EP Meeting 9/21/2011 - Useful Energy Episodes

This meeting discussed two episodes about teacher's perceptions of what it means to have useful energy.  It was pretty incredible to have all of these talented people show up to watch my episodes and share their responses. First, we looked at Jessica's Useful Energy video from E1, where she discusses Shrinking People to represent the usefulness of the energy.  I am going to write down a random assortment of people's reactions to this episode.
1. Rachel suggested Jessica's suggestion might be a secret form of being "less" energy and whether Jessica really understood it to mean not as much usefulness as opposed to not as much energy.  Lezlie/others thought that even if Jessica knew this - students might not.  Lezlie said that we have seen students interpret less energy with stature in the past already.  Here, Jessica was worried that the opposite might be true.
2. Stamatis was concerned with what "usefulness" actually means for the teachers (and for us).  We talked at length about what the ultimate reason was for the energy and perhaps that teachers might think that the order of energy use matters.  For example, if the energy appears in a certain form at the end of a process, that form might be the most useful...?  Teachers might think that the energy that doesn't "do" the thing you were setting out to do is not as useful - even if it is used in the process.
Other ideas mentioned were:
-  that's not why you were doing it - (so it must be less useful)
- the turbine moving in the coal burning example is more observable, - Lane

- things that are moving and electricity are viewed as useful - Sam

- anything that you have a use for is useful! -Rachel

3. Amy asked how much of this is an association of entropy? Lane said if you don't use thermal energy, it will disperse and "go away."  At this point we started making a list of:

What makes energy less useful?

a. Less useful by changing form - Jessica
b. less useful by spreading out
c. by using it
d. increase in energy ?
e. can't be stored
f. can't be controlled
g. becomes less available


Care should be taken not to make it sound like it is always a one way street - as in it always becomes less useful - unless we are intentionally planning to state that.

4. Both the way usefulness is talked about and Azzam's control comments bring up a human element of use.  We talked about quality vs. usefulness next.  Quality - not requiring humans - Usefulness - what is supposed to be done with it.  Sam and Stamatis brought up the idea that the teachers and ET need constraints.  Jessica thinks that you can't run the movie backwards - she needs/wants the constraint in place. Two constraints that are not there that Stamatis wants are: 1. Can't have Gs--> Ts and 2. How do we show the irreversibility of ET?


5. We watched the second episode - Derrick's talk of the quality of energy from E2, briefly before closing.  Line 40 was discussed (Derrick uses "liberate") - Lane says, 'Run free, little ball, run free!'
Line 38 Tim says the thermal is gone which is a dead end comment!
Line 51 Derrick says, "less that's available to you" and we ended with the big question,
"What is it that makes energy more or less useful?" 

Talk about a great question!  Thanks everyone for the rich discussion!

PRST-PER Paper on Substance Metaphor for Energy

Eric Brewe just published a PRST-PER paper on "Energy as a substancelike quantity that flows: Theoretical considerations and pedagogical consequences." I haven't read it yet, but it sounds like something that is particularly relevant to this project.

The Cabin in the Woods (part 2 of EPSRI Congress presentation)

The other part of my EPSRI Congress presentation was to present my thinking on an analogy that Hunter and Rachel came up with for instruction, and how it applies to different instructional knowledge.

Here's the analogy:

• Cabin in the woods = Content knowledge
• Path to cabin = Instructional method
• Wilderness skills = Scientific thinking skills
• Navigation skills = Problem-solving skills

Most physics instructors care about their students getting to the cabin (there may be supplies there that you need for the next leg of your journey). But most physics instructors also agree that just getting to the cabin is not enough; it matters how you get there and what you learn along the way. However, there are lots of different ideas about which method is best.

Here is my characterization of different teach methods' relationship to the cabin in the woods:

• Leslie’s Teaching Method (SGSI / Responsive Teaching) – Ask questions to get them started on path towards woods, let them find their own path, redirect them if they’re on a path that is clearly not going towards the cabin.
• Guided Inquiry – Guiding along a specific path
• Pure Discovery – Exploring the woods (who cares if you ever get to the cabin?)
  
• Direct Instruction – Helicopter air drop

Peter Shaffer said he found this explanation extremely helpful and comforting. He had been worried that we were just letting the teachers wander lost in the woods, and this helped him understand what we were doing and that it was not the thing he feared.

Energy Theater Force Diagrams and the Five Laws (from my EPSRI Congress Presentation)

The recent posts about energy theater diagrams have inspired me to finally post about my EPSRI congress presentation.

In E2 this year, they tried to answer the following challenge:

Give a causal or mechanistic description of energy transfers and transformations.
Why does energy transfer or transform? (Wealth analogy)
Must have something to do with forces…
What is relationship between energy & force?
(Physicist answer: W=F.d)

As an answer, they came up with the following five laws of forces and energy:

1. When forces transfer energy, they transfer kinetic energy.
2. Kinetic energy is present in all transfers and transformations (potential energy always transforms into or from kinetic energy).
   
3. (a) A force on an object in the direction of motion increases kinetic energy. (b) A force on an object opposite the direction of motion decreases kinetic energy. (c) A force on an object that is not in motion neither increases nor decreases kinetic energy. (d) Forces within objects transmit energy.
   
4. Transfers of energy are due to contact forces. Transformations of energy are due to non-contact forces.
5. Forces transfer or transform energy proportional to their magnitude.

To check these laws, they invented another kind of "Energy Theater Diagram" which they used to determine the relationship between forces and energy transfers and transformations in a particular scenario. Below are a couple frames from a movie of a hand pushing a ball under water, and a picture of a diagram on the front board picture representing the analysis of a single time step in this movie:




The idea is that you draw all the forces in the scenario, and each force must correspond to a transfer or transformation of energy, or you have to use the laws to explain why it doesn't. For example, Fbh, the force of the ball on the hand, corresponds to 2KEh -> 2KEb, or the transfer of 2 units of kinetic energy from the hand to the ball. This is a transfer of kinetic energy, consistent with laws 1 and 2, it is in the direction of motion and giving kinetic energy to the ball, consistent with law 3, it is a contact force transferring energy, consistent with law 4, and the number of energy units, 2, is determined in relationship to the number of energy units involved in other transfers and transformations by the relative magnitudes of the forces, consistent with law 5.

This was a very disciplined use of diagrams, and led to lots of questions (and answers) about the scenario that would not have come up otherwise. Leslie and I are still talking about exactly how to analyze this, but one idea would be to look at the questions it produces and how commitment to the laws and the representation leads to these questions.

Energy Theater Diagrams E1 Examples

Here are some examples of the Energy Theater Diagrams that E1 used this summer (2011).  I thought it might be interesting to look at these and compare them to your ideas. 
1. This first one is interesting because it circles the final energy form and uses arrows to show us the progression of an energy chunk.

2. This next one is really different than our version - it uses different moments in time to show the progression of the energy. Does this work for your rules?  How would the arrows work here or could they work?

3. Here is a third example of the energy involved in a light bulb.  They use arrows as well.  It might be interesting to do "our version" of energy theater diagrams for these and compare the situations.

ET for Raising and Lowering a Ball at Const. Vel. Part 2

Rachel and I have again reconstructed our ideas about raising a ball at constant velocity and also worked on lowering the ball at constant velocity. Below show our pictures of these ideas.  We have made changes we *hope* will reflect a better snapshot of what is happening.

• Kinetic Energy Issue: We took out steps 3 and 4 (not just 3 as Lane mentioned in the previous post's comments) because we agreed that the ball would then be gaining kinetic energy. We did not put in an extra K in the ball and the hand because we believe that it is evident that the ball is moving because of the gain in gravitational energy. 
• Friction btwn Ball and Air: We also felt better about our ideas surrounding the friction of the air with the ball/hand because we added in a K for the air. This K is the bulk movement of the air as it gets pushed out of the way by the ball/hand. We called this "macro" movement. As a secondary process, this "macro" movement dissipates into smaller "micro" movements, which we represented by transforming the K to a T in the air. 
• We drew new BLUE arrows to represent this change and I thought perhaps this might be related to entropy??
• Overall Effort from the Human: We erased some of the C-->T transformations in the hand during the lowering process based upon our observations that the body gets warmer when "walking up stairs" as opposed to "walking down stairs" at the same rate.  We are still unsure about this and how it relates (or if it relates) to the fact that the force exerted by the arm/body on the hand is the the same for both situations!  
• How can it be that you are exerting the same force (doing the same work) but using more energy? 

Raising the Ball at constant speed: 

 

Lowering the Ball at constant speed: 

Therapy?

Leslie Atkins relayed the following conversation she had with a student:

A student stayed after class yesterday and said to me: "you talk just like my dad does -- and he's a psychotherapist.  Have you been a therapist in the past?"
Me: "what do you mean?"
Her: "You say things like -- 'what I hear you saying is... did I get that right?" and "Can you say more, I'm not sure what you mean?" 

I think it's a good sign.

Me too!

Energy Theater Diagrams

When I'm figuring out the energy dynamics of some system by myself, or with one other person, I can't do it with energy theater, because there aren't enough people.  I could use energy blocks, but I am usually trying to document the analysis that's being conducted, so I need something static that I can take a photo of and post to a blog.  I've settled on a representation that works pretty darned well for me, which I call an "energy theater diagram."  Benedikt and I used (developed?) this kind of diagram to analyze refrigerator energy dynamics last year (part 1, part 2).  The rules of the diagram are:

• Each object in the scenario gets a designated area of the whiteboard.
• Each unit of energy is represented by a letter.  The letter tells you the form of the energy: T for thermal, K for kinetic, etc.
• Arrows on the diagram represent transfers and/or transformations of energy.  If K in one object --> K in another object, the "-->" represents transfer, as if we were mapping the path of a walking person in energy theater.  If K-->T, that's transformation, which in energy theater is shown by a person changing handsigns, nothing to do with movement.  (In the analysis Benedikt and I did, we sometimes show both happening at once and symbolize it with a single arrow.  People often do both at once in energy theater, too.)

Abby and I are using energy theater diagrams to figure out the energy dynamics of a hand lifting and lowering a ball.  It's very challenging and we're still in the process.  As we were accounting for each of the transfers and transformations that we were indicating, we decided on a new rule for energy theater diagrams:

• The color of an arrow corresponds to the process by which energy is transferred or transformed.

For example, we used red arrows for conduction (the warm hand transfers thermal energy to the cool ball), purple arrows for forces (the hand pushes the ball), and orange arrows for metabolism (exertion warms the hand).  

We did this in order to help ourselves keep track of our own reasoning, and I loooove it for that.  I feel like it really captures a new and important kind of information that I want to include in my analysis.  (I sort of did this a little bit in the refrigerator analysis, but not systematically.)  And guess what:  because we were being accountable in a new way, we immediately found ourselves faced with new questions.  They are killer questions - we can't answer them yet!  and they were forced on us by the representation.  We'll tell you about it when we're ready to post about the ball-lowering scenario.

A different kind of diagram development was in response to our finding ourselves making multiple drafts of our diagram, not only because we changed our minds, but also just to tidy it up.  We think magnetic letters would help us organize our presentation better.  Kids' alphabet magnets would be cute, but the colors are wrong and there are not enough of the letters we will need.  We are in the process of obtaining a large supply of blank white magnetic squares, which I intend to mark up with C's and K's and T's and so on.

ET for Raising a Ball at a constant velocity

Rachel and I have been working on our idea of what the energy theater would look like for the scenario of lifting (and eventually lowering) a ball at a constant velocity. We have made the following assumptions about the scenario:
1. The ball and hand start with no G's (gravitational energy)
2. The air starts with no energy. :)
3. The hand starts with as many C's as we will need
4. The ball and hand will both wind up with the same G's (assuming same mass).
5. The ball and hand have the same K's throughout the scenario.

Here is what we came up with initially.  The arrow color indicates "the reason" behind the transfer or transformation.  The key to the colors is at the bottom of the picture.  Metabolism (orange) indicates that there is some form of bodily process going on to transform the energy. Force (purple) here indicates a contact force (push from hand or ball) or friction (between air and ball).  Conduction (red) indicates thermal energy transferring by touching (hand to ball or hand to air). Finally, gravity (green) is sort of an uncomfy one for us.  It is our only non-contact force.  More is said about this below. The circled numbers correspond with the numbers in the list.  The list is also retyped here to make sure it is readable:
1. Hand warms ball - this assumes that the hand is at a higher temperature than the ball. AND probably we should have drawn a C --> T for the first T in this part like we did for number 8.
*2. Hand "moves" "up"
3. Hand move
4. Hand moves ball
*5. Hand moves ball "up"
*6. Hand moves ball and friction warms ball
*7. Hand moves ball and friction warms air
8. Hand warms air
9. Hand warms with effort

One note here is that for a given instant, the K's would be the same for both the ball and the hand, but here we have shown all of the transfers and transformations so if you look at all of the end results you will see that the hand and ball only have one K each, one G each, and different amounts of T.

So here is where we need to think more:
A.   For numbers 2 and 5, our question became where does the earth come into this diagram?  How do we talk about a force transforming energy without the object that is causing that force in the diagram?
B.   For numbers 6 and 7, we talk about friction warming both the air and the ball as they move against each other, but how does the friction between the air and the ball make kinetic energy in the ball transfer to thermal energy in the ball?   It seems like the air should be involved in this transfer inside the ball.  Additionally, I struggle with the idea that you can't have one without the other because they happen simultaneously.

These questions seem to be related to each other. They both address an internal transformation of energy that is caused by an interaction with or force by an outside object.  E2 talked a lot about forces and their role in ET, but both Rachel and I were focusing on E1 this summer.  Is there an easy explanation to these questions? 

Confusing Energies in Quantum Theory

Virginia is taking a class on inorganic chemistry, this semester. The textbook for the course is Miessler and Tarr, "Inorganic Chemistry."



Chapter 2 is titled "The Schrödinger Equation" and provides a short review of the basic principles of quantum mechanics, especially the Schrödinger equation and it's implications for the theory and things that are interesting to chemistry. The second page of the treatment of the Schrödinger equation looks as follows:




Note what is written in the red box:

The potential energy V is a result of electrostatic attraction between the electron and the nucleus. Attractive forces, like those between a positive nucleus and a negative electron, are defined by convention to have a negative potential energy. An electron near the nucleus (small r) is strongly attracted to the nucleus and has a large negative potential energy. Electrons farther from the nucleus have potential energies that are small and negative. For an electron at infinite distance from the nucleus (r = ∞), the attraction between the nucleus and the electron is zero, and the potential energy is zero.

The notation here is rather confusing, in my opinion. First, potential energy is attributed to an attractive interaction between the electron and the nucleus. OK, I can get behind that. In the next sentence, however, "attractive forces [...] have a negative potential energy." How can a force have energy? But, as if this isn't confusing enough, in the next sentence, the electron "has a large negative potential energy." Metaphorically speaking, first the force "owns" the potential energy, then the electron does. Which one is it? And then, in the last sentence, the potential energy is again attributed to the interaction. How confusing is that???

Yes, this is not a physics textbook, but I'm sure we could find these kinds of inconsistencies in physics quantum textbooks, too. How are students supposed to understand energy, when even textbooks use inconsistent descriptions and notations?