Monday, October 7, 2013

Fruit vectors: checking for understanding in the mechanics classroom

Here's a small idea I had while teaching mechanics that turned out to have very surprising and fruitful results in my classroom.

So our class has been working on mechanics for a few weeks now, we think we know the basics from a physical and a mathematical view. It's time to look at something harder now: circular motion.  But just before we do that, let's check we really understand.

Can you draw vectors, any sort you like, and tell a story about what is happening here?

.. and this one ....

How about this one?

It was surprising just how much discussion resulted from just these three diagrams, by asking students to draw velocity vectors, acceleration vectors and force vectors - and then tell a narrative in mathematical and in physical terms. Many misconceptions dealt with!

And now for the reward, setting things up for circular motion. What are the acceleration vectors (and hence the force vectors) for this picture?

By the time you have finished working out the vectors it's very clear what is required to move in a circle, even at a constant speed. What I love about this activity is that the students have developed an intuitive mathematical sense for what the result should be even before we start doing the detailed analysis to get the acceleration and force equations.

Resource: Here's a version of the diagrams I gave to students to scribble on:

or get this from Google drive: Thinking about motion (free download)