You are talking to a friend who insists that the seasons are caused by a varying Earth-Sun distance over the course of a year. What other fact does your friend likely know that completely contradicts this view of how the seasons are caused? Can you think of other examples of two beliefs that many people feel are both true but which completely contradict each other? How does science view this situation?

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)