When boiling water, a hot plate takes an average of 8 minutes [min] and 55 seconds [s] to boil 100 milliliters [mL] of water. Assume the temperature in the lab is 75 degrees Fahrenheit [°F]. The hot plate is rated to provide 283 watts [W]. If we wish to boil 100 milliliters [mL] of acetone using this same hot plate, how long do we expect the process to take? Acetone has a boiling point of 56 degrees Celsius [°C]. The specific heat capacity of water is 4.18 joules per gram degree Celsius [J/(g °C)]. Acetone has a specific gravity of 0.785 and a specific heat capacity of 2.15 joules per gram degree Celsius [J/(g °C)]. [Hint: You must determine the efficiency of the hotplate.]

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)