Which equation expresses the conservation of mechanical energy in a system that involves kinetic energy, gravitational potential energy, and elastic potential energy?

Abaseball is thrown a distance of 20 meters. what is its speed if it takes 0.5 seconds to cover the distance

What is the energy of a photon of ultraviolet radiation with a frequency of 4.4 × 1015 hz? planck’s constant is 6.63 × 10–34

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)