A careless pilot leaves an empty coffee cup on top of his instrument panel as he accelerates along a horizontal runway. There is friction between the instrument panel and the coffee cup, but it is insufficient to hold the cup in place. The cup slides off the instrument panel and bangs into the pilot as he accelerates down the runway. 1)As it slides along the instrument panel toward the pilot, the work done by friction on the cup is negative. positive. zero. 2)The direction of the frictional force acting on the cup is towards the front of the plane. towards the back of the plane. undefined, since friction does no work in this case.

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)