Today WAS to be the day that we officially defined acceleration !! But we did not quite get there. We have slightly shorter classes this week due to our ninth graders going through the ACT Aspire testing. The plan was to create instantaneous velocity graphs that we could use to define acceleration, figure out what the slope of the x vs. t^2 graph is, and build the general kinematic equations. We only got the graphs created.
The way we generate the graphs is by a little Logger Pro magic. Yesterday we defined instantaneous velocity as the slope of a tangent line to a non-linear position- time graph at a instant (clock reading) and a position. The students use their EOL from the x vs. t^2 graph to have Logger Pro plot a position-time graph that has more data than they gathered, then use the tangent feature (under the Analyze menu). We skip the first and last points, but still have plenty because we generated the times and positions.
From there it is just inserting two graphs. As you all know, the velocity -time graph will be linear. Based on our set-up, half the class will have a positive slope (and hence acceleration) and the other half will have a negative slope (and acceleration). It’s aways interesting to watch some students wrestle with a negative acceleration showing the object getting faster. Truth be told, I always look forward to this.
So, tomorrow we start with the white-board-apalooza.
Yesterday we established the characteristics of images formed by planar mirrors. Today was the day we learned how to draw ray diagrams to explain (and predict) the images we see.
We stated with the easiest possible case, one object parallel to one mirror:
Here is the ray diagram we arrive at using do=di and knowing that for us to see the image, light from the image must make it into our eye:
Then we progress to the only other possibility; one object NOT parallel to one mirror:
We check both of these with our CD case ‘mirrors’. The really work well.
The individual practice is to complete a practice sheet with 3 variations of this, including to mirrors parallel to each other, and two periscopes. We’ll also look at a corner reflector and a two-way mirror. The cool thing is we actually have all this equipment so the students will predict the images and then we get to see them for real…. err I mean virtual!