A syphon is used to transfer water from a 8 m deep open tank filled with water using a hose of diameter 5 cm, that has one end placed in the tank at 5 m below the water surface in the tank. The hose exits the top of the tank to a height of 4 m above the water level then drops vertically downward so that its exit to the atmosphere is 1 m below the inlet to the hose in the tank. Determine the exit velocity (m/s) of the water from the syphon.

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)