Lesson 10 of 11
Objective: Students will examine one-dimensional collision problems and use the principle of momentum to predict outcomes of those collisions.
Today we are beginning a one-day study of momentum - our last new topic for the school year. having students using the concept of momentum - and the fact that the momentum of system is a conserved quantity - is the major idea behind the NGSS Performance Expectation HS-PS2-2. Before diving into that today, I present my students with a conservation of energey warmup problem that reminds them of our most recent work and allows us to practice yet another Performance Expectation, HS-PS2-1.
The problem is a roller coaster, of sorts. Students compute the total distance traveled by the cart based on energy considerations, then represent the "energy budget" at a specific point identified as 90% of the total distance traveled. They work alone or in small groups and I freely provide assistance to any students who seek it. About one-third of the students need a reminder that we have an equation for the total energy for objects in motion that is a sum of the potential, kinetic, and thermal energies (due to friction).
After about seven or eight minutes, I send one of my students to the board to show the bar graphs he generated for the final question. Once he is done, I give students just another minute or so to wrap up before sharing solutions to both questions.
The first part is a computation based on the total energy that can be computed at the top of the roller coaster. After elaborating on that, I show the student solution to the bar graph question. As I do, he points out an error and we quickly change the numbers on his bar graph to reflect his updated thoughts.
I share with my students that everything we've done this year can be explained as a result of carefully considering energy. Today, that streak - nearly an entire year of Physics - comes to an end as the physics of collisions will need some other understanding to be explained.
I reveal four collision scenarios and ask students to privately, quietly, sketch in their notebooks their thoughts about what will happen in each case after the collision. They take 1-2 minutes to do so, then I ask them to turn & talk with a neighbor to share their thinking.
After that, we have a conversation where students explain how they see the post-collision outcomes and I ask, after each answer is volunteered, whether others saw it the same way. Every scenario gets some support and I share with my students that there are, indeed, many very reasonable outcomes that depend upon the exact nature of the collision moment - the types of surfaces, the contact surface area, and the elasticity of each surface are all characteristics that are not evident in any of these scenarios.
After soliciting ideas about all four scenarios, I bring students to the back of the room to test their thoughts with an air track. We have masses ("gliders") that are nearly the same, a frictionless surface, and the ability to adjust the velocities of the gliders. I have students volunteer to replicate the four scenarios and we look for insights into the nature of collisions.
Near the end of this time, students start to naturally explore the idea of an infinite mass - they press down on one glider to see the impact of a moving glider when it strikes one that is immovable. They have, without prompting, recreated the Physics-famous idea of "an immovable object!"
After exploring these situations, I have students return to the front of the room for some formal notes. We need to take our observations and out intuitions and see how they stand up to the reality of momentum calculations.
Formalized Notes on Momentum
Having speculated on the physics of collisions and having explored these collisions on an air track, students are ready to see the formal rules that account for collisions. I spend the remainder of class delivering direct instruction, with students taking notes in their notebooks. For the first time all day, I introduce the concept of "momentum," which I describe as a "quantitative way to measure inertia - the tendency to keep doing whatever an object is doing."
I reveal notes about momentum one section at a time. First, I simply define momentum and note how close it is to the concept of kinetic energy. Unlike kinetic energy, however, momentum, like velocity, is a vector and has a sense of direction. Momentum, therefore, can be cancelled by a momentum with an opposing sign.
Then I reveal the idea of the conservation of momentum. I show the vector sum of "n" particles as being a constant, then show an image of three particles in two dimensions. Though the individual momenta can change over time, the total momentum ("ptot" in the diagram) must be constant, despite the individual changes.
Finally, I show how that conservation principle can be applied to the simplest collision: two objects in one dimension. To close the loop, I show how this idea can be applied to one of our scenarios: the case of the glued objects heading toward one another with the same speed. The momenta on the left-hand side of the equation (pre-collision quantities) sum to zero, implying that, when the objects stick together because of the glue, they must not be moving.
Though time runs out today, this instruction provides the background for students to practice the collision problems that are featured on the final exam and the associated preview questions. Students have about one week to prepare for the final. The time in class between now and then is used to review for the exam in a very open-ended format.