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Problem 1: Two weights are connected by a pulley system at the corner of a tabletop. The lighter one sits on the table while the heavier one is suspended from the edge. The classic question: what is the acceleration of the heavier weight?

Each year, once my Physics 1 students learn about Newton and his apple, about free body diagrams, about the rate of a rate, about weight versus mass, I give them this question. They are given the whole period to figure it out.