Auniform board with a mass of 20 kg and the length of 1 m rests on two supports. support 1 is 20 cm from the left end and support 2 is 60 cm from the left end. an object is placed on the right end of the board. answer the following: a) what minimum mass must the object have in order to just begin to lift the board off the first support?
b) if the mass in a) is doubled, what is the net torque about an axis directly above the second support (in the middle of the board)?

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)