Atwood and Poggendorff: An Insightful analogy

Abstract

Atwood's treatise, in which the Atwood machine appears, was published in 1784. About 70 years later, Poggendorff showed experimentally that the weight of an Atwood machine is reduced when it is brought to motion. In the present paper, a twofold connection between this experiment and the Atwood machine is established. Firstly, if the Poggendorff apparatus is taken as an ideal one, the equations of motion of the apparatus coincide with the equations of motion of the compound Atwood machine. Secondly, if the Poggendorff apparatus, which works as a lever, is rebalanced, the equations of this equilibrium provide us with the solution for a compound Atwood machine with the same bodies. This analogy is pedagogically useful because it illustrates a common strategy to transform a dynamic in a static situation improving students' comprehension of Newton's laws and equilibrium.