Though our focus today is returning to the concept of work, I use the warmup time to keep another topic (vector addition) active in students' minds. I want the global concept of vector addition to be reinforced today as well as the more specific application of a "net force." Though we won't be looking at Newton's Laws for quite some time, I want to plant the seed that, when multiple forces might be acting on an object, we have strategies for determining the overall impact on the object.
Students work solo or in small collaborative groups to address these warmup questions. I circulate to affirm or redirect students and to ask probing questions. After ten minutes or so, I show sample solutions (for problem 1a and for problem 2) on the board.
I previously invited students to select a demonstration in electrostatics to bring to the class. I wish to do one or two demos per day for the next few classes but, before going live with these demos, I want students to have a chance to rehearse and practice. I provide time today for students to do exactly that.
While this time provides students with an opportunity to practice, I also gain insight into the particulars of their demonstrations. If some demos are too ambitious, or too simple, I can intervene with a conversation and steer the activity towards a more appropriate scale. In addition, I solicit volunteers for the next few lessons; by the end of this section of class I know which students will be presenting in the next several lessons.
Here are some photos from the day's activity:
These students are attempting to create a bubble within a bubble, using soapy water. Their intent is to show how the outer bubble will be attracted to a charged object, while the inner one will be shielded.
This student is trying to float a small piece of plastic wrap above a charged balloon.
These students are trying to create an electrostatically-driven spinner.
While there is a sense of playfulness about this activity, there is also a real sense of engagement and the development of intuition about charges and their interactions. As charges are obviously invisibly small, I use this exercise as a way to get students to see the impact of collecting large numbers of charges on one object or another. Furthermore, though students are not exactly creating models of these interactions, NGSS Performance Expectation HS-PS3-5 suggests that students need to understand these atomic and molecular level interactions.
I introduce some new thoughts about "work." My immediate goal is to have students recall the way in which we've defined work (as an area under a Force vs. Distance graph) and to recognize the somewhat clumsy nature of that approach. I hope students will see the value in a more algebraic or computational approach.
I show the redefining work notes on the board, but reveal just a few lines at a time as I want the conversation to proceed in a certain manner. I want to use the conservation of energy as a springboard for a better way to calculate the amount of work done on an object. Once we establish that one object gains energy at the expense of another, I reveal a second page of notes that students copy into their notebooks. We are building the idea that the amount of work done on an object can be related to its change in overall energy.
Then I work through a sample problem with my students, emphasizing the connection between the concepts of "conservation of energy" and "work." My students look back in their notes for the formulas that are necessary (elastic potential energy and kinetic energy). A key concept of "idealization" comes up in the problem and it provides me the opportunity to talk about the idea of an ideal transfer of energy. I show the solution for the first three parts and we discuss the answer to the final part - though we don't have an explicit formula for friction, we can invoke the conservation of energy and confidently state that the friction from the floor has "worked" on the ball to bring it to a stop. With the completion of this problem, we can take some time to try some problems independently.
Having identified work as being related to the change in energy of an object, I present my students with a mix of energy transformation problems. Some involve springs, some involve kinetic energies, and some are related to other kinds of energies. Many of these energies are new to the students but it is my hope that they can see the big picture (energy is conserved and can be transformed from one type to another), and not get hung up on the variety of formulas that are presented.
There are only about ten minutes remaining in class, so the goal here is to try to do one problem well. We will take more time in the next class to attend to these rich and important problems. The concept of thinking about work as a resulting change in energy is essential to an upcoming goal in electrostatics - seeing the work done on charges as a change in electric potential energy.