A45.0 kg girl is standing on a 159 kg plank. the plank, originally at rest, is free to slide on a frozen lake, which is a flat, frictionless surface. the girl begins to walk along the plank at a constant velocity of 1.38 m/s relative to the plank.(a) what is her velocity relative to the surface of ice? 1 m/s(b) what is the velocity of the plank relative to the surface of ice? 2 m/s

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)