I haven’t even started thinking about this beyond just asking, so join in!
Say you have a half-atwoods setup with friction on the horizontal object. You start with a light enough hanging vertical mass such that the tension is not large enough to break static friction. Everything stays put, and so the tension is equal to the weight of the hanging mass.
Let’s say you then keep adding mass until it breaks static friction. The moment you break static friction, two things change:
- The tension in the string lessens, and
- and we switch from static to kinetic.
What are the different possibilities of things that can happen? Under what circumstances do they happen?