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01 December 2019

Don't present work = force * distance right away. Start with energy bar charts.

I've been using annotated energy bar charts to good effect for many years now.  They force students to define a system and to identify what forms of energy are present in that system before they consider the end goal of a problem.  In this manner they serve the same purpose as free body diagrams for Newton's Second Law problems - I don't care what you're supposed to solve for, draw the free body or the energy bar chart first, and then you'll be able to solve or explain any aspect of the problem.  These devices make problem solving about physics understanding, steering the process away from a game of "let's plug some numbers in to some equations and do some algebra to get the desired answer."

But I'd always been hung up on the definition of "work."  See, students can come to an operational definition of potential energies (both spring and gravitational) and kinetic energies just through their equations.  It's simple for a first-year student to see that gravitational energy must be included in the bar chart when an object has a height above the lowest point.  "Because PE = mgh and h is not zero" is a good enough reasoning for now.  Similarly for kinetic energy: "The cart has KE because it's moving, so it has a v in KE = (1/2)mv2."  Work isn't so simple.

Work can't be understood simply from the equation "W = Fd."  Students must understand the idea of a force being parallel or antiparallel to a displacement.  The scalar nature of work.  The meaning of negative work.  That this equation only applies when a force is steady.  The difference between net work and work done by an individual force.

Until this year, I'd always spent part of a class defining work, and giving examples of when work done by various forces is positive, negative, or zero.  I showed how the net work on an object is the (scalar) sum of the work done by all forces; or, how net work done on an object is just force times distance, where "force" is the net force.   Then we did a couple of problems for practice.

And every year, I came up against the corollary to Rule Two of teaching.

  • Rule Two: Your students don't listen to you.  That's okay, they don't listen to me, either.  
  • Corollary: Nevertheless, students have sharp and selective recall of what you say when it provides maximum inconvenience.
I always hoped and expected that, as we moved to energy bar charts, students would adapt to using "W = Fd" as the same sort of operational definition as "PE = mgh," only with complications that we'd discussed at the outset about the meaning of work.  

Well.  My class certainly did remember W = Fd.  As an equation to be applied with brute force in any and all situations, to the exclusion of the energy bar chart.  Which stinks, 'cause the vast majority of problems which ask "how much work is done..." should be solved by finding the difference in total energy at two positions - that is, using an energy bar chart, not the equation W = Fd.

I turned the tide this year - by ELIMINATING the discussion of the definition of work.

Yeah, that's counterintuitive, isn't it... but that's how so much of teaching works.  More often than not, the less you present formally, the more and better comprehension you get.

This year, we started with energy bar charts in the simplest of situations - just with gravitational energy, kinetic energy, and work done by an external force.  Importantly, I didn't say what exactly work is.  We showed how work could be positive or negative, depending on what the bar chart requires - for example, if kinetic energy decreases with no change in gravitational energy, then negative work was done on the system in order to keep the right number of bars in the energy bar chart.  The students had access to a fact sheet which explained the direction of force and displacement for positive and negative work, but I didn't discuss or even mention this in class.

And so, every problem became an energy bar chart problem.  

Evidence, Greg?

Our trimester exam included several energy questions.  No one tried to use "W = Fd" inappropriately.

In particular, I assigned the classic problem to test this misconception.  Consider a baton: two massive objects connected by a very thin, light rod of length L.  The object of mass m is vertically above the object of mass 2m.  How much work is required to flip the baton 180 degrees so that the heavier object is on top?

Most years, the vast majority of the class uses W = Fd, getting all sorts of incorrect answers.  They make the d term equal to a part-circumference of a circle, they use all combinations of mg and 2mg and 3mg for the ill-defined "force"... ugh.

This year, no problems at all.  They made an energy bar chart.  They saw that gravitational energy went from mgL to 2mgL.  They saw that there must have been mgL of work in order to make the bar chart work.  QED.

I've never seen such success on this problem.  And all because I *didn't* teach something from the front of the room.


1 comment:

  1. I'm with you on the general complaint as to kids reaching for a formula first and not thinking about it. I've generally had success, though, mandating that kids follow a 4-step process with work: 1. Draw the F vector. 2. Draw the dx vector. 3. Draw the angle between F and dx. 4. THEN draw conclusions. And I enforce, in a very harsh way, that I will give no credit for step 4 unless steps 1 through 3 were all followed.

    I respect your method, though. Conservation laws are such a departure from what often comes before them in the physics curriculum, and one almost can't blame kids for wanting to apply a past formula (like F = ma) to the new knowledge (If W = Fd, then W = mad... I've actually seen a teacher pose this formula as, "Remember, kids: 'Work' makes me 'mad!' Get it?! Ha! Get it?" *sigh*

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