Tag Archive | Preconceptions in Mechanics

Day 35: Toothbrushes and Friction

College-Prep Physics: Today will likely be our last round of voting for while. As per Preconceptions in Mechanics, we started this round of discussion on friction with a Pre-Instruction quiz. I set up a toy buggy (without the tire treads) connected to a friction sled by a rubber band to help visualize the scenario:

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In previous years, I’ve used a pair of hair bushes to model friction between surfaces. But the black bristles made it hard for everyone to see. So I took PiM’s advice and bought a class set of toothbrushes.

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And gave everyone a toothbrush so they could interlock brushes with a partner and observe.

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“And you get a toothbrush! And you get a toothbrush! Everybody gets a toothbrush!”

Much better!

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##BFPM

NGSS Science and Engineering Practice #2: Developing Models
NGSS Science and Engineering Practice #6: Constructing Explanations

Day 32: Interaction Diagrams and Force Diagrams

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College-Prep Physics: Now that we have gravitational forces, spring forces, and normal forces under our belts, we can analyse more complex situations. Today was a direct instruction lesson* on drawing interaction diagrams and forces diagrams. You might notice some changes from how I drew them from last year.

I’m using agent-object notation on the force diagrams, rather than last year’s force type + agent, in order to combat the misconception that the force diagram represents what the object is doing, rather than what is being done to the object. This also helps with getting the students to focus on the objects that are exerting the forces, because “every force has a source.” To make the force diagrams easier to read and label, we’re not including the force types on the force diagram vectors. Force types are labeled on the interaction diagram only, to help reinforce that a force is a single interaction between objects.

I’m also starting with complex scenarios early, and also asking students to draw more than one force diagram for a given situation. Last year, some students had the misconception that there must always be one force up, down, left, and right. The didn’t realize you could have 2 forces in one direction or no forces at all.

Drawing multiple force diagrams also allows for identifying 3rd Law pairs (the two vectors with circles in #4 above, though we haven’t formally called them 3rd Law pairs).

We also started with numerical values early. Although the scenarios don’t ask a specific question, we determined the values for as many forces as we could based on what was given.

In hopes of avoiding another common misconception, you’ll see that in both scenarios the normal forces aren’t equal to the weights of the objects.

We are only looking at static cases right now. Up next is tension, then friction. After friction, we’ll consider the dynamic cases.

The two scenarios pictured are taken from Preconception in Mechanics, though PiM doesn’t have the students draw interaction diagrams or force diagrams — a fault I found out too late last year. You can get the entire handout here: ForcesSchemaFBDDevelopmentStatic2015

PS: I haven’t been using the HW sheets from PiM at all. Rather, I’ve been using the occasional PiM HW problem as a bell ringer/do now/warm up.

*If you have a more engaging way of introducing interaction diagrams and force diagrams, please share!

##BFPM

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

Day 31: Equality of Normal Forces

College-Prep Physics: On Friday, we established that the table must be pushing up on the book. Today, we explored a different scenario to determine if normal forces between objects we equal in size. (Based on a similar sequence in Preconception in Mechanics.)

VOTE #1: Compare the forces between the wood stick and the car. (target)

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I set up a slow buggy driving into a wood dowel that is hanging down from a ringstand clamp. If you remove the tire treads, the buggy wheels will continue to spin, showing that the buggy is continuously pushing against the dowel.

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Some students says the forces are equal, some say the buggy is pushing harder because it’s trying to roll into the stick, and some way the stick is pushing harder to keep the buggy in place.

I don’t give the answer, but give them the next scenario instead.

VOTE #2: Compare the forces between the hand and the spring. (anchor)

Most kids say they are the same. It helps to think of a small, motionless board in place between the hand and the spring. Since the board is at rest, the hand and the spring must be pushing equally on the board. Now gently slide the board out from between the hand and the spring. Have any of the forces changed? So how do the forces compare? If I push harder on the spring, what happens? Are the forces the same now? How does the spring know how hard to push? (A lot of kids talk about the spring adjusting or compensating until the forces are equal. Some even refer to the spring lab we did previously. While the forces are ALWAYS equal, even while the spring is moving, I let that detail slide because we’ll return to the dynamic case in another lesson.)

VOTE #3: Compare the forces between the stiff and loose rubber band. (bridge)

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Again, most kids got that the rubber bands pull equally because the ring is at rest. How is this possible when one rubber band is stretched more than the other? What happens when you try to make one of the rubber bands pull harder? What happens if the ring is removed and the rubber bands are tied together? Are the forces still equal?

VOTE #4: Compare the forces between the rubber hose and the car. (bridge)

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Now I have the slow buggy drive into a piece of flexible rubber hose. The slow buggy works well because the hose will visibly flex and while keeping the buggy in place.

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Again, students say the forces are the same. How does the hose “know” how hard to push? What would happen if we replaced the slow buggy with the fast buggy?

VOTE #5: Compare the forces between the wood stick and the car. (target)

We return to the first scenario and re-vote. Students make the connection that the wooden stick still bends and the force between the car and the stick must be equal. Then I quick run through the book scenarios from the previous lesson and ask them to compare the forces (the same, the same, the same, …)

##BFPM

NGSS Science and Engineering Practice #2: Developing Models
NGSS Science and Engineering Practice #6: Constructing Explanations

Day 30: Does the Table Push Up on the Book?

College-Prep Physics: Today we did another round of voting (a la Preconceptions in Mechanics) to answer the question “Does the table push up on the book?”

One snafu that happened this year that didn’t happen last year: Because we studied gravitational forces first, kids were confused by the question and thought about the gravitational attraction between the book and the table. This was something I did not anticipate. So I had to clarify the scenario (explaining that table’s gravitational force on the book pulls the book down rather than push the book up as per the question).

Last year, that confusion wasn’t an issue because we did normal forces first, which is the suggested sequence in preconceptions in mechanics. But I was dissatisfied with that sequence because there were questions about normal forces between individual objects that are stacked on top of each other. We were talking about the object at the bottom of the stack having to support the weight of the objects on top. Those complex scenarios are easily analyzed using system schema and free-body diagrams, but we hadn’t talked about gravitational forces yet.

So, despite the confusion this year, I still think gravity should be done before normal force. So for next year, I’m revising the questions. I’m going to start with the hand on the spring question, since the answer is obvious and we just wrapped up the spring lab. Hoping that question puts kids in the proper mindset, then I’ll move to the table on the book question. And instead of the foam question, I’ll replace the foam with springs. (My foam never really deformed much anyway.) wpid-photogrid_1413554685985.png

Here’s the revised slides I’ll try next year:

##BFPM

NGSS Science and Engineering Practice #2: Developing Models
NGSS Science and Engineering Practice #6: Constructing Explanations

Day 26: What Causes Gravity?

College-Prep Physics: Even though we now have a mathematical relationship between mass and weight, we still don’t know what causes Earth’s gravitational pull. So first, we took a short survey:
GravitySurvey
Download a copy here: GRAVITY Survey 2015

Then we went through each of the four claims in survey question 4 and did a testing experiment for each claim.

 

CLAIM #1: Earth’s Magnetism

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CLAIM #2: Earth ‘s Rotation

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CLAIM #3: Air Pressure

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CLAIM #4: Earth’s Mass

We also compared characteristics of different planets using a table of planetary data.

This sequence of claims and questioning is based off one found in Preconceptions in Mechanics. On Tuesday, we’ll discuss the relative strengths of the gravitational pulls that 2 masses exert on each other.

##BFPM

NGSS Science and Engineering Practice #6. Constructing Explanations 

Day 16: Relative Motion

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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.

##CVPM

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

 

Day 31: Visualizing Friction

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College-Prep Physics: Here’s a great demo (stolen from Preconceptions in Mechanics) for visualizing the “interlocking bumps” model for sliding friction. Try pulling/pushing two wire brushes past each other (I actually have hairbrushes pictured).

  • Ask about which direction the bristles push on each other to help students see the directions of the frictional forces acting on each of the objects.
  • Use it to discuss how “smart” static friction is by “knowing” just how hard to pull to keep an object at rest: the bristles bend more/less — similar to our previous discussion of “smart” normal forces.
  • With 2 identical brushes it’s easy to discuss the equality of the friction forces. Swap out one brush for another with bristles of different material (wire, hair, plastic, etc.) and ask about equality again — similar to our previous discussion of balanced forces produced by springs/rubber bands of different stiffness.
  • The effect of normal force on friction: The larger the normal force between two surfaces, the more those surfaces are compressed together, and the more the bumps/bristles interlock making it harder to pass through each other. You can noticeably see and feel the difference using the brushes.
  • If you want students to have their own brush models to play with, PiM suggests giving a pair of inexpensive toothbrushes to each group of students.

##BFPM

Day 17: Forces – Revisions for Next Year

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College-Prep Physics: Three weeks in, and I’m already thinking of changes for next year. As I’ve said before, I’m using Preconceptions in Mechanics as the foundation for our forces unit. Pictured above is the recommended sequence, which I’m finding out isn’t quite working. Changes I’ll make:

  • Do Gravitational Forces 1 first. Understanding the nature of gravity and how it acts will help make normal forces easier to understand, particularly when analyzing stacked masses. Also, gravity is the force everyone knows about. Why ignore its existence until much later?
  • Integrate system schemas and free-body diagrams into the HW problems. PiM doesn’t do them (which makes the book more flexible for fitting into instructors’ different teaching styles). But without SS and FBDs, we have a less structured way of analyzing the forces in the HW problems, which is likely causing some confusion. This means that I cannot simply photcopy the PiM HW sheets as is, but I will need to re-write them and add supplemental problems.

What I love about PiM:

  • Newton’s 3rd Law is treated throughout all the lessons. The static case is developed first, with the dynamic case delayed until later. In fact, 3rd Law reasoning is essential to developing the proper models for each force.
  • The voting and discussion that happens around the anchor-bridge-target scenarios. (I personally need to work on getting more students involved, though.)

Next year’s anticipated sequence:

  1. Bowling Ball and Mallets (get at qualitative model for forces and motion)***
  2. Dueling Fan Carts (qualitative model for NET force and motion)***
  3. Gravitational Force I
  4. Gravitational Force vs. Mass Lab (simple lab, one data set, focus on making good graph)
  5. Normal Force (ball-and-spring model leads into spring lab)
  6. Spring Force vs. Stretch Lab (simple lab, 2 data sets, focus on taking data over a wide range of levels, each spring will likely NOT have same set of levels).
  7. Tension (Equal tensions along rope leads to forces in tug of war.)
  8. Friction Forces
  9. Friction of Shoe Lab (1 data set, focus on range of levels AND multiple trials per level, graph all trials to see uncertainty in data)

So far for THIS year, we’ve only done 1,5, and 6. Looks like I’ll have to head back and do 2, 3, 4, then introduce schema and FBDs, followed by 7, 8, and 9.

*sigh* This teaching thing would be so much easier if I just assigned textbook reading and end-of-chapter problems.

##BFPM

*** UPDATE 7 OCT 2013: Now thinking of delaying the bowling ball and the fan carts until after the sequence of forces. Trying to separate the static and the dynamic cases. Kids get the static case — balanced forces means constant zero velocity. Having all the forces under our belt will allow for a deeper analysis of the dynamic cases (bowling ball and fan carts).

Day 15: Normal Force Conundrum

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College-Prep Physics:

Student A: “The forces are ALWAYS EQUAL. That’s what we’ve been talking about for the past week.”

Student B: “Well, if B is at rest, then the two forces must be equal.”

Student C: “The force from C must be greater since it bears more weight.”

Student B: “But if the force from C is greater, then B would move upwards.”

***

We’re in a difficult spot right now, and I probably should have delayed this question until after we talked about gravitational forces in more detail. But, it was on the HW sheet for a Preconception in Mechanics lesson that we already did, so I just photocopied the worksheet without really looking at it first. *hangs head in shame*

We were able to get to a point where:

  1. We understand that the force from C must be greater because the surfaces between B & C deforms more than the surfaces between A & B, since surface C is supporting the weight of both block.
  2. We don’t understand why block B remains at rest, since the 2 forces on B are different in size.

My best answer to them was to put a big question mark on it and return to it later. We don’t have all the pieces to this puzzle yet. Students didn’t really like that answer and left class a bit frustrated.

really resisted doing an impromptu gravitational force lesson, since I’m saving it for later because that’s how Preconceptions in Mechanics does it. I think the reason they delay gravitational forces and do normal forces first is because kids often confuse the two forces when objects are resting on top of each other. For example, using the problem above, many kids think that the gravitational force on A literally is the normal force of A pushing down on B. In this case, they have the same magnitude, but they are really two distinct forces.

##BFPM

Day 11: Equality of Normal Forces

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College-Prep Physics: I’ve been using the normal force vote/discussion lessons from Preconceptions in Mechanics. This is the target scenario for the second lesson. Although you can’t tell, the buggy is turned on and the wheels are spinning with the buggy in place.

Which force, if either, is larger: the buggy pushing on the bolt or the bolt pushing back on the buggy?

The rest of the lesson leads students through several different scenarios (including the Dueling Rubber bands from Day 10) carefully selected and sequenced so that they can return back to the target scenario and have a model/mechanism for the answer.

FYI: That board with the bolt came in very handy today.

  • I put a Pasco matter model over the bolt so I could show how the compression/normal force changes direction as the board changes angle from horizontal to vertical. The bolt kept the model from sliding down the board.
  • Later, I took the matter model off the board and put a book on the board, tilted the board, and the bolt prevented the book from sliding — and we talked about the directions of the normal forces between the book & board and the book & bolt.
  • And finally I used it to introduce the Hooke’s Law lab by hooking a spring on it and pulling with a spring scale (“What do you notice?”).

***

The previous normal force lesson dealt with the nature of the normal force and introduced the ball and spring model. Here are some responses to the HW for the first lesson:

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##BFPM