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. If the samples are 12 cm from the axis of the rotor and the ultracentrifuge spins at 70,000 rpm, what is the magnitude of the net force on the rotor due to the unbalanced samples?

Short answer

The magnitude of the net force on the rotor is 64.5 N.

Step-by-step solution

Given information

radius r = 12 cm = 12 x 10^-2 m

Mass : 10 mg = 10 x 10 ^-6 kg

angular speed ω = 70,000 rpm = 7330.4 rad/sec

Explanation

The net force is given by :

F = m ω²r .................................(1)

Substitute the given values in equation (1), we get

$$\begin{gathered} F=(10\times {10}^{-6}kg)\times (7330.4rad/s{)}^2\times (12\times {10}^{-2}m) \\ F=64.5N \end{gathered}$$