A 5.1 kg black bear cub weighs 49.98 N. The cub is carried by its mother up into the safety of a white pine tree. How much GPE will the cub have as he rests on a sturdy branch that's 4 m above the forrest ground? How much work did the mother bear do in carrying her cub to this height?

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)