One of my favorite mechanics labs is the classic PSSC lab that uses falling coffee filters to characterize the drag force. I decided to use this as a challenge problem to wrap up the BFPM unit with my honors classes.

The first thing my students did was figure out that the filters were falling at constant velocity using the motion detector. Once they do this, they quickly draw the following free body diagram.

FBD for falling filter. The drag and gravitational forces are equal

Then the students realize you can add a filter to the coffee filter, and suddenly take raft of data before the can really realize what they’re doing. In no time, they have a graph like this

A plot of drag force vs. velocity

As you can see, they’re still in the “graph first, ask questions later” mode, but a few questions reveal they’re really starting to think deeply about physics.

Me: What does the horizontal intercept of this graph tell you.
S: if the filter had that velocty, the drag force would be 0.
Me: and the vertical intercept?
S: That if the speed were zero, somehow the air would exert a force opposite the direction it normally does.
Me: do either of these things make sense?
S: no.
Me: So what if you graph the drag force vs the square of the velocity?
S: Why would you do that? .
Me: try it and see

And so they quickly find this:

A graph of drag force vs the square of the velocity. This shows that the drag force is proportional to the square of the velocity.

S: Hey, this tells us that the drag force and velocity squared are directly related.

Of course, at this point, kids really don’t have any idea what they’ve just discovered. So we dig deeper.In order to get kids to do more proportional reasoning, I ask “hey, when you double the number of filters, doubling the drag force, what happens to the speed?” They see the speed isn’t double, it’s only a small amount larger. “Why?” I ask. Soon, they realize that it must have something to with the relationship they just discovered that the drag force and velocity aren’t directly related, the drag force and the square of the velocity are directly related.

But the big confusion comes when you ask the kids to tell you what the drag force depends on. Inevitably, they say “speed and mass.”

“Yes,” they say ” when you add mass, the weight increases and we see that the drag force is bigger.”

“So if I’m I’m driving down the highway at 55 mi/h and I pick up a passenger, the drag force of the air on my car will increase?” I ask.

“Well, no. But in our experiment, as we added mass, the drag force got bigger.”

About 5 why’s later, the kids turn back to their FBD, and realize that the reason drag force and and weight are equal is only because the filter is traveling at constant velocity, and as the filters get heavier, it takes longer for them to reach a higher terminal velocity. These are the small things I would have probably glossed over a few years ago that really show deep understanding, and end up being the focus of many of our group discussions. It’s awesome to see kids figuring this out together, and then working to make sure every student gets it.

October 10, 2010 1:20 pm

Concerning the confusion about the relationship they’ve just found (“drag force depends on velocity and mass”), I’ve seen the same thing this year with my students’ interpretation of spring force. Several days after we’ve done the lab to find that F_{spring} is proportional to stretch, I ask again what we learned about springs. Some kids say “that spring force is proportional to mass” or (even worse) “spring force is always the same magnitude as the gravitational force.” That is, they are having trouble separating out the specifics of the lab from what they deduced from the lab. I think this might be due to a poor timing issue, where we had a rushed post lab on the spring force experiment, followed by a confusing class discussion on our next meeting two days later. Maybe, maybe not, but as we spend more time this year explicitly talking about the relationships we’ve found, I notice that many students (who, in the past, would have just kept quiet) are having a very tough time realizing/remembering what relationships we’re looking for. It apparently doesn’t occur to them to jog their memories by looking at the graph they made!

2. October 10, 2010 2:52 pm

Mark,
I’ve seen similar responses from my kids. I think there are two problems:

They don’t recognize that we sometimes measure forces by producing a situation where the forces on an object are balanced using a known force, and then the unknown is equal to the known force. This reminds me a bit of the old work we used to do with Physics by Inquiry. Maybe it makes sense to pull out the balances, get the kids to figure out what it means to be balanced, and then see how this could be a great tool for measuring unknown things. Then we could extend this analogy back to BFPM.
I don’t think my kids are doing enough to take away big ideas from discussions. Although they really make some great insights, I’m not quite sure they know what to do once the insights are made. I’ve tried asking “so what are the big ideas we’ve learned?” at the end of disucssion, photographing whiteboard, and I’m trying to find a natural way for kids to feel comfortable taking notes in discussion, but I haven’t hit upon anything yet. Let me know if you find something.