Blocks A and B have masses M and 2M, respectively. The blocks are connected using a light string and an ideal pulley in the Atwood machine shown. When the blocks are released from rest, block B accelerates downward with acceleration a. Block B is replaced with a block that has twice the mass. The blocks are again released from rest. Which of
the following is a correct expression for the new acceleration of the blocks?

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)