A car is traveling to the right with a speed of 29\,\dfrac{\text m}{\text s}29 s
m

29, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction when the rider slams on the accelerator to pass another car. The car passes in 110\,\text m110m110, start text, m, end text with constant acceleration and reaches a speed of 34\,\dfrac{\text m}{\text s}34
s
m

34, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction.

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? ( be thorough on your answer)