One of your summer lunar space camp activities is to launch a 1210 kg1210 kg rocket from the surface of the moon. you are a serious space camper and you launch a serious rocket: it reaches an altitude of 203 km203 km . what gain in gravitational potential energy does the launch accomplish? the mass and radius of the moon are 7.36×1022 kg7.36×1022 kg and 1740 km1740 km , respectively.

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)