Today students created their own Posterous websites to publish the drafts of their capstone projects. As their first “Hello World” post, I asked them to write a short analysis of the video above. Thanks to Fran Poodry and Tim Couillard for tweeting about the video (which I had forgotten about). And be sure to check out the rest of the videos from Derek (@Veritasium). Awesome stuff!
We opened with this demo today in AP. There are pink erasers placed on a meterstick every 5 cm. We used the high speed camera to film the drop and watched the video, asked some questions, and discussed what we observed.
“Why do some erasers stay on the meterstick and others don’t?” they asked.
“The erasers that don’t stay on the meterstick all fall together and are lined up horizontally,” they noted.
One student explained why: “The end of the meterstick must accelerating faster than gravity because it falls out from under the erasers. The ‘bend’ in the falling erasers happens at the point where the meterstick is accelerating at 9.8 m/s/s.”
Playing the video back frame-by-frame, we deduced the eraser at 60 cm stays on the meterstick, the one at 65 cm kind of stays on, and the one at 70 cm definately did not stay. Next we determined theoretically where the “bend” should be: 66.7 cm (or 2/3 m).
I have found that by doing demos (concrete) FIRST, followed by the theoretical derivations (abstract), the students see a purpose to the derivation and have some initial footing about the phenomena at hand.
BTW, in College Prep today, we did the colliding carts for visualizing Newton’s Third Law. I already wrote about that here: Newton’s 3rd Law (or How to Make Effective Use of Video for Instruction).
So this didn’t actually happen today, but too good not to share. AP students are solving the “rolling ball down a ramp, off the table, and into a can on the floor” real life problem. I told them if they correctly predicted where to place the can, they’d get mastery on the appropriate standards.
Notice the two factions in the photo: the group on the left is using a kinematics/dynamics approach, while the group on the right is using an energy approach.
So who won? Neither group. We hadn’t discussed rolling yet, so they treated the ball like an object sliding down a ramp. Their predictions were too far out.
“But why didn’t it work?” they asked.
“You knew we weren’t going to get the ball in, didn’t you?” they asked.
Yep. But now they all wanted to know how to factor rotation into the analysis.
Sometimes failure can be a great motivator.
String, clamps, and spring scales. But I do use PASCO’s force table paper for easy angle measurement.
But today was to much me, not enough students. I should have made them draw the vector addition diagram for the situation to scale to see if it is closed as predicted. Then I should have asked them to try to “break” the model by trying new setups. (Changing angles, forces, number of forces, etc.)
What actually happened: I lead them through the situation using an unscaled vector addition diagram I drew on the blackboard. I assumed the diagram was closed and used the Law of Cosines fire two of the forces in order to predict the force of the third spring. Then I gave them a problem with a person pulling a wagon. Not a good lesson, in my opinion.
Students were asked to make their own treasure maps that had a displacement of zero. (Silly, right?)
What pattern do we see? (All the diagrams are “closed.”)
Does the order of the list of directions matter? In other words, could the same set of paces yield an open diagram? (This is where the IWB comes in handy, as seen in the movie.)
The point is to extrapolate from the treasure map exercise is to see if the pattern of “open” (net displacement) and “closed” (no net displacement) vector addition diagrams for displacements also applies to forces.
AP students had a question from their homework. I don’t have time to work out all the problems out ahead of time anymore, though. This one was a bit tricky, and I wasn’t quite sure of the path to the solution. So I modeled a think aloud. Sure enough, I made a few mistakes (students caught them), asked them a few questions when I was unsure (they answered), and went down some unknown paths (they helped me find the way).
We were successful in the end. Though I’m not sure whether everyone found it helpful. Particularly in AP, where there are lots of “tricks” for solving problems, I’m always debating how much for me to do and how much for them to do. (For example, my students didn’t know you can divide two equations to eliminate variables. They thought you always had to solve one and substitute.)
Today we wrapped up the mass-weight lab and shared results.
“What does the slope of the graph mean?”
“Why doesn’t the graph have a y-intercept?”
“What would the graph look like if we repeated the experiment on the moon?”
Which then lead to an interesting conversation about moon gravity and two capstone ideas:
1. Design/modify a sport to be played on the moon. Support your (new) rules with physics.
2. Design and build a demo that would allow a person to “feel” gravity on different planets. (One suggestion: Modify 9 soda cans so to weigh what they would on each of the planets.)