Gibbons, small asian apes, move by brachiation, swinging below a handhold to move forward to the next handhold. a 8.5 kg gibbon has an arm length (hand to shoulder) of 0.60 m. we can model its motion as that of a point mass swinging at the end of a 0.60-m-long, massless rod. at the lowest point of its swing, the gibbon is moving at 3.2 m/s .
what upward force must a branch provide to support the swinging gibbon?
express your answer to two significant figures and include the appropriate units.

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)