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Advanced Mechanisms
Scissors, Salad Tongs and Tin Snips:
Uncovering Algebra in Everyday Mechanisms
The purpose of these activities is to develop some basic concepts of algebra and geometry through a study of common utensils and tools. Students begin by examining some of these devices, and trying to find their common features. Through this activity, they develop ideas about input, output, motion and force. Next, they sort some common mechanisms according to lever classes, and then do a qualitative exploration of mechanical advantage. Students then collect data showing the relationship between input and output position of a pair of salad tongs. The result is expressed by a linear function. To investigate force, as well as distance, students use spring scales to find the force exerted by the return spring of a pair of salad tongs. An investigation of angular dependence leads to a discussion of vectors. This is followed by a study of the relationship between force and distance, which provides an example of a nonlinear function, as well as an introduction to the Law of the Lever, which is a special case of Conservation of Energy. The concluding activity looks at the tin snips, as an example of a compound lever. How can the mechanical advantage be calculated for this device? The answer involves an introduction to composite functions.