Adding Friction: N2L Labs That Work

I recently wrote about some Newton’s 2nd Law Labs that have actually worked for students to get solid data. One negative, however, is that they are all single force labs. I set out, as a result, to find another lab that would work for students. Caveat; I haven’t actually performed this lab with students. We are past our Unbalanced Forces unit, and I collected this data myself just to see how well it would work; astonishingly well, it turns out.

All I did was add a friction block being towed by the cart in a modified Atwood setup where the tension is measured directly (see last post for more information on that setup).

mod atwood cart setup

I’ve done a similar lab in the past, using just the friction block. The problem there is that there is a very narrow range of hanging masses that work; once it starts accelerating from a mass, a small addition of mass results in large increases in acceleration and thus difficultly in getting good measurements. This version, however, has enough system mass where hanging masses from 50-100 grams gave very nice results.

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I first pulled the cart at a constant velocity, and measured friction directly as 0.37 \pm 0.03 \ N, where I used the mean and standard deviation of the force vs. time graph for those values. The mass of the system of the cart and block was measured to be 0.554 \ kg. The N2L equation, linearized, is F_t=ma+F_f, so the slope should be the mass of the system and the intercept should equal friction. The results show below that we are well within uncertainties on those values.

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The trend is nice, the accelerations are reasonable and therefore should be relatively easy to collect, and best of all, it’s a simple extension of a lab students have already performed. I’m excited to try this with my students in the future. I may even do the first version with the block on top of the cart so that the only change in the 2nd version is the addition of friction; the system mass stays the same, thus so does the slope, but the intercept changes.

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Newton’s 2nd Law Labs that Work

Modified Atwood with Ft measured directlyIn the last few years I have finally found some N2L labs where students in a general level physics class can consistently get decent data. I have compiled those labs here for use and modification. Below are some teacher notes about these labs.

First of all, the course for which these were designed is a general level physics course taken by a high population of seniors (approximately 1/4 of the graduating class), most of whom are not going into science. Those going into science tend to take our AP offerings.

Another thing to notice is that I have students plot acceleration as the horizontal variable and force as the vertical, knowing that this violates the x: independent variable, y: dependent variable guideline. I think doing so has two benefits; it allows for the slope of the line to be easily recognized as the mass of the system, and it shows students that we can manipulate the axes if it is convenient to do so, a precursor to linearization. The guideline is in fact only a guideline.

The fan cart lab is obviously only possible with fan carts. I got lucky this year and was able to pull them together. I have the pasco carts ($250 each!), but vernier makes a cheaper version ($105 each). I can’t speak to the effectiveness of the vernier carts as I have never used them.

I am confident that the force readings for both the cart on a ramp and the fan cart labs could be done with decent spring scales rather than force probes. Modified Atwood, however, requires force probes. I like the direct measure of tension as it takes away the black box of Modified Atwood setups where masses have to be switched from the cart to the hanging mass; I am confident that my students wouldn’t understand the nuance there unless we dived deep into it, and I prefer to make the system pretty obvious (the cart by itself).

I have also done the modified Atwood lab with friction blocks with some success. It is more difficult, however, for students to consistently get good results. There is a pretty narrow range of masses that will actually accelerate the cart, but not too much so that acceleration is difficult to measure.

The last thing to note is that I set aside at least two 45 minute class periods for each lab. Generally the first day is data collection and the second is analysis and discussion (often a board meeting where students compile data on a whiteboard and then we compare their results). I try to have groups with different masses for both the fan cart and modified Atwood labs so that the relationship between slope and mass is more obvious. I like having a day between collection and analysis where students can work on something else, that way if students were gone or their data didn’t work out well they can perform the lab on that in-between day.  Any lab worth doing is worth doing again!

Let me know in the comments or on twitter if you have questions or ideas!

Google Doc of N2L labs that work

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.

 

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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.

Elevator Situations: An Introduction to Unbalanced Forces

I’ve been meaning for some time to compile some items that I’ve developed over the years, since the courses I teach don’t lend themselves to using the straight up Modeling Instruction curriculum. I develop items mostly to fill gaps I see in understanding or content, depending on need. I wanted to be able to share this work with the larger physics community.

That said, I do need to issue a disclaimer; I think it is possible, likely even, that some of the materials I hope to post came out of conversations with others, or even after seeing someone else’s materials. If I’ve inadvertently stolen anyone’s work, please let me know and I will remove it immediately. To the best of my memory, however, the materials are original.

This first item arises out of a pretty standard physics problem; analyzing an elevator that is accelerating. I wanted a worksheet, however, that emphasized the similarity between speeding up while moving upward and slowing down while moving downward; likewise, slowing down while moving upward and speeding up while moving downward. I wanted to be able to point out that the common feature in these situations is the direction of the acceleration, and thus the direction of the net force. I also wanted to re-emphasize from our work with Constant Acceleration that a negative acceleration does not necessarily mean slowing down. Finally, I wanted to give students some easier situations before we moved on to ramps and angles.

I use this worksheet with my first year physics course that is similar to AP Physics 1 (it’s concurrent enrollment through the U of MN), and it’s the first thing we do after we build the model by pulling carts with spring scales (kinda like what Kelly does but with 1N spring scales). I also started last year doing it after model building with my ‘regular’ physics class, which is oddly between a standard HS physics course and a conceptual physics course.

I took the liberty of applying a creative commons license to the work, so it may be shared and/or adapted with attribution for noncommercial purposes under CC BY-NC 4.0. This is mostly so that it couldn’t be used for commercial purposes; feel free to use and change (and tell me about it)!

Without further ado, here’s the worksheet, enjoy!

Making Homework Work for My Students

Homework seems to be a perpetually debated topic in education circles. I’ve written about homework before, (and that post contains links at the end to some great reads on the subject), and this is really the “Where are they now” post a couple of years later. After thinking through how homework can work better for students and teachers, I got the chance to implement a new policy alongside a course I started last year, AP Physics C. I’ll now be expanding it to another course for next year, a college-at-my-school course similar to AP Physics 1.

So here’s the gist; @LCCTA tweeted last year about an interesting homework policy and I modified it for my purposes. I wrote this description that I passed around twitter for feedback, then I implemented it during the 16-17 school year. In summary, the policy goes something like this;

  • student does something to try to improve learning of physics outside of class (and there’s some choice built into those somethings)
  • student documents that something
  • student submits documentation and gives themselves a homework score

My primary reason for this policy is to extend an emphasis on learning (rather than answers) from my classroom to homework, and I think that was moderately successful.

Students responded well to the policy, based on the end of year survey;

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The comments indicated the students appreciated the flexibility and choice.

All that said, there were a couple of things I’d like to improve on. First, allowing students to submit a variety of media as evidence, including videos showing the work they had done, proved too cumbersome for me. A student flipping through pages in their notebook is difficult for me to actually look at, as it turns out (who’d of thought?). The new policy will ask them all to simply submit a Google Doc template including pictures of their work (all our students have Macbooks so this is not really an equity issue for our school).

Then there were a few students who just watched videos; I’ve made it more clear in version 2.0 that problem solving must be at least part of each check.

I’ve added a table for students to actually keep track of when they work and what they do; valuable information for all of us. Along with this I added a requirement to space out the work they do; cramming for 5 hours the night it’s do is anti-the point.

Finally, I’ve made a reflection portion that’s more specific, asking students what helped them, what they still have to work on, and what questions they have.

I’ve shared a draft of the Google doc template here, which includes all of the above changes alongside some things that have stayed the same from version 1.0.

I’m still conflicted to some extent about grading. I’m fairly certain at my school there will be too many students who prioritize other graded homework over studying physics if it’s not worth a grade at all, so last year I compromised by making homework a small, 10%, category. I’m certainly open to ideas on this.

I feel like I’m getting closer to the policy I’d like to have, but would love your feedback; please comment here or chat me up on twitter (@rutherfordcasey).

 

 

Choosing to Engage

I have Franco* in a course I’m teaching for the first time this year, Foundations of Physics. FoP was designed to help students who really struggle with math and reading, identified by test scores, to earn their required Minnesota physics or chemistry credit. It’s a below grade level class filled with students who largely have been unsuccessful in school in the past, and is certainly has an overrepresentation of students of color**. Franco has to some extent been a thorn in my side. He’s boisterous, distracts other students, and won’t stay in one place. He’s also demonstrated that he’s very bright, and he has a great sense of humor.

Earlier in the year I mentioned that we were going to perform a lab over again, and Tahvo* stood up and said “Another one!” Franco was among the students laughing; clearly this was a thing. I ignored it and moved on. A few days later it happened again, then again a few days after that. Finally I asked about it. “Just Google ‘DJ Kahled'” they told me, snickering. Turns out it’s a short clip that’s fairly mild (I expected way worse) that has become a meme. So here’s the thing; I could have assumed they were laughing at me. I could have reacted. By engaging in conversation instead, we’ve now gotten to the point where ‘another one’ is a class meme. It’s helped build culture in my classroom.

Another time Franco put an ear bud in my ear; it was NWA, which I recognized (I grew up listening to NWA, Easy-E, and Dre, coming back now with Straight Outta Compton). I’m not immersed in hip-hop culture now, but I can certainly have a conversation with kids and show a bit of interest. When they put in their earbuds, I can engage with them rather than react against them.

Today after class Franco was one of the last ones out the door so I stopped him.

“Hey, what’s your plans after school?”

“I don’t know…I gotta figure that out I guess.”

“Yeah, well, you got a lot of potential. You could do something really great. You just gotta figure out what that thing is.”

“Dang, you don’t hear that from many people.”

You don’t hear that from many people. Meaning, most people have written Franco off and he knows it. He’s been unsuccessful for undoubtably a variety of reasons. But he’s still a kid, and he still deserves to be believed in. I can engage in his positives, rather than react to the negatives. I can choose to engage.


*None of the student names in this story are their real names. 

**I’m happy that our school district is working hard to correct this, both by ending below-grade level courses except for those required for students to graduate off their IEP (including this being the last year of FoP), and by implementing an Excellence in Equity team to find solutions for our students we have traditionally failed to help. 

The Seeds of Climate Change Denial (or Newton’s 3rd Law)

Today in class we were working on practice 3 from my Momentum Transfer Model (MTM) packet (which is a combination of standard modeling questions, Kelly’s questions, and a couple I wrote maybe). In first period we did problems 2 and 3, below, in a row. After problem 3 I gave students one of my standard speeches about how some students decide physics is about choosing an answer and then switching it because they know they’ll be wrong. I try to emphasize a number of times throughout the course that a good scientist isn’t one who’s initial intuition is correct; she is one who is willing to take a step back, consider the science of the situation, and then make sense of it. Anyway, in 1st period, almost every student choose that the VW experienced a greater force in 3a, despite the fact that we did quite a bit of work with Newton’s 3rd law, work I still think is pretty effective, back in November. The problem is, students haven’t made it second nature yet to start with science and end with conclusions. They start with their gut and go from there.

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During 2nd hour I inadvertently gave my speech between questions 2 and 3. Every kid said that the forces were equal in 3a. Every kid.

This helped me to realize that even when students understand a concept at some point, they still tend to revert back to gut-first thinking over time. In this case, the students were attempting to make sense of the situation, but without considering the physics involved they tend to confuse acceleration (the affect of the collision) with the force of the collision itself. Instead, if they start by applying Newton’s 3rd law, such that the forces are equal, then apply Newton’s 2nd to show that the effect of that same force depends on the mass of the object, it makes sense that the forces are equal but that the effect, the acceleration, is different.

So it’s not really that big a deal in the scheme of things when students’ don’t correctly analyze a collision, but it’s a much bigger deal when we have policymakers denying climate change. The problem is summed up in a picture from a tweet that came across my feed the other day;

truth

Teaching science should mean giving students the tools to analyze situations and make logical conclusions while at the same time emphasizing how to do so in a variety of situations. If we fail to give students the tools of science, or show them how they apply, or challenge them with different situations, or reiterate their prior understandings, we leave room for them to revert to gut-oriented thinking. I hope that my preaching about starting with science rather than intuition can help in some small way to move our society from one where people try to ‘prove’ their own biases to one where we use data on a real quest for truth.