# 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.