# Tag Archives: whiteboarding

## Forces that Change Direction in the Central Force Particle Model

My students historically struggled with the notion that some forces can change direction depending on the situation. I developed this worksheet to specifically help them recognize that forces can be up or down at the top of a vertical circle. I use this as my second discussion worksheet, after the standard first worksheet where they discuss the direction of the net force for circular motion. They have also already developed a formula for centripetal acceleration.

The day we discuss this worksheet is usually one of my favorites, as it’s designed to bring about tension in the classroom, only to be resolved at the end of the period. Like much of modeling, the magic happens in how the worksheet is used.

I start a 45 minute period by having students work for 10-15 minutes on the worksheet. This gives them time to familiarize with the situation, but, in my experience, not enough time for them to figure out the ‘punchline’. I then assign 2 groups to do part a, 2 groups to do part b, 2 groups for part c, and 1-2 groups each the rest of the parts, depending on how many groups there are. The two groups for parts a and b are particularly important; I try to either choose 2 groups that have drawn normal force opposite directions at the top of the loop, or guide one group to draw the opposite of the other.

I then have both groups for part a present simultaneously, and there is usually a raucous discussion about which board is correct. Just when the tension is highest, and unresolved, I say “ok, next board!”.

Students: “Wait, what? But….the answer….”

Me: “Trust me. We’ll get there. Next board!”

Again, with part b, I try to have groups who chose opposite directions for normal force. That way their equations are different in that one has a positive Fn and one a negative. (aside; I have them do Force Addition Diagrams, you can see examples of them for this worksheet on this post). Again, just when tension is highest as they argue which is correct, “Next board!”

They really don’t like this.

As a result, when the groups do part c, one gets a negative and one gets a positive normal force.

Me: “Which is correct?”

“……”

The resulting discussion is great. It is easiest to resolve at this point by having them make a force addition diagram that is quantitative. That way they can see that if Fg is 637 Newtons, and Fnet is 234 Newtons, both down, then Fn must be 403 Newtons up (note that the numbers now are slightly different than the boards in the link above; as I recall, the old numbers resulted in an odd coincidence that sidetracked conversations, something like centripetal acceleration being half of gravity). This becomes very clear when drawing the numbers on both FADs.

Once we have figured out that normal force must indeed be up for a-c, d and e follow fairly easily.

Usually when I do this worksheet I end up with kids fervently arguing, then feeling very satisfied at the resolution that finally comes toward the end of the period. That tension is what makes this discussion work so well.

One final note: in my AP Physics C course, I actually set this up by looking first at a qualitative situation with a banked curve, where friction could be up or down the incline. We have that discussion, then after we resolve part c of this worksheet kids recognize that they are the same type of situation, where forces can change direction depending on the speed of the object.

## Reluctant Participants and Board Meetings

As I start my 3rd year of Modeling Instruction, I’m happy to be in a place where I can start tweaking rather than making sweeping changes to my courses. My primary goal this year is to give more help and attention to students who struggle, and one of the ways I plan to do this is to pointedly seek methods for engaging them more during class. My first plan of attach on this concerns board meetings.

If you are not familiar, a “board meeting” is loosely defined as having students form a large circle so that they can observe each group’s whiteboards. I typically use this method of whiteboarding to have groups compare data from the same lab in order to induce aspects of a particular model.

Despite having 25 students in a class, I noticed last year that board meetings tended to be dominated by less than 5 people. I want to try to get all the students involved; I want them all contributing and wrestling with the data. This year I’m going to have board meetings start by giving students 1-2 minutes to simply look around and make at least one observation. I want them to do this silently, individually. I think that sometimes there are students (like me) who are comfortable word-vomiting immediately about what they see, which then overwhelms students who prefer to sit back, take in info, and process before speaking. I want to give that second group time to process. After this time period, I’m going to have them turn to share their observation with the person next to them. Again, I want every single student in the room interacting about the data. After that I think I’ll have them go around the circle to share with the whole group. I thought about letting groups volunteer or cold-calling on groups, but by going around the circle I can step out and simply record their thoughts with minimal guidance and intervention.  As groups report in, I think I’ll stick with my observations/claims approach to help students organize the information reported out.

I think throughout the year I will slowly remove the scaffolds like turning to partner or going around the circle in favor of more organic approaches, but I’m thinking I’d keep the 1-2 minutes of process time. I really want to help the processors engage before the vomiters get in their way.

I know this isn’t new in general (yeah, yeah, it’s basically ‘think pair share’), but I think applying the idea specifically to a board meeting has some merit. I’ll report back with how it goes. I’ll also hopefully be posting with other possibilities for getting *all* students engaging in the various aspects of a modeling classroom.

UPDATE: I did this will all my classes and I believe it was very successful. In addition, we had finished collecting data in one class period but didn’t have time to whiteboard it, so I had them put it in their lab notebooks (sketch a graph, record the equation in words, write the slope and intercept with units and uncertainties), and then to write a couple of sentences summarizing what the results meant. When they came back the next day, I had them take 2 minutes to discuss their paragraphs with each other. I like that this both helped them think about the data first, and then also incorporated some writing, which I hope to do more. After discussing their summaries, I had them gather in a circle and do what I described above. I really believe that this process helped get more students directly involved in wrestling with the data than only doing a standard board meeting.

I want to thank Patrick Briggs, who keynoted for our all-district kickoff yesterday, for explicitly pointing out  that many students need time to think and prepare before they are willing/able to have an academic conversation.