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 29: Spring Lab Debrief

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College-Prep Physics: Yesterday, students designed their own experiments to determine the relationship between the stretch of a spring and the force applied to the spring. Today we shared out our results.

This year, I chose to use 2 different springs: one with a pre-load (red) and one without (green). My goal is to drive home that not all trends will go through the origin. Some groups still tried to fit a trend through the origin, though. Looking back, if I had been monitoring groups better, I would have asked those groups to go back and take more data for small stretches….hopefully continuing the linear trend down to the y-intercept.

##BFPM

NGSS Science and Engineering Practice #4: Analyzing and Interpreting Data
NGSS Science and Engineering Practice #5. Using Mathematics

Day 28: Do Unequal Masses Pull Equally On Each Other?

College-Prep Physics: Another round of voting, inspired by Preconceptions in Mechanics. Yesterday we determined that the Earth and tennis ball pull mutually on each other. But what about the strengths of the pulls?

VOTE #1 (Target scenario): How do the gravitational forces between the tennis ball & Earth compare? [Almost everyone said F(E on TB) > F(TB on E)]

VOTE #2: (Anchor scenario): How do the gravitational forces between 2 identical tiny masses compare? [Everyone agreed they were equal in size.]

Next we used the whiteboards to draw and label the gravitational forces between tiny mass A and tiny mass X. A surprise to me: most groups were not able to properly label the forces as F(A on X) and F(X on A) — they had the labels reversed. So it was important for me to go to each group and coach them for proper arrow labels and placement (arrows attached to objects, not hanging in mid-air).

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How many pulls on A? How many pulls on X?

Then we added attached another tiny mass Y to tiny mass X. Does that change the interaction between A and X? [No.] Do we need to add more forces? [Yes.] Draw them.

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How many pulls on A? How many pulls on XY?

Then we added tiny mass Z to mass XY. Do the existing arrows change? Do we have to add more arrows?

I also modeled the situation on the blackboard using magnetic hooks as the masses and rubber bands to represent the gravitational forces between the masses.

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VOTE #3 (Bridge scenario): How many forces on A? How many forces on XYZ? So how do the strengths of the gravitational forces compare? [The same?!?]

VOTE #4 (Target scenario revisited): How do the gravitational forces between the tennis ball & Earth compare? [The same?!?]

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VOTE #5: Jack weighs 800 N. How hard does Jack pull up on Earth? [800 N]

“But why doesn’t the Earth rise up to meet Jack if the pulls are equal?” Great (anticipated) question from the class. So we talked about how Earth’s 800 N pulling on Jack’s mass has much more of an effect than Jack’s 800 N pulling on the Earth’s entire mass. (And the Earth is like, “Jack, do you even lift?”)

Great lesson in all, though it took a lot of time because I wanted the kids to reach the conclusion on their own rather than me just telling them. I hope it sticks!

##BFPM

NGSS Science and Engineering Practice #6: Constructing Explanations

Day 27: Is Gravity a Mutual Force?

College-Prep Physics: On Friday, we discussed what causes gravity. Today, we discussed if it was a mutual force. We started by voting on the target scenario: “Does the tennis ball exert a gravitational force on the Earth?” Students shared their thoughts. In one class, everyone said yes, though I doubt everyone actually thought that. So as a way to encourage kids to think about alternate viewpoints, I asked, “Why might a thoughtful person claim that the tennis ball does not exert a gravitational force on the Earth?” In addition, the stigma/fear of sharing an incorrect answer is practically eliminated by framing it as “why might a thoughtful person claim …” rather than “put your hands up if you said … “

Then we put the target scenario aside and voted on the anchor scenario: “Does Earth 2 exert a gravitational pull on the Earth?” The anchor scenario is one where most kids should have an intuition for the correct answer. We shared our thoughts again and came to consensus. (As an aside, I brought up the notion of a Counter-Earth, and blew a few minds.)

Then we moved to the bridging scenario, where we have the Moon (less massive than Earth 2, but more massive than a tennis ball): “Does the Moon exert a gravitational pull on the Earth?” We shared our thoughts again, several students mentioned tides as evidence, and we came to consensus.

What if we make the mass of the moon smaller and smaller, until it was the same as the mass of a tennis ball? We moved back to the target scenario and re-voted.

Lastly, I asked the students to discuss whether gravity was a one-way or two-way (mutual) force, based on our discussion. I should note that we have not discussed Newton’s Third Law yet. Tomorrow we’ll discuss if the mutual gravitational pulls between unequal masses are equal or unequal in size.

(The sequence of voting questions is based on those found in Preconception in Mechanics.)

##BFPM

NGSS Science and Engineering Practince #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 25: Think Aloud

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AP Physics C: A homework problem I assigned last night turned out to be much more difficult than what I originally thought. So today was a great time for a Think Aloud while we discussed the problem on the spot. I tried to verbalize my thinking and reasoning as much as  possible. In the process, we hit a dead end, then made a breakthrough realization, then made a common mistake, and then tried to find the mistake. Hopefully students realize that even if they don’t know what to do when they first tackle a problem (I didn’t in this case), they see that “experts” aren’t afraid to dig in and get messy, go down blind alleys, and start over again when a strategy fails.

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