The ultracentrifuge is an important tool for separating and analyzing proteins i

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 9.0 cm from the axis if the rotor and the ultracentrifuge spins at 6.6×104 rpm , what is the magnitude of the net force on the rotor due to the unbalanced samples?

Explanation / Answer

We know that the magnitude of net force on the rotor due to the unbalanced sample is given by

F =mw2r

Given that

The mass is 11mg greater than the opposing sample than (Deltam) =11*10-3kg

The radius (r) =9cm =0.09m

The angular velocity is (w) =6.6×104 rpm =6.6×104 *2pi/60 =6908rad/s

Then the net force is

F =mw2r =(11*10-3kg)((0.09)(6908)2 =47243.259N

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