Can someone please answer all these

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)

An athlete is holding 24 lb of weights at a height of 6 inches above the stack as shown. to lower the weights, she applies a constant force of 5 lb to the handle. determine the velocity of the weights immediately before they hit the stack.

An important dimensionless parameter concerned with very high-speed flow is the mach number, defined as v/c, where v is the speed of the object such as an airplane or projectile, and c is the speed of sound in the fluid surrounding the object. for a projectile traveling at 1170 mph through air at 50 ˚f and standard atmospheric pressure, what is the value of the mach number?