This paper describes an investigation of student ability to apply the principle of momentum conservation in one dimension. As part of the investigation, we conducted interviews with students who had completed introductory calculus-based mechanics. We found that some of them attributed special significance to a certain limiting case: An (elastic) collision between a light incident object and an initially stationary massive target. They used their correct prediction of the observable outcome of such a collision to support an incorrect view of momentum. A tutorial designed to help students understand this special case improved their performance on examination questions on more general collisions. The process of developing curriculum based on students’ spontaneous, productive reasoning is illustrated.
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See also
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A list of research articles by members of our group, many of which are published in Am. J. Phys., can be found at ⟨www.phys.washington.edu/groups/peg/pubs.html⟩.
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We typically find that the results from multiple course sections that are similar with respect to tutorial instruction fall within about ±5% of the average over all sections. Therefore, we quote the average over all comparable sections rounded to the nearest 5%.
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In most sections, the problem included the momentum-transfer, incident-change-in-momentum, and final-momentum tasks in that order. In a small fraction of cases, one of the first two tasks was omitted, with no apparent effect on the performance on the remaining questions.
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In the center of mass frame, the relative speed is unchanged (from before the collision to after) in an elastic collision in order to preserve constant (zero) linear momentum and to fully restore the kinetic energy. The speeds of the bodies relative to each other are the same, regardless of whether the speeds of the bodies are viewed from the center of mass frame or the laboratory frame. If the collision is one dimensional, then the relative speeds are either a sum or difference of the laboratory frame speeds, depending on the relative direction of travel. If the initially at-rest target is more massive than the incident body, then the bodies never travel in the same direction, and so this relative speed is a sum of the laboratory frame speeds.
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).© 2010 American Association of Physics Teachers.
2010
American Association of Physics Teachers
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