Motion & Energy - Day 2
Lesson 9 of 11
Objective: Students will extend their understanding of the conservation of energy as it applies to objects in motion subjected to frictional forces.
After a week-long delay, we return today to the study of energy conservation as it relates to objects in motion. I continue the year-long emphasis on energy conservation, connecting it to objects subjected to frictional forces. The trade-off between kinetic, potential, and thermal energies is another example of energy being transformed and conserved (the critical idea behind NGSS Performance Expectation HS-PS3-1). While that is today's major emphasis, we begin with a warmup problem that helps to solidify our understanding of forces on an inclined plane, our topic of this past week.
Our process for inducing the normal and parallel forces was a bit compromised (problems with the software, state-wide testing interruptions, and a personal absence all contributed to a difficult process). Given that, I begin the day by sharing a simple diagram that summarizes the way that weight is distributed on a ramp. Most students did, eventually, get to this point in last week's exploration but, given the confusion along the way, I thought it would be best to confirm the final outcomes. We spend just a few minutes reviewing these ideas, then I show the warmup, clarify that the cartoon figures on the ramps are assumed to be pushing on the blocks, and students begin their analysis.
Students can work individually or in small groups as they record their thoughts in their notebooks. I wander from student to student to provide insight, redirection, and general feedback about progress. After a few minutes, I locate a pair of students who have come up with solutions to the second warmup problem and I ask them to put their work on the board for others to see.
I then begin to show solutions at the board, starting with the student solutions and working my way backwards to the first problem. I note, in particular, the choice made by the student in scenario C: she identifies the frictional force (Ff) as the positive direction. While there is nothing inherently wrong with this choice, I alert students to the inevitable result: if the person is successful pushing the mass up the ramp, the resulting acceleration becomes negative.
I wrap up by showing the solution to the first problem. I delay inserting any numerical information until very late in the problem. This allows us to notice that the mass will drop out of the analysis which provides me with an opportunity to share Galileo's insight: acceleration due to gravity is independent of mass!
Today's new content begins with me sharing an image of a ball rolling down a curved ramp onto a straightaway. The goal is to enhance student thoughts about the conservation of energy by including the impact of friction on objects in motion. Up to this moment, we had idealized the exchange of potential and kinetic energies by ignoring the influence of frictional forces.
Students write down in their notebook their response to a prompt: Are there places where one could, in principle, calculate any of the forms of energy we are familiar with? Can you identify five of those locations and/or energies if we assume a frictionless surface? In addition, I ask students to consider which of those calculable energies would be modified if were were to include the effects of friction. After two minutes of thinking and writing, I ask my students to take 45 seconds to check in with their neighbors before I collect responses at the board.
Students are aware, naturally, that friction causes objects to slow down. In addition, I refer back to our work in the first semester - thinking of work as the area under a force versus distance graph - and so students are quite ready to see how we need to enhance our conservation of energy statement about objects in motion.
Having introduced the work done by friction (Wf), I give students a formative assessment problem to check for understanding. They take two or three minutes to wrestle with this problem, after which I solicit student thoughts at the board before moving on to some guided practice.
As a way to formatively assess my students' understanding of the influence of friction, I provide a set of problems for them to practice. Like the warmup problem, students work on these problems either individually or in small groups. I move from student to student to provide targeted feedback.
While there are only three problems, each has multiple parts either explicitly stated or implied in a complicated problem. Regardless of the complexity of any given problem, the common theme is the idea that the energy of any object in motion is distributed between its potential energy, its kinetic energy, and the thermal energy ("work done") lost to the surroundings as a result of frictional forces. Furthermore, though the potential and kinetic energies of the object can increase OR decrease, the thermal energy can ONLY increase. The exercise is very algebraic in nature. Students record their answers in their notebooks and work until the end of the period.