# AP Energy Linearization

Since I used the PUM/ALG introduction to energy to define work and derive quantitative energy relationships (described in a previous post), I still had all these cool energy relationships to use as testing experiments for conservation of energy.

Rather than ask everyone to do the same paradigm labs, I gave students free reign to design their own experiment. Some chose experiments based on dropping stuff straight down, or on a ramp. Many chose something related to elastic energy, as shown below, but there was a lot of variability in the details of the experiments.

This group was trying to approximate a “launch sequence” they’d seen in some roller coasters, and measured the effect of stretch distance on velocity:

Each group was asked to predict what they’d have to graph in order to get a linearized graph, and calculate an expected value for the slope based on parameters like mass and spring constant. THEN they collected the data and compared their actual slope to the predicted slope.

This group did a similar launching experiment, but used a push-pull spring scale to launch the cart. They got a slope that was lower then their predicted value, and interpreted it to mean that a significant amount of energy was dissipated within the spring scale when it popped forward.

Since we’ve already defined work, we can use this as another quantifiable relationship. This group looked at the effect of stretching distance on sliding distance. (This is precisely the same experiment done with my ninth graders, but the AP students calculate both a predicted and experimental value for the linearized slope.) They attached some mass to the dry erase marker to increase the sliding friction to a large enough value that they could measure it.

This was a little crazy, and we could have used a little more lead time preparing, since they didn’t have much experience with linearizing, but it ended up being pretty awesome!

# Ball Bounce Complications

We’re finally doing the ball bounce lab – after our qualitative energy unit on the edge of talking slope analysis and moving to cvpm. I know that many folks use this lab on the first day of school, but saving it until after energy with ninth graders has some advantages!

For one, students are already thinking about the energy transfer involved, so the slopes can be interpreted using LOL diagrams with an awesome emphasis on multiple representations.

It’s also a great opportunity to have conversations about the complications that can come up. For example, the decision to measure from the top or the bottom of the ball is a tricky one, but students who have some experience with “Eg = 0 reference lines” or proportional relationships can make an intelligent decision with real reasons for their choice.

We’ve talked a little bit at this point about predicting a range of possible values, but that becomes a real focus in this lab for the first time. Since it’s so hard to get bounce height data that’s spot on each trial, our prediction should reflect that uncertainty with a larger range.

That ping pong ball on the right there provides another interesting wrinkle. Over 2m it’s obvious that the bounce height drop height lab is not linear… but it’s temptingly linear – enough that you could reasonably believe that it fits. I’ve decided to show them data that I’ve collected, and ask them what they think of my best fit line… Lets hope they’re not fooled!

##expdesign ##etm ##physicsfirst ##practicumlab

# Two Ramps Prediction

Trying to tie up our energy unit means working with a surprisingly difficult skill I’ve identified for my SBG: I can use the conservation of energy to make predictions, and explain these predictions using energy terms correctly. Students have a surprisingly hard time with this, but it’s worth devoting time to. It’s kind of the point of the whole unit, after all!

I’ve made a practice sheet that shows two ramps end to end, one shallow and one steep. The ball is dropped from the top of the steep ramp (Moment A), and shown moving quickly at the bottom (Moment B), but the highest point the ball reaches on the shallow ramp (Moment C) isn’t shown. First, students are asked to draw an LOL for these three moments, ignoring friction.

THEN (and only then), students are asked to use their LOL to help them predict how high the ball will reach on the shallow ramp. The prompt related the skill mentioned above reads, “Explain your prediction using some of these terms: conservation of energy, store, transfer, increase, decrease.” Without these suggestions, the answers are just too vague…

On the opposite side, the same question is asked, but the ball is dropped from the shallow ramp. If students thought through the first side carefully (and are really using energy to make their prediction), they should see immediately that the questions are identical. If not, then they’ll get hung up on things like ramp steepness…

I tested it out for real, which involves some friction of course. Ideally, I would have tested it both in the PhET Skater and with real stuff, but I ran out of time!

They’ll have a quiz on this soon, involving sliding blocks. I was kinda shocked last year when they had as much difficulty as they did with prediction questions, so I’m excited to see whether this conversation has helped!

##physicsfirst ##etm ##practice ##practicumlab ##sbar

# Chalk-Smashing Ability

Today in AP Physics we finished up our discussion of momentum and moved on to energy. Rather than start directly with the energy paradigm lab, I used the PUM/ALG/ISLE sequence. It’s a beautiful piece of work!!

I began by identifying the “chalk-smashing ability” of a system. (I used an egg today because I couldn’t find chalk… but it was a little violent.) I told students I was going to ask them to focus carefully on the direction of the force I was exerting on a cart defined to be in the system, and the direction of the displacement of the cart while the force was being exerted. First I raised the cart upwards. Force upwards, displacement upwards. Chalk/egg smashing ability increased. Then I pushed the cart sideways, increasing its speed. Force to the right, displacement to the right. Chalk/egg smashing ability increased. Then I pulled the cart backwards against a rubber band. Force to the left, displacement to the left. Chalk smashing ability increased. Lastly, I increased the speed of the cart with a force directed diagonally upwards using a string. Component of force to the right equal to Fcos(theta), displacement to the right.

We then demonstrated that it would be possible to decrease the chalk-smashing ability of the system by exerting force on the cart in a direction OPPOSITE the displacement… Hmm… I think I’m tarting to see a pattern!

At some point, I defined the chalk smashing ability of a system to be the energy stored in that system, and the process of increasing or decreasing the chalk-smashing ability as “doing work”, a quantity equal to F deltax cos (theta). From this relationship, it’ll be a cinch to quantify all the energy relationships with experiments and simple reasoning.

This is a sequence that I think ISLE really gets spot on. Not that the energy paradigm labs aren’t awesome, but they seem to dodge around the idea of what energy actually is. We spend all this time using energy conservation to come up with these equalities, but end up having to do a little bit of hand waving to start using the relationships we want to use.

Rather, if we first simply look for this pattern, then we can define work as a useful quantity before anything else. THEN it’s easy to build those relationships by analyzing situations where ALL the work done goes into Eg, or Ek, or Eelas, and check whether the results of those paradigm labs work out with the relationships we’ve defined. Emphasizing energy as a measured quantity of a system in this way seems more fruitful, especially because it lays the groundwork for thinking about electric potential energy in terms of work later on.

# Conclusion Section Whiteboards

This is day one of our discussion of what sorts of conclusions we can make for our rubber band block experiment and the ball and block experiment. I have a sheet with a few relevant LOLs, and then four questions related to interpreting graphs and making conclusions. Each group took one question.

What can you say about the relationship you studied? Is it proportional?

This group said yes for their rubber band lab, but got a lot of push back from other students. “Didn’t we see that the pattern was a curve back when we played with the spring simulation?” One student even said, “I wrote down in my Consensus Notebook that relationships that deal with elastic energy are usually curved, not straight.” Chills down my spine!!

This prompted a huge, lively discussion about whether curved trend lines even exist. Some students have seen Logger Pro fit a curve and some haven’t. But it’s a good conversation to have early, so we can be sure that when we fit a straight line we’re doing so because we actually think it describes the pattern we see.

Do you think the pattern would continue for larger values of the IV?

This group spotted immediately that the pattern probably wouldn’t continue, because the rubber band would break eventually. They ASKED to go after the previous group, because they thought it would resolve some of the dispute about curved patterns.

It seems like a no-brainer now that I can’t expect to get good conclusions in the lab reports unless I really devote time to discussing what coming to conclusions can mean!!

Since the priority of our qualitative energy unit is less to nail down the energy relationships and more to get a strong feel for analyzing energy transfer, I wanted to use a few labs that had a slightly different flavor from the classic energy paradigm labs. Specifically, I was interested in confirming the relationships that we’d analyzed within the PhET simulations, using real stuff.

I’ve done this using two different labs, both designed to use “sliding distance” as a pseudo-quantification of energy. That is, by measuring the distance a block slides, we can get some idea of the energy that has dissipated, and therefore infer conclusions about the energy that was stored in other forms in the system to begin with.

For example, a really simple and clean lab involves big rubber bands and wooden blocks. All students investigated the effect of stretch distance on sliding distance, first by stretching the block back in the rubber band:

Then by letting it slide to a stop:

The next lab involved rolling balls down a slope and into, you guessed it, a wooden block! (Or, in the case of this group, a dry eraser…) some groups varied the mass of the ball and some varied the height, but everyone used sliding distance as their dependent variable. After all, we don’t really know how to measure much else…

This is a great set of activities for this spot in our unit. It stretches our energy muscles a bit, AND provides a great opportunity to think about experimental design. Both experiments are prettu straightforward to get working, but not completely trivial (the rubber band is the easier of the two). Both yield data with significant but not too much variability for discussing uncertainty and making predictions. And the two together provide a nice contrast between proportional and non-proportional relationships.

Next class, we’ll whiteboard some questions related to discussion that should go in a conclusion section – graph analysis and connections to energy.

# Doubling Down on Bar Charts

It’s hard to see the whiteboard in this picture, but it shows a list of suggestions made during a discussion with students about features that they noticed about their gravitational energy relationships graphs. That is, students used the PhET skater bar chart to perform a “virtual” experiment, using the bar chart itself as a measured value. There were various different experiments done, investigating the relationship between height, mass, or g-field and gravitational energy, and they all came out proportional. So it seemed like a good time to have a little discussion about what we saw in the pattern.

I’ve been worried, though, that students are ONLY seeing linear relationships. If we only study things that come out as a line, they’re less inclined to see those results as amazing, right?

So, part of the discussion was devoted to discussing the graph on the left, of the relationship between “stretch distance” and elastic energy, as measured on the bar of the PhET mass and springs simulation here: http://bit.ly/phetsprings . (This trend line was put there to show that it DOESN’T describe the pattern we see…)

Enough with all these simulations!! Next class, we’re going to do a couple labs where this stuff shows up for real: launching blocks across the floor with rubber bands (to look for a relationship between stretch distance and sliding distance) and rolling balls into blocks on a ramp (to look for a relationship between ball height or mass and sliding distance).

These are kind of a substitute for the energy paradigm labs. We decided that developing the true quantitative relationships for energy wasn’t crucial at this point, but we did want to use energy concepts to drive some solid experiments. These experiments help solidify understanding of energy concepts, providing real evidence from the non-virtual world, and they’re good practice interpreting quantitative data using LOLs. AND they’re both situations where it’s easy to generate quantitative predicts and tests, so we can hone our skills “predicting a range of values.”

##etm ##graphing ##phet ##physicsfirst

# Tough Corrections

Students took a quiz on LOLs today, and then marked up their own quizzes immediately afterward. Most did well with their corrections, I think, but some were very confused. We’ve seen again and again that two diagrams don’t have to be identical in to both be correct, but this can make it quite challenging to figure out what’s correct.

That’s the point, of course, but I think I did my students a disservice by asking them to check their quiz this way without giving them any extra support. This student, for example, had a perfect solution to a wind up bunny question, then changed it completely when asked to compare to my solution.

I think that I missed an opportunity with these corrections to instead identify factors that ARE important about the energy transfer in each example. For this question, the “key” should have read:

Gravitational energy stays constant, and is consistent with choice of Eg = 0 line. Kinetic energy stays constant.
Elastic energy decreases.
Dissipated energy increases.

Of course, identifying these things is the point of asking the questions in the first place, but it would have been a much more illuminating experience to correct this way.

(Come to think of it, I DID this with the pie charts quiz last year, but since I got rid of pie charts I didn’t see it. ##setbacks!)

##etm ##assessment ##physicsfirst

# Measuring Bar Lengths

I had written this intro our PhET Skater lab energy introduction, but we haven’t really tried to use it until now. The idea is that we can measure the gravitational energy using the length of the bar chart itself in the simulation. As an introduction to trying to investigate relationships relevant to energy, this seemed like a nice small step.

(We could even use this method to investigate elastic energy using the PhET Masses and Springs simulation, and see that stretching a spring the same amount further doesn’t necessarily store the same amount more energy – a nice intro into doing work.)

Other teachers at my school who used it didn’t report any problems, but I’ve run into some trickinesses. Here are a few:

Students didn’t understand why they’d ever want to put a ruler against their computer screen. This was entirely my fault. I broke the second rule of good physics teaching by giving students instructions before motivating the work.

Students didn’t think that the relationship between Eg and “height” was something they needed to investigate. We’ve used “higher up means more Eg” for a while now, so they didn’t see it as a valuable question. I tried to convince them that we didn’t have evidence that the relationship was actually linear, but pretty soon I just moved on to investigating mass and g-field.

Since they were looking at a bar graph, many students instinctively made a bar graph. Our discussion from a while ago about what graphs are most useful for seeing relationships and making predictions didn’t so much sink in, but I guess it was good for me to see that!

It’s also unfortunate that the default settings coincidentally end up making bars that are 1cm long for each 1m of height in the sim… Makes me think that if I’m going to do this at all, I should do height as a demo, then turn students loose to investigate anything else they can find.

Maybe the better solution is to abandon it completely. Any thoughts?

##etm ##physicsfirst ##setbacks ##phet

# Jump Graph

I have to admit that I felt a little poorly planned going into AP Physics class this morning. I’m trying to step up the difficulty in our forces unit, and set the stage for a transition to momentum and collisions.

I decided to ask students to whiteboard a force vs time graph for a jump, and to draw force diagrams and accelerations for a few important moments. It was an enormous success, and I got a number of suggestions that looked like this:

The students talked for a long time about whether the graph had to be symmetrical, and started making allusions to falling on concrete vs falling onto a bouncy castle. When we finally tested it (on a Vernier force plate), I felt the need to try TWO jumps: a jump where I landed with “cushioned” knees, and a jump where I landed with stuff knees. They knew exactly what to expect!

During the discussion, one student essentially came up with the idea of impulse without any prompting. This is my writing, after we were running out of time and I felt the need to back up the student’s argument with some algebra.

All in all, a perfect transition into momentum!!

##ufpm ##whiteboarding ##vernier ##mtm