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This paper is the first of two that describe how research on student understanding of Archimedes' principle is being used to guide the development of instructional materials on this topic. Our results indicate that standard instruction on hydrostatics leaves many science and engineering majors unable to predict and explain the sinking and floating behavior of simple objects. A number of serious and persistent difficulties with the concepts and principles used to analyze such behavior are identified. Although some of these difficulties are specific to the concept of the buoyant force, many others seem to reflect lingering confusion about concepts that are widely assumed to be understood by students before the study of hydrostatics begins.
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