Catastrophic cancellation in elastic collision lab experiments

Catastrophic cancellation in elastic collision lab experiments

Error analysis consumes much of the focus in introductory physics labs. Catastrophic cancellation is a spike in error that occurs when subtracting two measurements of roughly equal magnitude. Often termed loss of significance or subtractive cancellation, this effect can easily relegate experimental results to utter worthlessness no matter how precise the measurements. A lab activity that exposes the ill effects of catastrophic cancellation in experimentation was carried out by three undergraduate students at California State University, Fresno under the direction of a faculty advisor. This lab employs the traditional elastic collision experiment performed in countless labs across the country. Traditionally, lab designers try to lower experimental error as much as possible for students to confirm conservation of momentum and energy. In this lab activity, however, the calculations performed by the students was purposely modified to generate ridiculous levels of error based on nothing more than the order in which experimental values were summed. This lab therefore teaches students that measurement is not the only source of error in an experiment; that is, the order in which mathematical operations are carried out not only introduces error into calculations, but that this error can completely obscure experimental results. Applications to common problems in numerical analysis are also discussed.

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