AP Physics C: As a wrap-up for our energy unit, I challenged my students to predict where a ball would land after rolling off a propped-up table. I knew, however, that they would all overestimate the landing spot because they wouldn’t take into account rotational kinetic energy. And why would they — we haven’t talked about it yet! However, the failure of their current model motivates the development of a new one which includes rotational energy. Later, we roll different shaped objects down the hallway ramp and notice something interesting:
Several students didn’t believe the energy skate park simulation that, without friction, the skater always returns to the same height even if the U shaped track is asymmetric (has a different steepness on each side). So I set up an impromptu real life version using 2 dynamics tracks of different lengths. Kids were impressed.
Started pie charts today. Used these toys to develop progression from identifying energy stored by object to the need for naming the different flavors of energy.
1. Hoverpuck and launcher: Energy stored in rubber band –> energy stored in puck.
2. Pull back bunny car: Energy stored in car –> energy stored in car (uh oh)
Need for flavors. Introduce elastic and kinetic. Redo #1 and #2 in terms of elastic and kinetic.
Elastic energy stored in rubberband –> kinetic energy stored in puck.
Elastic energy stored in car –> kinetic energy stored in car.
3. Pop-up toys (popper, spring jumper, ice cream shooter): elastic energy stored in toy–> kinetic energy stored in toy –> ???
Need for gravitational energy. Contrast with using these toys in space (elastic to kinetic only). Kinetic energy decreases bc of earth's gravitational pull.
Elastic energy stored in toy –> kinetic energy stored in toy –> gravitational energy stored in toy (toy-earth interaction)
4. Hoverpuck (off, slides with friction) and launcher: Elastic in rubber band to kinetic in puck to ???
Introduce thermal energy… Video of infrared camera showing bike stopping on concrete. Demo showing diffusion of dye in cold vs hot water. PhET friction applet. Thermal energy = microscopic kinetic energy.
Elastic energy stored in puck –> kinetic energy stored in puck –> (delta) thermal stored in puck and table.
After yesterday's experiments, I decided we should have decided upon a standard unit for energy. In this case, a standard rubberband pulled back some distance stores 1 unit of energy. Need to test how much energy a cart has? Send it into a rubber and see how far it stretches.
I know this isn't perfect, but we aren't developing quantitative relationships now. Just trying to get at the factors which affect the amount of energy in moving carts and stretched rubberbands.
(A puck launcher is pictured here because I forgot to take a picture of my actual set up: two large colored rubberbands from Staples are looped together and stretched across the width of the lab table, secured with c-clamps. A puck launcher would make a nice portable energy measurer. )
Looks like we’ve got some work to do regarding: (1) Controlled experiments; (2) Conservation of energy ; (3) Writing scientific explanations in “claim-evidence-reasoning” format.
College-prep students using carts and rubber bands to design their own qualitative energy experiments. The focus is "What factors determine the amount of energy stored in a moving cart? In a stretched rubber band?" In pre-lab, we brainstormed possible factors, then I assigned each group one cart factor and one rubber band factor to investigate (with some overlap among groups for consensus purposes).
I forgot how painful it can be watching students design their own experiments. I might even have them do it over again, but with more guidance from me.
(But that's OK, because now they'll be ready for the guidance, having experimented on their own first. Right? I'm thinking about Schwartz's "A Time for Telling.")
Today in college-prep physics we wrapped up our discussion of energy with Richard Feynman’s lecture on the conservation of energy. Before doing so, I gave some background about Feynman, including the intersection of art and physics in Edward Tufte’s new exhibition “All Possible Photons: The Conceptual and Cognitive Art of Feynman Diagrams.”
I also mentioned the irony of Feynman’s brilliant lectures and his perception of their failure. From the Preface of Six Easy Pieces (and also the Preface of The Feynman Lectures of Physics):
I don’t think I did very well by the students. When I look at the way the majority of the students handled the problems on the examinations, I think that the system is a failure.
I think, however, that there isn’t any solution to this problem of education other than to realize that the best teaching can be done only when there is a direct individual relationship between a student and a good teacher—a situation in which the student discusses the ideas, thinks about the things, and talks about the things. It’s impossible to learn very much by simply sitting in a lecture, or even by simply doing problems that are assigned. But in our modem times we have so many students to teach that we have to try to ???nd some substitute for the ideal. Perhaps my lectures can make some contribution. Perhaps in some small place where there are individual teachers and students, they may get some inspiration or some ideas from the lectures. Perhaps they will have fun thinking them through—or going on to develop some of the ideas further.
RICHARD P. FEYNMAN
We listened to an audio recording of Feynman’s toy block analogy for the conservation of energy.
I also provided students with a text copy of the lecture and some follow -up questions: 03_U5_ws1_Feynman_Lecture
(NOTE: While researching links for Feynman and Tufte, I came across an article on The Feynman-Tufte Principle … A visual display of data should be simple enough to fit on the side of a van. An nice, short read.)
“On a group whiteboard, draw an Energy vs. Time graph for the cart
hitting the rubberband. Include:
(1) A graph for Ecart
(2) A graph for Erubberband
(3) A graph for Ecart + Erubberband
End your graph when the cart is moving full speed in the opposite direction.” Again, we haven’t talked about what energy means or the different
“flavors” of energy. I just wanted to see what notions the kids had
about this system. There was some interesting discussion as to whether
the rubber band started with some energy before the cart even hit it. Other things:
** By including the push in the graph, we can talk about open/closed
systems and when energy is conserved.
** I like begining with focusing on where the energy is (in terms of
the objects) rather than the flavors of energy (kinetic, elastic,
etc). Kinda reminds me about whether we label forces like Fg or
Fearth. I think starting with objects lends some concreteness to it.
"On a group whiteboard, please answer these questions:
(1) What do you observe?
(2) What do you think might be happening?"
In one class, every group said energy transfers from one pendulum to the other and back again. In my other class, each group said something different: force caused motion to transfer, energy transferred, vibration transferred, forces interacted, something about weight, and something about inertia?? (pendulum on left was at rest until right pendulum acted on it).
In the first class, I asked them to make an energy pie chart…and no sooner had I said "pie" when a student immediately said "Wouldn't a line graph be better since it's changing over time?" So I ran with it, and skipped pies in the second class and went steady to the line graph.
I asked for two lines on the graph, one for each pendulum. Later, I asked them to add a line that represented the sum of the energies.
Pictured is one group's work.
(Note: We haven't defined energy in class yet. I just wanted to see where they are new and what they would draw. One student realized we didn't have a way to measure energy yet, so we were arguing over something we couldn't verify…