In physics education research it has been common to interpret student errors on conceptual questions in topic-specific ways, rather than in terms of general perceptual or reasoning difficulties. This paper examines two alternative accounts for responses to questions related to the concept of center of mass. In one account, difficulties are said to be perceptual in nature; in the other, difficulties are said to be tightly linked to the concepts in question. Hypotheses derived from the former perspective are tested in studies conducted among university students in introductory physics courses. The results do not provide strong support for the perceptual hypothesis; in fact, there is evidence that performance on perception tasks may be influenced by subjects' ideas about the physical scenario. While the results do not provide general support for one perspective versus the other, the paper serves as an illustration of the type of investigation needed to develop the kind of rich representation of student thinking that will allow instructional resources to be most effectively targeted.