The Effect of Friction in Pulleys on the Tension in Cables and Strings

Abstract

Atwood's machine is used in countless introductory physics classes as an illustration of Newton's second law. Initially, the analysis is performed assuming the pulley and string are massless and the axle is frictionless. Although the mass of the pulley is often included when the problem is revisited later in the context of rotational dynamics, the mass of the string and the friction associated with the axle are less frequently discussed. Two questions then arise: 1) If we are ignoring these effects, how realistic is our model? and 2) How can we determine when or if we need to incorporate these effects in order to make our model match up with reality? These questions are connected to fundamental issues faced by physics teachers, namely the frustration students sometimes feel when they do not see how they can use the results of the problems they have been working on and how we can help our students develop effective models for physical systems.