What do to when students start begging for components…
I’ve written previously about why students shouldn’t use components until they beg. Overall, this method generates students who really understand what vectors are, and you’ll know you’re successful when students see a situation like this that asks them to find the net force,
And you hear them say something along the lines of, “I see that F1 is 4 up and 1 right, while F2 is 2 down and 3 left, and F3 is 4 to the right, so the total must be 2 up and 2 to the right.” And if you do it right, you’ll hear this a lot. Students are actively finding shortcuts, and in truth, I’m not sure they need much more to discover components completely on their own. But sometimes I can’t shake my worksheet generating habits, so I put this together, and would appreciate any feedback:
I should note that there are complications that crop up to the graphical vector addition method. Like almost everything else, it becomes easy for students to think that adding vectors just means “making polygons” (or even worse, triangles) and so they struggle when they find that some vectors when added don’t form a closed polygon. They also really need to work to understand the meaning of “head-to-tail addition”—often it just sounds like a memorized procedure to rattle off to the question “how do we add vectors?” I have gone as far as trying to talk about seeing the vector animals in the zoo, and carefully labeling their parts—the head (arrow tip) and tail, and then asking about the two ways that we can tell them apart (by size and direction–so two vectors with the same size and direction are the same).
And then this year, I came across a problem with students learning vectors I hadn’t seen before. Thanks to a few variations on the type of question I ask (“Find the sum of these forces” vs “Find the additional force that will cause the net force to be zero”) and an untimely introduction of vector subtraction, it seems my students are having more difficulty with fully understanding vector addition. Here’s one warm-up question I created to try to tease this apart.
I’d love to know if other people have encountered similar difficulties when students are trying to make meaning our of graphical vector addition.