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Matt Greenwolfe has an outstanding bridging activity to help students move develop the balanced forces model and see a synthesis between system schemas, free body diagrams and velocity vs time graphs.

Here’s the packet that describes the activity:

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I’ve tried using this activity for a few years now. A couple of years ago, I gave each student a box with a brick, and had them work through these questions in groups of 3 or 4. The problem is, pushing a box with a brick in it along a concrete floor can lead to students to lots of misconceptions, and it was very hard for students to carry out qualitative experiments that would give them real insight.

Last year, we didn’t even give the students boxes, and simply asked them to imagine the situations. This was both better and worse—students worked more quickly since they weren’t doing any of the experimentation my students did the previous year that led them off track, they were generally developing explanations that led to more fruitful discussions in our whiteboarding session.

Still, I didn’t feel right asking students to do a 5 page whiteboarding activity that didn’t involve any real experimentation. In a move that I should have done years ago, I decided to ask Matt how he does this activity, and he wrote back this wonderful response that I have reposted below with his permission.

I have an actual cinder block – quite heavy. I place it in the cardboard box with the rubber bottom and get a strong looking boy to “give it a shove across the floor.” It never makes it across the whiteboard circle to the other side. I give them the instructions verbally and they draw their force diagrams on a whiteboard. So a lot of the misconceptions are negotiated during group work or during class discussion. We may put a motion detector on the box to resolve any questions about the motion. I request that the velocity vs. time graphs be approximated by straight-line segments – no curves. The issue comes up about whether there is still a force from the person after the shove. I’ve learned to validate the idea that **something** was transferred from person to box, but it’s not force, and usually someone can talk about energy and/or momentum so we anticipate that coming up later. Then we continue in this vein with the cardboard, then it’s placed on an actually dry-ice slab. ¼ of a 50lb dry ice block makes a nice flat slab and you can place the heavy cinder block on it and it just glides across the floor. As Mark Schober says, “It’s heavy enough that they can feel inertia.” I have all the students push the cinder block around as it rides on the dry ice in order to feel the inertia with the lack of friction, and because it’s fun and memorable.

I used to treat the dry ice as if it were the frictionless case, but that wasn’t working well. So I added a fourth case where they imagine it as completely frictionless. That works better. They can see it as the limit of the sequence we’ve been going through.

Friction misconceptions come up, and it’s very instructive for them to see that the block is just as heavy, but now glides easily. As they try to explain things, they will even propose a velocity-dependent model of friction. I try to validate that as well, talking about how some friction – air or water (fluids) – acts like that, but not surface friction. The idea that the box is difficult to move because it is heavy also brings up directionality of forces and what it takes for a force to be balanced. I do some demos with ropes or with a force table to see if we can balance forces by pulling in a perpendicular direction.

So yes, if you just gave students a box to push, a ton of misconceptions would come up and they could arrive at wrong conclusions. But the point of designing the activity was to **get** those misconceptions to come up so that we could have an explicit class discussion about them and do some other demonstrations to dispel them. And digging back, I wanted to design an activity to do that because I found that leaving these misconceptions unaddressed prevented students from really understanding Newton’s First Law. I don’t think giving students individually or in groups a smaller box and smaller piece of dry ice would be effective. It’s the huge size of the cinder block that really makes it work.

I continue to think there’s real value in actually going through the sequence. With the packet, though, I tend not to refer to it during class except that some students need to read the instructions after I’ve given them verbally, and absent students can work through it on their own, then stop by to discuss with me and hopefully push the cinder block around a little. Without it written up like this, they would have greater difficulty catching up.

My slab of dry ice is cut out of a 50lb block at Air Gas Dry Ice. I bet you have something like that in Wilmington. The 10lb slab costs me about \$20 and can be preserved in a cooler for a couple days and still be big enough to float the cinder block. The cinder block itself is probably close to 50lb.

One other concern I had about these particular 5 pages in the packet is that they are particularly text based, and can seem overwhelming to students at first glance. I also wanted students to see more of a connection between how the the velocity graph follows naturally from the free body diagram which follows naturally from the system schema. I did a bit of work to redesign the activity and came up with this:

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