Give me the magic youtube video

Amy just stepped into my office to discuss a prevalent theme in the Energy 1 - Personal Energy Understanding Narratives. She is noticing that many of the teachers are mentioning a desire for specific prompts/demos/videos to catalyze student engagement with energy ideas. I think I can empathize with the teachers on this one. The level of engagement and productive discourse in our Energy workshops is consistently very impressive to me. I would like to see similar engagement in my energy course for college freshmen which begins tomorrow. Part of me is looking for just the right prompt/demo/video to spark this engagement. Unfortunately, another part of me knows that the prompt is only a small piece of instructional context which enables excellent engagement and discourse. Productive discourse depends on a wide array of subtle and elusive factors that characterize the learning community. Certainly, one of the most significant factors is the learners themselves. Teachers happen to be a group which is pre-disposed toward engagement with the learning process. College freshmen will be different, pre-college students will be different. Nevertheless, I believe we can identify a number of coherent and generalizable strategies for creating and nurturing a climate which is conducive to production scientific engagement. This is a significant goal of the teaching seminar this coming academic year.

Thermal energy of a caught baseball

I was intrigued by a question that was raised in the modeling workshop at SPU this past summer. Does FΔx for a baseball caught by a mitt give the change in kinetic energy of the baseball or the change in total energy of the baseball (including a rise in thermal energy)?

My model says that it depends on what Δx is. If Δx is the displacement of the center of mass of the ball then FΔx_cm would equal the change in kinetic energy. If Δx is the displacement of the point of application of the force on the ball then FΔx_force would give the change in total energy of the baseball. Since the ball compresses a bit Δx_cm will be slightly greater in magnitude than Δx_force. Both the change in kinetic energy of the ball and the change in the total energy of the ball would be negative but the magnitude of the change in total energy would be smaller. The difference would account for the rise in thermal energy. So maybe FΔx_cm is -100J and FΔx_force is -95J this would mean the ball lost 100J of kinetic energy and gained 5J of thermal energy is produced in the ball. The remaining 95J of thermal shows up elsewhere.

Now I want to try out this thinking on two more scenarios; (A) a rigid metal ball that is stopped by a glob of clay and (B) a glob of clay that is stopped by a rigid metal wall. Let's assume that in both scenarios the change in kinetic energy is 100J, so FΔx_cm is -100J in both scenarios.

In scenario (A) the ball is rigid so FΔx_force would be the same as FΔx_{cm , -}100J. So the rigid ball doesn't get any of the thermal energy directly. The glob of clay gets the entire 100J.

In scenario (B) the wall is rigid so FΔx_force would be zero. In this case the glob of clay get's the entire 100J of thermal energy. The rigid wall doesn't get any.

I guess the moral of my story is that whatever squashes gets the thermal energy. In the case of the baseball, the baseball doesn't squash much so it doesn't get a very big share. The mitt, arm, shoulder squash a lot and get most of the thermal energy.

Walking uphill makes us sweat - some scientists agree

I have been reading some older papers on mechanics of walking:

Cavagna GA, Margaria R. 1966. Mechanics of walking. J Appl Physiol 21: 271–278.

Cavagna GA, Saibene FP, Margaria R. 1963. External work in walking. J Appl Physiol 18:1–9.

One interesting piece of evidence that I came across was the following: Margaria (MARGARIA, R. Atti reale accad. naf. Lincei, Ser. VI. 7 : 5, 1938.) has shown that, in uphill walking (positive work), the efficiency, as expressed by the ratio of body lift to energy expenditure, tends to a maximum value of 0.25, while in downhill (negative work) walking or running it tends to 1.20.

I take this to mean that if I use 100J of chemical energy to walk uphill I could hope to gain as much as 25J of gravitation energy and generate 75J of thermal energy. On the other hand if I use 100J of chemical energy to walk downhill I would lose 120J of gravitational energy and generate 220J of thermal energy. In order to gain 100J of gravitational energy I would have to use at least 400J of chemical energy and generate 300J of thermal energy. So for the same change in height more thermal energy is generated on the way up, 300 vs. 220.

Physics work and physical work

The standard physics treatment of activities involving the human body tends to ignore the energy of the body entirely. We may recognize that the we do positive work on an object when lifting and negative work on an object when lowering it. We may even recognize that when we do negative work on the object, the object does positive work on us. In general, most physics courses shy away from seriously exploring the implications of the positive work that is done on human bodies. Such an exploration would necessitate a move away from the clean energy accounting system which physicists love into much messier work.

Physiological work is much more complicated then other types of work physicists typically teach about. Compare the work done by an elastic trampoline to the work done by a person. When a trampoline does negative work on a falling object the trampoline stores up elastic energy which can be used to launch the object back into the air. In contrast, when a person does negative work on heavy books as they take them down off a high shelf they certainly do not store up energy which can be used to raise the books back onto the shelf. In fact, both the positive work done on the books and the negative work done on the books causes the person to get tired. I would suggest that getting tired is exactly what we associate with physical work. So, in this case, doing positive physics work and doing negative physics work both require physical work. In this case, lowering the books requires less physical work because it is negative. If that last sentence seemed like a pathetic explanation, that is precisely the point. In the case of human work, teachers of physics are just not speaking the same language as manual labor.

The role of thermal energy is another source of discord between a traditional physics approach to energy and an experience based approach to human energy. In the case of the trampoline the role of thermal energy is fairly predictable. If everything were perfect, frictionless, vacuum, etc... then the object would bounce just as high off the trampoline as it fell from and no additional thermal energy would be generated. In the real world, the object doesn't bounce quite as high and the difference can be attributed to a variety of ways in which energy is tranformed into thermal energy. This simple approach simply doesn't apply in situations involving human work. If a person were a perfectly efficient book lifter they could transform chemical energy entirely into gravitational energy. If they were a perfectly efficient book lowerer, what would they be transforming the gravitational energy into. Of course not. The idea that thermal energy is generated when things aren't perfectly efficient does not apply to human work.

If embodied cognition is a significant piece of how we understand our physical world then it seems likely that the disconnect between physic work and physical work would have profound consequences for learning about the energetics of physical processes. Can we construct models for energy processes which explicitly use our embodied experience of effort and thermal energy. If so, will these models allow learners to more completely address the complexity of energy processes, both those involving the human body and those which do not.

The following is an elicitation question which is intended to explore these ideas.

Sue lives at the 15th floor of an office building. She like to get exercise by climbing the stairs to her office rather than taking the elevator. The building is air conditioned and always kept at a constant temperature of 72 F. She always walks up the stairs and down the stairs in the same amount of time. Sue notices that she consistently perspires more on the way up the stairs then she does on the way down.

What do you think is different about the energy transfers and transformations that Sue experiences on her way up and down the stairs? How can you account for the observation that she perspires more on the way up the stairs?

There is some very interesting dialogue in which people are struggling with the difference between physics work and physical effort in the comment thread following this blog post:

http://scienceblogs.com/startswithabang/2010/03/the_physics_of_an_inclined_tre.php

'Some physics isn't quite right here.

Last time I was on an inclined treadmill, my head (and attached torso) did NOT go "UP" as I hiked along. Most of me stayed at the same gravitational potential.

I did have to lift my legs more than on a flat treadmill but that, near as I can tell, was the only additional work I had to do. Not nearly as much work as climbing a hill.'

This comment blog comment inspires me to offer a second elicitation question:

Is it possible to engineer a treadmill to light a light bulb with no external energy source other than the person running on the treadmill? If so, should the treadmill be inclined, declined or horizontal?