Given the preceding result and the formula we derived in class for the heat produced during a completely inelastic collision (.e. such that the colliding objects end up sticking together), what should be the minimum value of the relative velocity of two snowballs, weighing at 1/2 lb each, so that they both melt as a result of a head-on collision? for simplicity, assume the snowballs are at zero degrees celsius. give answer in m/sec. (this problem will make you appreciate how much energy is stored at the molecular level, relative to the kinetic energy at macroscopic scales. the amount of energy stored in chemical bonds is even greater, which explains why we burn fuel to move heavy things around.)

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)