Students practiced a problem today where a child goes down a slide that is 4m high. Students are asked to first calculate what the speed of the child at the bottom should be if there were no friction. Then they are given the actual speed data and asked to determine how much energy was “lost” due to friction. Everyone gets the first part right, so I want to talk about solution paths to #2

Solution Path #1:

Calculate the theoretical kinetic energy at the bottom and subtract from that the actual kinetic energy at bottom based on actual data.

Solution Path #2a:

Construct the Equation PEi + W = KEf (often based on pie charts), and solve for the work done by friction.

Solution Path #2b:

Construct the equation PE + W = KEf, and actually try to solve for the symbol f, by using W= f Δx, and often (mistakenly) plugging in 2m (which is height not distance along which friction acted). Some students go so far as to try to calculate μ, using f =  μ N.  I try to refrain from saying that these students are trying to solve for the force of friction or the coefficient of friction, because I think they are just solving for variables, not trying to determine any quantities in a physical sense.

Solution Path #3:

Calculate the Initial Energy (all PE), Calculate the Final Energy (All KE), and look at difference.

Solution Path #4:

Subtract the theoretical speed from the actual speed, and use that difference in speed to calculate a kinetic energy (essentially doing KE = 1/2 m (Δv)²

Solution Path#5:

Ignore the actual data. Calculate potential energy and then the theoretical final energy (based on speed answer to part one), and then examine the difference, actually finding a very small one due to rounding.

Solutions #1, #2a, and #3 all work. I find that Solution #1 and #3 are more thoughtful. Solution #2a can be thoughtful for some, but for many its just a routine. Solution #2b sends signal to me that student is in “algorithm of an energy problem mode”. They aren’t thinking; they are just doing. They probably also don’t understand what the difference between Work due to friction, force of friction, and coefficient of friction. Solution #4 is incorrect, but I still like it. It’s a plausible idea, and shows me they are thinking. There’s also something to build off, to learn from, etc. Solution #5 is odd. I suppose it’s good that they are trying to look at a difference, but they act of not including anything about the actual speed of the child sends a signal to me that they are also not thinking, they are just doing.

What do you all think?