I'm currently reading Kleppner and Kolenkow's "Introduction to Mechanics", and I'm working through the problem sets. I'm only on chapter 2, but I happen to know Lagrangian mechanics. When I get stuck on a problem I occasionally take the Lagrangian approach to find the solution, and then I try to reverse-engineer the solution using old-style force diagrams and force analysis. I'm currently looking at this problem here: Problem & Solution (PDF) The PDF shows problem from the textbook, and also Lagrangian solution that I was able to work out. However, I'm 100% baffled as to how one would obtain that solution using only force diagrams and force analysis. This is a chapter 2 problem, so the authors presumably expect you to solve it using more primitive methods, but I'm completely stuck. Could anyone perhaps shed some light on how one might approach this without Lagrangian mechanics?