Getting clever with the sliding ladder

Abstract

The familiar system involving a uniform ladder sliding against a vertical wall and a horizontal floor is considered again. The floor is taken to be smooth and the wall to be possibly rough—a situation where no matter how large the static friction coefficient between the ladder and the wall, the ladder cannot lean at rest and must slide down. Clever arguments that circumvent fully fledged mathematical analyses are presented to establish two more interesting properties: no matter how large the kinetic friction coefficient between the ladder and the wall, (a) the ladder must be speeding up at all times while sliding down, and (b) the ladder must break off the wall at some point during its slide. This work serves as an example of an intuitive rather than a mathematically detailed approach that often provides a shorter route to understanding the properties of a physical system, making it pedagogically valuable. It is also shown how the arguments presented can be easily extended to a non-uniform ladder as well.