# Day 35: Stack-o-graphs, the sign convention for ‘v’ and ‘a’and Bridging to Curved Mirrors

The plan for today was to WB a WS that had 7 stack-o-graphs.  For the first 5 problems, the given information was a ramp and tower set-up.  Here is an example:

The students created the position, velocity, and acceleration graphs.  I call them ‘stack-o-graphs’ because I like to stack them vertically like this:

For the last two problems, the students are given the velocity-time graph and asked for the other two graphs AND the ramp setup to produce the graphs.

I use this sheet to provide practice for the kids sketching the graphs and to develop the sign convention for velocity and acceleration.  After each problem is presented, and we have answered any additional questions, we add a general statement about what is happening to the object (getting faster or getting slower) and the sign on the velocity (+ or -) and the sign on the acceleration.  It does not take very long for the students to see a pattern:  If the object gets faster, the signs on the velocity and acceleration are the same and if the object slows down they are opposite.  We then extend this to the velocity and acceleration vectors point in the same direction or opposite direction.  I still like to WB this type of practice because during the explanation, one or more students usually say something to the effect that the acceleration is negative because the object slows down (if when they it could, be slowing with a positive acceleration).

SIDEBAR:  I was tempted to play the mistake game that Kelly O’Shea has developed (explained here) but was concerned that  some of the students may not have understood the kinematic stack -o-graphs well enough to realize the mistakes… maybe that is the point though.

General Physics:

As promised, here is the set-up for the two-way mirror demo.

Last week we work with planar mirrors.  Today started our transition to curved mirrors.  I used a bridging activity similar to the one we did with curved refractive surfaces.  Here is what it looks like:

To check the predictions (once the students have discussed it in pairs), we use our Craftsman laser levels magnetically attached to the big WB, with planar mirrors.  This activity does a really nice job of building the concepts a converging mirror and diverging mirror, and showing where the focal point for each is.  Tomorrow we extend it to predicting the image characteristics with ray diagrams, then checking them with the actual mirrors.

# Day 22: Kinesthetic Experience with v-t Graphs and Aerial Images

As I explained yesterday, We just started looking at v-t graphs that we developed from x-t graphs.  We followed the same pattern we did previously and had the students creating and then matching some velocity graphs using the motion detectors.  Sometimes I wonder if having the students do this activity is worth the class time,  but then I think about (or re-read) Chapter 2 in Arons.  He talks about the importance of a direct kinesthetic experience to fully register the concept.  It always amazes me that I can have a student perfectly explain a v-t (or x-t) graph, but then not be able to walk it to match it.

General Physics:

Yesterday we the focus was sending parallel light rays into a curved refracting surface.  It allowed us to develop many ideas, but most importantly converging and diverging lenses.  Yesterday, at the end of the hour,  I set myself up for today, by asking what a converging lens would do to light rays that are not parallel.  Remember, I’m all about the transitions!

So after a short assessment on Snell’s Law, we answered that question. The flow in the class lead us to the development of how a real image forms, what the characteristics of a real image are, how to draw ray diagrams for lenses and will even set the stage for a thin lens experiment by defining the object distance and image distance. Not all of this was covered today, but I will keep referring back to this setup as we develop each idea.

We used the formation of an aerial image to build these concepts.  I first learned about aerial images at a Phox Share session about  8 or 9 years ago from Jeff Elmer and Ed Wyrembeck, both incredible physics instructors.  Here is the article published in The Science Teacher that explains the entire thing.  Go read it now, I’ll wait.  No, really,  go read it, especially if you have never heard of an aerial image.

Based on what was shared at that share session and subsequent ones, the set up has been modified.  Here is a picture:

Here is another diagramAerial Image Set-Up.   When the students see the aerial (real) image for the first time without the paper screen, it blows them away, as it should. It is totally incredible.  As you read in the article, one of the important concepts in helping students understand how this image forms is the light cone.  The aquarium gets filled with “professional Haze” then covered.  The light cones are visible. I’m sure this picture will do it justice.

You should try this.  As mentioned above this day sets the stage for quite a bit of optics to come.