# Day 18: Speed of Sound

*College-Prep Physics:* Today we did the traditional speed of sound lab using Vernier microphones and Logger Pro. It turns out that our 4-sided meter sticks worked great as tubes. We stood them vertically on the floor so the floor acted as the reflecting surface. We got nice data:

We used the thermometer in the room and Hyperphysics to determine the actual speed of sound in the room. Most groups got with a few percent!

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*NGSS Science and Engineering Practice 4: Analyzing and Interpreting Data*

# Day 17: Ball and Spring Model Lab

*AP Physics C:* I decided to turn the example problems in the first sections of Chapter 4 of *Matter and Interactions* into a lab. Last week, they determined the relationships for adding springs in parallel and in series. So today, we started with this as a warm-up (thanks Rhett for the diagram!):

Then we put that aside and started the lab.

**PART ONE: Determine the diameter of an atom**

Groups were given:

- a small metal bar that had 1 mole of atoms (from Pasco’s Mole Set)
- a balance
- a ruler
- an AP Chemistry periodic table

First, they had to determine which element their bar was made from. Then they had to determine the size of an atom using the materials listed. Lots of great discussion in the groups.

**PART TWO: ****Determine the interatomic spring constant for copper**

I don’t have any lab equipment for stretching a long wire, so we watched the following video (thanks Bruce!) and collected data:

Although the wire in the video is brass, I said we could assume it was made entirely of copper. We also used the diameter of a copper atom from Part One. More great discussion within each group. It’s a tough problem to reason all the way through — lot of steps. And in the end, they get a spring constant which is similar to the springs they used in the series and parallel lab….which blows a few minds. Most kids think the interatomic spring constant should be really stiff.

The warm-up and both parts of the lab took an entire 80-minute block.

*NGSS Science and Engineering Practice 4: Analyzing and Interpreting Data*

# Day 16: Relative Motion

*College-Prep Physics: *This year I decided to bring relative motion into my curriculum. It’s a unit in *Preconceptions in Mechanics,* a book I used a lot last year for introducing different types of forces. My hope is that vector addition of velocities (which can be easily demonstrated, see below) will help some kids understand that vector addition of forces act the same way.

I modified the lesson cycle from the Preconceptions in Mechanics, Unit 2 Day 1 Lesson.

I started off the lesson showing the first 15 seconds of of this Japanese video in which a baseball is shot at 100 km/hr out of the back of a truck moving in the opposite direction at 100 km/hr (you could even do the first 3 minutes if you’re evil):

They’re hooked. “What happens?”

Next, I handed out the voting sheets. Here are the slides with my questions for each stage of the voting:

For the first vote, students write down their vote, an explanation, and a “makes sense” score. Then we share out responses. I don’t tell them the right answer, but just move on the the next voting question.

“WAIT! What happens? Why are you moving on?” they ask.

“Don’t worry, we’ll come back to that question later. But first I want you to consider these situations.” I say.

So we go through votes #2-#4 on the slides. After writing their vote, explanation, and makes sense score on the sheet, we share out responses, and try to come to a consensus. After consensus is reached, I demo the scenario using buggies and a short Pasco dynamics track (pictured above). The track is clamped to 2 flat-top constant velocity cars from The Science Source, which have the same motors and wheels as the typical red and blue buggies, meaning they go the same speed. For questions 2 and 3, I use a slow blue buggy (1 battery) to represent Adam running east and west and fast flat-top cars (2 batteries each) to represent the faster train moving east.

The best is when we get to vote #4, in which Adam is running at the same speed as the train. So we use a fast red buggy (2 batteries) to represent Adam. The results were perfect:

Then vote #5 returns to original question: What’s the velocity of the ball as it leaves the truck? We share out, come to a consensus, and then watch the rest of the video from Japan.

I also follow-up with a short *MythBusters* clip in which they replicate the same experiment, but use a soccer ball instead of a baseball. Great results:

As a check for understanding, we did the HW sheet for Day 2 (not Day 1) in class. They knocked it out of the park, so I don’t think doing the Day 2 or Day 3 lessons from *Preconceptions in Mechanics* would be good use of time.

We didn’t do any of the voting questions about non-parallel velocities, and I don’t plan to with my college prep kids. If I did, I’d make that an entire lesson with its own set of voting questions, rather than stick it at the end of Lesson 1 like *PiM* did.

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*NGSS Science and Engineering Practice 6: Constructing Explanations and Designing Solutions*

# Day 15: Springs in Series and Parallel

*AP Physics C: *Students designed their own lab experiments to determine the relationship between the spring constant of an individual spring and the effective spring constant for: (a) identical springs in series; (b) identical springs in parallel.

*NGSS Science and Engineering Practice 3: Planning and Carrying Out Investigations
NGSS Science and Engineering Practice 4.: Analyzing and Interpreting Data*

# Day 14: To Catch a Speeder

*College-Prep Physics:* Today we went out to the lawn to film cars zooming by in front of the high school. Then we went to the computer lab to learn how to analyze the video in Logger Pro in order to determine the speed of the cars. (We set the video scale using fence posts along the road — they’re 10 feet apart.) We shared out our data to determine if there was a speeding problem in front of the school.

It’s not even October yet, and students have already had a hand at using each of the different data collection techniques we’ll be using throughout the year: Desmos on Day 9, Logger Pro probeware on Day 13, and Logger Pro video analysis today.

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##videoanalysis

*NGSS Science and Engineering Practice 4: Analyzing and Interpreting Data*

# Day 13: A New Approach to Colliding Buggies

*College-Prep Physics:* Modeling Instruction’s standard lab practicum for the constant velocity unit is colliding buggies. Lab groups take data to determine the speed of their buggy, then the buggies are quarantined and groups are paired up. Each group pair is then given an initial separation distance for their buggies and are asked to predict the point were the buggies will collide. Once they calculate the answer, they are given their buggies back to test their prediction.

It’s fun, but there are some frustrations. Groups that have poor experimental design or data collection techniques won’t calculate the correct buggy speed, which means they won’t accurately predict the collision point. Also, since only the separation distance is given, there isn’t much focus on the *position* of the buggy and students are less likely to use a graphical method to find the collision point. They try all sorts of equations instead. In the end, one person in the group typically does the calculations while her partners just copy her work.

This year, I decided to shy away from the calculation aspects of the buggy collision lab and instead use the activity to get students more familiar with some of the digital tools we’ll be using throughout the year.

*Logger Pro:* Students used a motion detector and Logger Pro to find the speed of their buggies. They learned how to select portions of the graph and how apply a linear fit. This also reinforced the concept that the slope of a position graph represents velocity. They printed a copy of the graph and taped it into their lab notebooks. Then I quarantined the buggies.

*Position, not distance: *Pairs of groups were then assigned a starting position relative to an origin (marked on the floor) and a direction of motion. Careful advance planning let us have a variety of collision scenarios — some head on, some where a fast buggy catches up to a slow buggy moving in the same direction.

*Desmos:* Groups were then required to model the collision scenario in Desmos in order to determine the collision point. For me, the physics is in formulating the correct models to type into Desmos, not actually solving the set of simultaneous equations or graphing them by hand. Surprisingly, there were some interesting mistakes in this stage: Some groups didn’t use the proper sign for the slope to indicate a buggy heading north/south. Some groups just used the sign from their Logger Pro graph (positive or negative, depending on whether they made their buggy move towards or away from the motion detector). And still some groups used the y-intercept from their Logger Pro graph as their starting point instead of the starting point they were assigned. Once the mistakes were realized, it was a quick fix in Desmos — much less frustrating than reworking a set of simultaneous equations. Then they tested their predictions and included their Desmos graph in their notebooks.

It went well this way, and took about 40 minutes from start to finish. It was something that even students with weaker math/algebra skills could find accessible. Plus, there was more reasoning and discussion about what the slopes and intercepts mean and how to model the situation rather than a focus on solving equations.

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*NGSS Science and Engineering Practice 2: Developing and Using Models*

# Day 12: Inventing Average Velocity

*College-Prep Physics:* We had a great discussion/debate about the meaning of average velocity today. Rather than give students the definition, I simply asked them to determine the average velocity for the following position-time graph (thanks Kelly O’Shea):

Students generated 8 different possible ways to compute the average velocity and I wrote them on the board (see top pic):

- The average of the magnitudes of the non-zero slopes.
- The average of the non-zero slopes.
- The average of the magnitudes of all slopes.
- The average of all the slopes.
- A time-weighted average of all the magnitudes of all slopes.
- A time-weighted average of all the slopes.
- Total distance divided by time.
- Total displacement divided by time.

Then we calculated each one and saw we got mostly different answers.

Students: “Which one’s right?”

Me: “So, how do we find the velocity for part of the trip?”

Students: “It’s the slope of the position-time graph.”

Me: “So how about the whole trip?”

Students: “The slope from start to finish?”

Me: “Yep.”

Students: “That’s 6 m in 6 seconds, so 1 m/s north.”

Me: “Did any of your methods yield the same value?”

Students: “Methods 6 and 8.”

Me: “Can you see why?”

And so we discussed how those two methods and the “net slope” method of finding the average velocity are really all the same thing.

It was a really great discussion.

A copy of my handout (with Kelly’s graph) is here: WORKSHEET Interpreting Position Time Graphs 2015

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*NGSS Science and Engineering Practice 6: Constructing Explanations and Designing Solutions*