Question

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.

Answer 1

Complete Question

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Answer:

The net force is  $F_{net}= 6.44 *10^{-4} N$

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

                     $F_{net} = \Delta F_{cen}$

and the difference in centripetal force  $\Delta F_{cen}$ is mathematically represented as

               $\Delta F_{cen} = \Delta m* rw^2$

Which the difference in mass multiplied by the centripetal acceleration

  Substituting 10 mg = $10 *10^{-3}g$ for $\Delta m$ , 12 cm = $\frac{12}{100} = 0.12m$ for radius

  and  70,000 rpm = $70,000 *[\frac{2 \pi rad}{1 rev}][\frac{1 min}{60s} ] = 7326.7 rad/s$

              $F_{net} = \Delta F_{cen} = 10*10^{-3} * 0.12 * 7326.7$

                     $F_{net}= 6.44 *10^{-4} N$