I'm a beginning graduate student, and I have 2 years before I have to pick a specialization. I would like to know which areas of physics call for the most intuition or physical insight. If this sounds like too vague a question, let me give an example.
See the problem below: "A rubber band with initial length L has one end tied to a wall. At t = 0, the other end is pulled away from the wall at speed V (assume that the rubber band stretches uniformly). At the same time, an ant located at the end not attached to the wall begins to crawl toward the wall, with speed u relative to the band. Will the ant reach the wall? If so, how much time will it take?"
I wasn't able to solve this problem completely, but I could get good qualitative insight into the behavior of the system simply by imagining a few things happening as the rubber band was stretched. Is this possible in just about any area of physics or are there specific areas which contain problems that can be tackled using pure intuition?
I really want to be in an area which I enjoy so your answers will be much appreciated.