Lesson 4 of 11
Objective: Students will enhance their understanding of friction and explore more complex free body diagrams.
We continue to explore variations on Newtons' Second Law of Motion (NGSS Performance Expectation HS-PS2-1). Today, we move to a more sophisticated definition of friction than the one we developed recently.
As we return from a weekend, I want to ease my students back into the mode of doing Newtonian analysis. Knowing that my warmup problem is a novel situation, my goals are to get students, based on their limited experience last week, to articulate helpful strategies for successful solutions to Newtonian problems.
To achieve this, I set up a free-write/pair-share exercise. The prompt for the free-write is straightforward: I ask students to think about the 2-3 best steps to take when beginning a Newtonian problem. I give them about one minute, then immediately give another minute for talking with a neighbor about their thoughts. At the end of that time, I collect ideas on the board, asking students to volunteer one thought at a time.
I then compare the student responses with a 3-part strategy that I want them to adopt. Their ideas are reflected perfectly in this strategy and it's nice to be able to show how their thoughts align with mine. At the end of this segment of class, I urge students to adopt this strategy as a way to confront novel situations.
To build upon the free-write activity, I provide a warmup which presents a novel situation to students. Unlike last week's work, there is no single person responsible for "applying" a force. Likewise, the familiar frictional force is replaced by something similar, but different. The point of the exercise is to apply the 3-part strategy we just learned.
Students may work individually or with others. I check in with groups of students to ensure some traction with this problem. Where necessary, I remind students to draw the Free-Body Diagram - too often students want to calculate an answer before fully considering the number and the directions of the forces. After about 7-8 minutes, I give them a two-minute warning, allowing them to wrap up their work before we consider the solutions.
When showing the solutions, I intentionally show the free-body diagrams and the Fnet equations before inserting any of the given data. I want students to understand that there is value in accomplishing these steps. Once we establish the correct diagrams and governing equations, I show solutions to both the downward and upward accelerations.
More Thoughts about Friction
Before giving some time for practicing Newtonian analysis, I want return to return to the exit ticket from previous day. The purpose of the exit ticket is to demonstrate the limited nature of our first interpretation of "u" (the coefficient of friction). We had defined it as the "percentage of an object's weight" that is turned into friction. While this is helpful in many situations, the exit ticket diagram makes it clear that friction exists even in situations where the weight is NOT directed towards a surface.
I mimic the exit ticket diagram by applying a small amount of pressure on a blackboard eraser, pinning it against the wall lightly. With my other hand I tap gently, parallel to the board, on the eraser and it slides downwards, despite my pressure towards the board. Then I lean in with all of my weight and show how that same light tap is ineffective. The wall-ward force has obviously increased the amount of friction between the eraser and the board - and it has nothing to do with the weight of the eraser or the surfaces, which have clearly not changed!
This force needs a name. I share with my students that it is referred to as the "normal" force, though "normal" in the mathematical sense of a line perpendicular to a surface. With this information, I add in the forces on the exit ticket diagram and we amend our earlier definition to the following:
Ff = u * Fn where Fn is the normal force
I also take a few minutes to describe u as a measure of the "relative stickiness" of two surfaces - low for, say, a metal on ice but high for, say, rubber on rubber.
Finally, I share two equations of motion that can be handy once one knows an acceleration. The symbols are familiar and I encourage students to think of them as part of their toolbox of analysis tools. They use all of these tools in solving the problems of the practice set in the next segment of class.
For the final 25 minutes or so of class, I have students work a set of Newtonian practice problems. Like the warmup, students may work individually or with others. I circulate and ensure that students are following our three-step strategy for success. Any conversation with a student begins with me asking the student to locate his free-body diagram. This is the kind of practice time that I normally would pair with one-question quiz, but there's only enough time for the practice to happen. I use this time, and my conversations with students, to formatively assess student understanding. Students hold onto these problems as they can be used in a later class for additional practice.