# Day 40: The Kinematic Equations, and Tom Petty

We started the class by reviewing the graphs we obtained from the ramp lab and the meaning of the slope for each  linear graph. We also reviewed how to use the golden graph, or the velocity – time graph to solve constant acceleration problems.   I reminded them that the practice sheet they were assigned last week  was due Wednesday and they should be prepared to present the solution to each problem graphically or with the kinematic equations.

“Wait, what?  solved with the kinematic equations…. what kinematic equations?”  Now I have them ! I reminded them that they really had 2 of the three kinematic equations from the EOLS  (Equation Of the Line) for each linear graph we developed in the ramp lab.

The EOL from the v-t graph —> vf =aΔt+vi  —> Traditional Kinematic Equation #1

The EOL from the v^2 – Δx graph —> vf^2=2aΔx + vi^2 —> Traditional Kinematic Equation #2

I refer to the traditional kinematic equation #3 as the “Granddaddy” because it covers all of what we have seen so far. This one is xf=1/2aΔt^2 + viΔt + xi.   To arrive at this one, we go back to the v-t graph once again.  The one I draw has an initial positive velocity and a positive acceleration. I make use of the total area trapped to develop the ‘Grandaddy’.

There has been some debate in some circles lately about only solving problems graphically and not even helping the students develop the kinematic equations.  A large percentage of my advanced students are going to take another physics course in college, and I want them to have seen and worked with the equations they will most likely be given in a single lecture.

We then transitioned into an example of constant acceleration. Once again I went back to our ramp experiment and recreated the stack of graphs we developed.  Then I make the ramp a bit steeper and one more time making it as steep as possible:

The last ramp that is as steep as possible is a vertical ramp.  In each class, one student (thankfully) speaks up and says, “Will the car even roll down the ramp?  Won’t it just fall?”  Thank you very much…. yes, we are going to call it free fall.

SIDEBAR:

I DO NOT call this the acceleration due to gravity… We have not defined ‘gravity’ yet so why would I define an acceleration based on something we know nothing about?

To gather data, I used playing cards to put the students in groups.  Odds gathered data today while the evens worked on the practice sheet, tomorrow we switch places.  I use three freefall timers (picture to come tomorrow) and one group uses our high speed camera to do video analysis.  I hang an electromagnet from the ceiling and attach a bright yellow softball (it has a metal washer taped to it). The electromagnet is turned off and the ball drops.  To help with the data gathering, I also add a light bulb in a socket so the students can see the electromagnet going off and the ball just starting to drop.  Tomorrow I’ll include a video clip with the post.

General Physics

Today was a day that was a bit out of my comfort zone.  We talked about the curved mirror ray diagram assessment they took on Friday and we had three short curved mirror problems to WB.  That only took about 15 minutes total.  For the remaining time, the students made use of the additional study materials we posted on Schoology.  It was another set of curved mirror problems including ray diagrams, and two conceptual reviews.  The solutions were opened up later in the day. I explained to the students that they were in the best position to know exactly which objectives they still needed practice  on.. they were yellow or red on and that there was practice posted to help with each objective.  It was out of my comfort zone because I usually prefer to direct the review a bit more.  For the most part I was pleasantly surprised with how hard most of them worked, and the level of discussion that went on.  We’ll see tomorrow if this plan worked out like we hope it will.