge is an important tool for separating and analyzing proteins i
ID: 2023217 • Letter: T
Question
The ultracentrifuge is an important tool for separating and analyzing proteins in biological research. Because of the enormous centripetal accelerations that can be achieved, the apparatus must be carefully balanced so that each sample is matched by another on the opposite side of the rotor shaft. Failure to do so is a costly mistake. Any difference in mass of the opposing samples will cause a net force in the horizontal plane on the shaft of the rotor. Suppose that a scientist makes a slight error in sample preparation, and one sample has a mass 11 mg greater than the opposing sample.If the samples are 11 cm from the axis if the rotor and the ultracentrifuge spins
at 7.4×104 rpm, what is the magnitude of the net force on the rotor due to the unbalanced samples?
Explanation / Answer
The unbalanced force is due to difference in centrifugal forces. Centrifugal force F = m r 2 Where m is the mass of sample, r is radius and is angular speed. Thus the force difference F = m1 r 2 - m2 r 2 = (m1 - m2) r 2 Given mass difference m1 - m2 = 11 mg = 1.1 * 10-5 kg ( 1 mg = 10-6 kg) r = 11 cm = 0.11 m = 7.4 * 104 rpm = 7.4 * 104 * 2 / 60 = 7.745 * 103 rad/s Hence force difference F = 1.1 * 10-5 * 0.11 * 7.745 * 103 = 9.37 * 10-3 NRelated Questions
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