Conceptual Understanding in Introductory Physics XXXVI: Geometry and Work

This question is particularly revealing in that it assesses whether or not students understand the coordinate-free nature of work as a dot product. Be prepared to hear such nonsense locutions as “negative force” or “negative displacement” but don’t be shocked when you hear them. I think it’s a product of the relatively poor treatment vectors get in introductory courses. We can fix that.

Make a series of drawings showing different pairs of force and displacement arrows representing their respective vectors. For each force-displacement pair, ask the student whether the work done will be zero or nonzero, and if nonzero ask whether it will be positive or negative. Use as much variation as you care to use, and certainly make sure every possible outcome is represented. Vary the magnitudes as well as the directions. UNDER NO CIRCUMSTANCE SHOULD YOU DEFINE A COORDINATE SYSTEM! That defeats the purpose of the question.

Feedback welcome!


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