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`

Step-by-step 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 =
`(12)/(100) = 0.12m` for radius

and 70,000 rpm =
`70,000 *[(2 \pi rad)/(1 rev)][(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`