Read the scenario and solve these two problems. when traveling at top speed, a roller coaster train with a mass of 12,000 kg has a velocity of 30 m/s. the kinetic energy of the train at top speed isj. given this kinetic energy, what is the tallest hill this roller coaster train can reach the top of? the train can climb a hill that ism high.

What is the length x of the side of the triangle below? (hint: use the cosine function)

What happens when chlorine reacts with bromine? a. electrons move from the chlorine atoms to the bromine atoms. b. electrons move from the bromine atoms to the chlorine atoms. c. electrons are shared between the chlorine atoms and the bromine atoms. d. electrons become delocalized among the atoms.

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)