Based on the evidence in this video, what are these ...
Tutorial 6 –Orange group
In this workshop, we’re going to watch video of students working on a mechanics tutorial. Boxed below are the questions they’re discussing: work through them collaboratively with your partners before we watch the video.
This tutorial introduces momentum conservation. Equally important, using momentum as an example, this tutorial explores the extent to which formulas relate to common sense.
I. What’s your view?
A. (Work individually) Which of the following best expresses your view about the relationship between physics formulas and common sense? (You can choose more than one.)
1 Many physics concepts make a lot of sense and connect to everyday experience; but formulas are more of a problem-solving tool than a sense-making tool.
2 It really depends on the formula. Some of them make sense, but you shouldn’t expect them to make sense as a general rule.
3 In general, physics formulas express some kind of common-sense ideas.
B. Compare your answers with the rest of your group. If there was disagreement, have a debate—not to convince each other, but to understand each others’ views. If someone makes a good point that disagrees with what you initially thought, summarize that point here.
Watch the first video (about 2 min). The transcript is provided below. Student 1 (S1) is in the left foreground, S2 is on the left in the back, S3 is on the right in the back, and S4 is on the right in the front.
Transcript: Orange 6-1
S4: What are your answers for question A?
S4: Uh...
S1: Three.
S4: I put one
S1: That's kinda true.
S3: No they don't.
S4: I think they're all true. Well, two's not so much, but one and three are definitely true.
S1: I mean, you look at a formula...
S2: I'm gonna say one because I don't understand formulas.
S4: I don't understand formulas either.
S1: Formulas express common sense, but I bet looking...
S4: I'm glad I'm not the only one, everyone's like ooh... (using)(?) formulas. That's a good thing.
S1: Yeah, like, that's why I can't use the book at all, because the book is all formulas.
S4: I read the first assignment, and...
S1: And then I haven't read anything, yeah.
S3: I didn't open the book.
S4: OK.
S2: No, I didn't open it either.
S4: Is there any disagreement?
S2: Considering he already said it's worthless, why am I gonna read it?
S4: I know, I'm mad that I bought the study guide now.
S2: Wait, someone said three? Didn't someone say three?
S1: I said three, but...
S2: Now you're changing it?
S1: Yeah.
S3: Change, good, so we don't have to write this one.
S1: Peer pressure.
S4: I agree with number three too.
S3: No you don't.
S1: I think formulas express common sense ideas, but I don't think that you can find the common sense from looking at a formula.
S4: Yeah, you have to be, like, explain what...
S1: You have to know what a formula has to do with.
Consider the following questions about the episode you just watched.
1 The three options are intentionally written so that a reasonable person could agree with any one of them, but i and iii seem contradictory. Nonetheless student 4 says that i and iii are both true. Explain what she might be thinking.
2 What is student 1’s relationship to formulas? What about student 4?
3 The students seem a little low-energy when answering this question, but they still engage with it fairly well. What do we learn from their discussion? In particular, what do we learn about their expectations for physics understanding, how they study, etc?
The students continue with the following tutorial exercises. Do them yourself before we watch the next video clip.
II. Figuring out the formula for oomph
An important physical quantity, the name of which we’ll give later, corresponds to the intuitive idea of oomph. The more oomph something has, the harder it is to stop, and the more ability it has to knock other things over. Let’s figure out the formula for oomph. If you already know the formula from a previous class, please “play along” and don’t give it away. We’ve structured this tutorial so that you’ll learn something even if you already know the formula. We know some of you don’t like mucking around with intuitions, but trust us, in this tutorial it’ll lead somewhere quickly, and you’ll end up practicing some physics.
A. (Work together) A small pebble and a larger rock are thrown at the same speed.
i. Which one has more oomph? Why?
ii. The rock is twice as massive as the pebble. Intuitively, how does the rock’s oomph compare to the pebble’s oomph? Is it twice as big? Half as big? Three times as big?
B. (Work together) Picture two identical bowling balls, one of which is rolling faster than the other.
i. Which ball, the faster or slower one, has more oomph? Why?
ii. The faster ball is exactly 7 times as fast as the slower one. Intuitively, how does the faster ball’s oomph compare to the slower ball’s oomph?
C. (Work together) The physics concept corresponding to oomph is momentum. Building on your above answers, figure out a formula for momentum (oomph) in terms of mass and velocity. Explain how the formula expresses your intuitions from parts A and B above. (For nutty historical reasons, physicists use the letter p for momentum.).
Watch the video (1 min).
Transcript: Orange 6-2
S1: Increasing mass equals increasing momentum.
S4: We have to consult an instructor now.
TA: What you got?
S1: p = mv.
TA: OK, so, did you get that because you knew it, or because you...
S1: No, actually, we didn't know it.
S4: Well, because from before, if you have larger, like, the rock is obviously gonna have more momentum than the little pebble
S2: directly related
S4: but they have the same velocity, so if this is bigger, than that has to be bigger.
TA: OK.
S1: Same thing with the velocity, because the bowling ball's... faster one (S4: but they're the same mass) has more oomph.
TA: OK. Has anybody seen the definition for momentum before? (All: No.) No? Have any of you guys taken physics before?
S4: No, you haven't. No, he's saying that I took physics before!
TA: All right, well... that's good.
S4: I've taken physics, but it was a long time ago, and I don't remember a lot.
S1: I took it in high school.
S4: Same here.
TA: Public schools [laughs]. All right, you can go ahead.
S1: We’re smart, we came up with it all by ourselves.
Consider the following questions about the episode you just watched.
1 The TA seems to think that some groups would have seen this formula elsewhere (the tutorial also acknowledges that possibility). This group says they came up with it themselves. Does that surprise you? Do you believe them?
2 Are you satisfied with the students’ reasoning? Why or why not?
The students continue with the following tutorial exercises. Do them yourself before we watch the next video clip.
III. Intuitions about collisions
Above, your intuitions about oomph led to a formula for momentum. Now let’s see if your intuitions about collisions lead to similar progress.
1 (Work together) A 1 kg cart, rolling with negligible friction at 6 meters per second, collides with and sticks to an identical cart. So, after colliding, the carts roll together as a single unit.
1 Using your intuitions, guess the post-collision speed of the two carts. Briefly explain your reasoning.
2 According to the intuitive guess you just made, is the overall momentum of the two-cart system after the collision greater than, less than, or equal to the overall momentum before the collision? Work this out using the momentum formula you figured out above and plugging in the relevant numbers.
2 (Work together) In a similar experiment, the 1 kg cart collides with a 3 kg cart but doesn’t stick to it. Instead, the 3 kg cart gets knock forward by the 1 kg cart, which comes to rest after the collision.
1 Again using intuitions, guess the post-collision speed of the 3 kg cart.
2 According to the intuitive guess you just made, is the overall momentum of the two-cart system after the collision greater than, less than, or equal to the overall momentum before the collision?
3 (Work together) Based on your work above, state a general rule about how the total momentum of a system changes during a collision.
4 Let’s look at one more collision. Two identical blocks, both of mass 0.5 kg and covered with Velcro™, slide toward each other at equal speeds, 6 m/s. The blocks stick together.
1 Intuitively, after the collision, how fast do the blocks move and in what direction?
2 In the cart collisions from parts A and B above, momentum was conserved; it was the same before and after the collision. Because conserved quantities are useful in problem-solving, it would be cool if we could define momentum in such a way that it’s always conserved in collisions (between objects that are free to move). Is there some way to modify or clarify the momentum formula you figured out at the top of page 2 so that momentum is conserved in the head-on collision between the two blocks? (Hint: Maybe oomph “cares” about direction.)
Watch the video (5 min).
Transcript: Orange 6-5
S2: Well, wait.
S4: What?
S3: I really think it's...
S4: What?
S1: Wait, you're not sure it doesn't change?
S2: If momentum's equal to mass times velocity, and velocity changes, and mass stays constant, how can momentum...
S1: No, because we didn't do that, cause look, the mass changes, and the velocity changes.
S4: The mass changes too, yeah, because it goes from one to two.
S1: And here, even when it's transferred, the velocity changes with the mass. So when one changes, the other one changes, basically.
S3: That's like... one more collision...
S4: So... they do not move in either direction cause they stick together.
S3: Slide toward each other...
S4: They're the same speed, the same mass, and they stick together at the end, they're not moving anywhere else. If one of them had stronger momentum, it would pull the other one, but it doesn't.
S3: After the blocks moves(?)...
S1: They stop.
S3: They stop, yeah. They collide with each other.
S1: They exert the same...
S3: force
S1: We're not dealing with force!
S4: Oomph? They've got the same oomph.
S4: Who made up that word anyway?
S1: They have the same momentum, and when they hit each other, they cancel out. Or will they bounce off each other?
S4: Well, it says they stick together.
S3: Yeah.
S1: OK. They should stop.
S2: Because their momentums are equal and in opposite directions, so it's gonna cancel out.
S1: Equal and opposite...
S4: momentums. (S1: momentums?)
S1: Oh no. Newton doesn't have momentum laws, does he?
S4: Maybe oomph cares about direction?
S3: Probably not.
S1: Well, if they hit each other and they stick together, if anything they're gonna want to bounce off each other.
S4: Yeah, if anything.
S1: But since they're stuck together, they're just gonna push into each other and they're not gonna move.
S4: Right.
S1: Cause they cancel each other out with the same size.
S4: I think it disagrees with part C.
S1: What was part C?
S4: No, no, it agrees, because...
S1: Cause momentum doesn't change.
S4: it's the same everything, right.
S1: No.
S4: But it doesn't care about direction.
S3: No wait, wait wait.
S1: Momentum does change, momentum goes to zero because they stop.
S4: Right, because they're equal and opposite, like he just said.
S1: So momentum doesn't transfer here.
S4: But what is this? That doesn't make sense to me.
S1: That would be oomph cares about direction.
S3: Well, I mean, if it...
S2: Cause if they're going like this, this side's positive, this side's negative.
S4: OK.
S1: So direction can change momentum, but momentum doesn't change just as a result of mass and velocity?
S4: Right.
S1: But velocity is direction?
S3: OK.
S4: I mean, velocity and mass can change momentum, but in the last example it didn't, cause it all equaled out.
S1: Cause it transferred. Momentum... transferred.
S4: OK.
S1: Well, cause here, this one's momentum changed.
S3: Mmmhmm.
S4: Because the mass changed.
S1: OK, well, momentum was transferred...
S4: This one's momentum changed too.
S1: Momentum was transferred from this cart to this one, right? So, this one had zero, and this one had the same momentum that this one had. So these two come at each other with the same momentum. They're both gonna...
S4: They're gonna transfer it to each other!
S1: They're gonna transfer to each other and both lose.
S4: OK.
S1: But that still doesn't make any sense.
S4: It makes sense to me.
S1: Are we anywhere on the wrong track? (?)
TA: Yeah. You guys are making sense. I mean, do you all agree?
S4: Yes. I think it all is right, everything we've said.
TA: Well then, write it down, and you guys can move on.
S2: So it disagrees, right?
S3: It disagrees.
S4: No, it agrees.
S1: It disagrees with what we wrote but agrees with what happened when we looked back at it.
S2: Right.
S4: Right, like, numerically, it doesn't agree, obviously, but...
S2: Well, it disagrees with what we wrote, which is what the question is asking about.
S1: Cause momentum...
S2: Oh, migraine...
Consider the following questions about the episode you just watched.
1 Look again at what student 2 says at the beginning of the clip. Why doesn’t he think the momentum stays the same during the collision?
2 About two minutes into the clip (line 45), the TA comes by but doesn’t say anything for over two minutes. What’s he doing there? What effect do you think his being there has on the students, if any?
3 In lines 82-84, student 1 says, “Direction can change momentum, but momentum doesn’t change just as a result of mass and velocity.” What does she mean? Do you agree with her?
4 Do you think the TA’s interaction with the students is appropriate, or does he let them off too easy? Why do you think so?
This last clip (2 min) picks up right where the previous one left off.
Transcript: Orange 6-6
S3: Wait, why does it disagree? I'm so, like, gone.
S1: We said momentum doesn't change and momentum does change here.
S3: Oh.
S1: But we decided that direction can change momentum.
S1: Right?
S4: Yes.
S3: Velocity can change momentum?
S1: So if the directions cancel out, momentum can cancel out?
S4: Yes.
S1: Is that what we're saying?
S4: I think so.
S3: So direction...
S4: And probably if one's bigger than the other, then the momentum will become (S2 Oh my god we have [inaudible]) smaller, but it'll still like... somewhat cancel out.
S1: What?
S3: Oh, we do?
S4: Yeah, we're perfect.
S1: OK, but let's say... see, my intuition would say if this was going eight, OK, then this one would go this way at two.
S2: Right.
S4: Yes.
S2: I agree.
S1: OK, so then...
S2: That's the same thing with net force.
S1: Direction cancels out... velocity.
S4: So yeah, the six cancels out, but then there's two.
S1: Direction cancels out velocity.
S3: Direction cancels out... wait, can...
S1: Because if direction cancels out velocity
S3: It changes the momentum.
S1: Because the mass isn't cancelling.
S4: Well, it cancels out momentum, but it can't cancel out mass, so it must cancel out velocity.
S1: Cancel out velocity.
S2: So you just said change momentum, that's fine.
S4: Yeah.
S1: Yeah, but I think that if I write that I will remember it to actually understand the concept.
S4: That makes sense.
S1: That's why I said it.
S4: Does this tutorial help anyone or just me?
S1: It helps me.
S3: It helps me a lot.
S1: It helps me understand, yeah.
Consider the following questions about the episode you just watched.
1 About 1 minute into the clip (line 19), S2 points out the momentum conservation formula that appears prominently later on that page of the tutorial. What is the other students’ reaction?
2 What do the students decide about what quantities cancel when blocks collide “head-on”? Do you agree with them?
3 Would you have thought the students were feeling so positive about the tutorial, based on the other clips you’ve seen? What would you have guessed if you were their TA?
-----------------------
?
AFTER
1 kg
1 kg
6 m/s
BEFORE
AFTER
?
6 m/s
1 kg
3 kg
BEFORE
stopped
AFTER
?
6 m/s
0.5 kg
BEFORE
6 m/s
0.5 kg
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