The Pulley: A Parable of Effort and Reward

摘要

The Atwood machine and various problems involving pulleys are sta(p)le diets of students when applying Newton's second law of motion. Interest in such problems can be increased and discussion enlivened by couching them in forms that have in them elements of suspense (sic!) or competition. Two didactic papers have suggested versions in this vein.1'2 Here we should like to present a discussion that contrasts models and theoretical constructs with a real-life situation. A mathematician N and a physicist P having identical masses m sit at the same height at the ends of a rope passing over a pulley, as in Fig. 1(a). They decide on a race to climb up the rope, the first one to reach the pulley wins. Which one of them will be the winner? Is it prudent to work hard, or does the indolent get there first by mere force of thought? The following qualitative discussion could be of interest when introducing the class to the Atwood machine.