Erik Born, a colleague here at Woodberry, teaches our junior-level general physics course. We aim this course essentially at the New York Regents exam, with a few tweaks of topics (e.g. we teach an astronomy unit, and we don't teach electric or magnetic fields). Erik wrote to me the other night:
I was wondering if you can give me a short overview of how you approach energy concepts. I am used to starting with work, and moving from that into energy, but I'm following the order of your problem sets, which has started out with introducing KE and PE first. I was wondering if you could give me some advice about conversions between KE and PE without talking about work or total mechanical energy. Maybe you have a specific blog post on it?
Well, I do now, I suppose :-)
At the AP / Honors level, Erik knows that I introduce the definition of work, and then my own version of the work-energy theorem: WNC = (KEB – KEA) + (PEB – PEA). You can see my reasoning for why and how I use this formulation at this post.
But at the general level, I approach energy concepts very differently. I ask the class to state and write out all energy conversions IN WORDS.
For example, a ball drops to the floor -- how fast is it going? They must start by writing, in longhand, (gravitational potential energy) converts to (kinetic energy).
Or, a waterskier takes off from water level at 14 m/s, and ends up going 13 m/s at his max height. They must write: (kinetic energy) converts to (gravitational potential energy) and (kinetic energy).
If a block is moving fast and stops on a rough surface, they must write (kinetic energy) converts to (thermal energy). If you want them to call this (kinetic energy) converts to (work done by friction) that's fine, too.
We haul up a block by a rope: (Work done by the rope) is converted to (potential energy).
In each case, once they write the words, then they translate the words into an equation: KE = 1/2 mv2 , PE = mgh, spring PE = 1/2 kx2, and work = Fd. Then they solve for whatever needs solving.
Erik continues: How do you deal with positive and negative work?
In regular physics, I *don't*. If we're writing the energy conversions in words, like I described, then we don't have to worry about positive and negative work. The sign of the work comes out in the wash of the equation written from the description. Examples:
Block is moving, comes to rest on a rough surface. (kinetic energy) converts to (work done by friction). * 1/2 mv2 = (Ff)d. Yes, I know that kinetic friction does negative work, but that's not necessary in this formulation. The equation and statement in words provide both conceptual understanding AND a path to solution for any relevant value, with no negative signs involved.
* I let them know that a source of "thermal energy" is "work done by friction." The distinction isn't important at this level; however, recognizing that the relevant equation for thermal energy here is (force of friction) x distance *is* important.
Block is pulled up by a rope. (Work done by the rope) converts to (gravitational potential energy). (tension)d = mgh. Once again, it's not important that work done by the rope in this case is positive: The sign comes out in the wash.
As a comparison for a teacher (not for the students), many textbooks teach a similar approach to calorimetry: don't use positive and negative signs, write out the heat gained or lost in words. For example, write (heat lost by hot iron) = (heat to raise liquid water to 100 degrees) plus (heat necessary to convert water to steam). Then mcDTiron = mcDTwater + mlsteam.