First Tutorial Orange Group The first video is of students working together on a mechanics tutorial. Boxed below are the questions they re discussing: discuss these with your partners group before we watch the video. Previous tutorials and Interactive Lecture Demonstrations introduced strategies for reconciling common sense with physics concepts when they seem to contradict each other. You ll practice those strategies here. I. Timmy s fallen down the well! To rescue a child who has fallen down a well, rescue workers fasten him to a rope, the other end of which is then reeled in by a machine. The rope pulls the child straight upward at steady speed. The child weighs 250 newtons, which means gravity pulls him downward with 250 newtons of force. A. (Work together) Draw a diagram of this situation that you can refer to during subsequent discussions. B. (Work individually) As the child is pulled upward at constant speed, does the rope exert an upward force greater than, less than, or equal to 250 newtons? Explain. If you have competing arguments, give them both! C. (Work together) If you didn t do so in part B, give an intuitive argument that the rope exerts a force greater than 250 newtons. D. (Work together) If you didn t do so in part B, use Newton s second law to determine whether the rope exerts a force greater than, less than, or equal to 250 newtons. (Hint: The rope pulls the child with constant velocity. So what s the acceleration?) E. (Work together) Are you 100% comfortable with your understanding of this scenario, or is there still something that needs to be reconciled? Explain. II. Refining intuition to reconcile Newton s laws with common sense Most students have, or can at least sympathize with, the intuition that upward motion requires an upward force, in which case the upward rope force must beat the downward gravitational force to make the child move up. Can we reconcile that intuition with the Newtonian conclusion that the upward force merely equals the downward force? In a previous tutorial and in lecture, you learned about Refining intuition as a reconciliation strategy. That s how we reconciled Newton s third law with the intuition that a lighter object reacts more during a collision. Let s see if refining intuition works here. A. (Work together) Consider the child, initially at rest, right when the rope first starts to pull him upward. During that initiation stage of the motion, is the upward force from the rope greater than, less than, or equal to 250 newtons (the child s weight)? 1. What does Newton s second law say about this question? (Hint: Is the child accelerating during the initiation of the motion?) 2. Does the Newtonian answer here agree with common sense? Adapted from Maryland CCLI Tutorial Project, A. Elby and R. Scherr
Watch the video (about 6 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 3-6 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 TA: So how're you guys doing? S1: Makes no sense. S4: It doesn't. S1: Nothing. We don't understand a thing. TA: Well, have you started working on number two? S1: We tried that, to see if it could help us figure it out, but it's not helping. TA: So what... what are you having trouble with? S4: Everything. S1: All we have is F = ma S4: That's it. S1: And we don't know anything else, and we don't know how that's supposed to help us answer the question. TA: Do you need that for this one? S4: Yeah / S1: It's Newton's second law. TA: OK. So, try... S1: So, Newton's second law says F = ma. TA: Right. S1: How's that supposed to help us figure out the force of the rope? Cause you just told us that the mass of the rope is negligible, it doesn't matter. TA: Right, you don't need... S1: So it doesn't really... we can't apply that equation TA: There's a force being exerted on Timmy. S1: Right. TA: It doesn't matter what's doing for what this problem's asking for. It could be, like, I don't know, some magic spirit. But the point is, Timmy's a mass. S1: Yeah. TA: And there's a force on him. S1: Yeah. TA: Is he accelerating, or is he not accelerating? And if he is accelerating, does that mean that there's a force on him or not? S1: But he's accelerating... S2: He's accelerating, he's going from zero to moving. S1: Well... he's accelerating in different ways. He's accelerating at 9.8 meters per second down... meters per second squared downward. S2: That's just velocity. 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 S1: Which is his gravity. And when he starts moving up, does that completely cancel out? S4: Yeah, it would have to. S1: Yeah, when he starts moving in a different direction, what happens to the gravity? TA: Well that, that is... S3: He's going against gravity. TA: You've hit an important issue on the head. So, he's got not one force pulling on him, not just the rope. S3: There's gravity. TA: There's gravity pulling on him. Now, when you guys did F = ma, what was the problem you were running into? S1: We don't have numbers to plug into it. TA: Well, you guys came, if I remember correctly, you guys figured out what his acceleration would have to be for him to go constant velocity, right? S2: be zero. S3: zero. S1: zero. TA: Zero. What... S1: That would mean no force. S4: Exactly. TA: What happens if gravity's pulling him one way, and the rope's pulling him the other way, at an equal...? S1: Oh, so, (S4: it's a different acceleration, it's a, like a positive acceleration) then he's moving upwards at 9.8 meters per second acceleration. TA: Well, 9.8 times... S1: Because the net force is zero? TA: Right. S1: So his upward force cancels with his downward force... meaning that the force upward is equal to the downward force meaning that they're equal forces. TA: Right. S1: OK. TA: Now that... that's kind of where we're going with this. But the issue now is, that was when he was going at a constant speed. Now we're talking... before he was going at that constant speed, he was originally at rest. What can you say about the force given that he went from being at Adapted from Maryland CCLI Tutorial Project, A. Elby and R. Scherr
99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 rest to going at a constant speed? Well, that's what the question's asking. S1: But why is he moving? TA: Well, that's what the question's asking. S1: No, but if it's an equal force, he shouldn't be moving. S2: Maybe because the mass... I think cause the mass of the machine's greater than the mass of Timmy. S1: Yeah, but that doesn't matter. S3: Yeah, that doesn't matter. TA: OK, let's imagine... let's imagine... S1: What is exerting the force doesn't matter in this situation. TA: Well, that brings in Newton's First Law. Did you guys learn Newton's First Law? S4: Mmmhmm. S1: Yeah. TA: What is it? S4: I dunno. I don't remember it. S1: We learned it. TA: OK, let's say we live in a world without any friction, without any air resistance. S1: Oh, if it's moving, it stays moving. TA: Right, unless there's a force. S1: Unless a force acts on it. S3: Unless something else acts on it, yeah. TA: Right, so when you don't have a force, what are the possibilities you could have with Timmy? S2: He can move forever. S1: He could be moving forever, or he could be staying still forever. (S3: until he reaches the machine and kills him) TA: Right. Either one of those two. 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 S1: But when he was sitting still on the ground, he still had a force on him. TA: Right. S1: Gravity. TA: Right. S3: Gravity, yeah. S1: A greater force than... S3: An equal force. TA: An equal force? S4: No, it'd have to be greater. S3: No, cause equal moves... S1: It'd have to be greater initially. S3: Equal moves, so it'd have to be greater initially. TA: That's what this question is getting at. S1: His acceleration has to change. S3: From -9.8? TA: You guys are on the right track. S4: Mmmm... you say that all the time, I don't think you really mean it. TA: No, you pretty much, I mean... the question is what would the force need to do initially in order to get him to go from zero to, um, to the speed he was at? This is qualitative, I mean, we don't have to give a number cause... S1: He has, uh... well, common sense tells me that it needs to be a greater force to get him moving. TA: Right, so that the total, the net force, the combination of the two would be... S1: Zero. Or no... positive. TA: Well, discuss, guys. Adapted from Maryland CCLI Tutorial Project, A. Elby and R. Scherr
Do you think the students are in good shape at the end of this clip? Does the TA think so? Why does he leave? This TA is in a typical teaching situation: He has not heard the discussion that took place before his arrival at the table. What does he do to get the students to fill him in? Based on what you see in the episode, what is the TA s diagnosis of these students? That is, what is he thinking their problem is, and what help does he think they need? What do you think S1 means when she says Timmy is accelerating in different ways? The TA interacts primarily with S1 in this clip. What are the risks of speaking only to her? What good reasons might the TA have for having done that? What single thing do you think he could have done better to improve that students understanding?
Now watch an earlier episode of the same students (about 40 sec). Transcript: Orange 3-5 1 2 3 4 5 6 7 8 9 10 11 S3: Is he accelerating during the initiation of the motion? S4: Yes, he has to be. He's going (S3: wait...) from zero velocity to that velocity. S1: Yes. The... no. He's accelerating downward. Timmy... S4: During the initiation? S1: has a negative acceleration when it first starts. S3: Because the force is... S1: 9.8 meters per second down. 12 13 14 15 16 17 18 19 20 21 S3: OK. S1: Cause that's what... right now, we are all 9.8 meters per second down. S3: Down. S1: Yeah. S3: OK. S1: So as it starts to get lifted, that's his acceleration. What new light does this earlier conversation shed on the later conversation with the TA? Does S1 s issue arise in that conversation? Is it addressed?
Next Tutorial Blue Group The next video is of students working together on a mechanics tutorial. Boxed below are the questions they re discussing: discuss these with your partners before we watch the video. You won t be able to do the experiments, but you will get the idea of what the students are working on. The motion detector refers to a sonic ranger that records the distance to whatever s in front of it and displays position, velocity, and/or acceleration graphs on the computer screen ask your leader for an explanation if you need one. I. Why think about your mistakes? In fifty minutes, even the best physics student doesn t have time to totally master a complex physics topic such as motion graphs. So, a major purpose of this tutorial is to help you learn strategies for avoiding and/or catching mistakes, strategies you can use throughout the course. Since reflecting on the purpose of an activity can help you get more out of it, let s start with this: F. (Answer individually) What do you see as potential benefits of explicitly thinking and talking about the mistakes you make while working through these activities? If you think dwelling on your mistakes won t be particularly helpful, explain why not. G. Discuss your answers with your group. If anyone gave part of an answer significantly different from yours, write a one-sentence-summary of that opinion. II. Distance graphs In order for this section to be effective, you must rotate who controls the computer and who does the walking. Change after every trial. A. Slow and steady, away. (Work individually) Predict what the distance vs. time graph will look like if you start 1/2 meter from the ranger and walk away from it slowly and steadily. Sketch your prediction with a dotted line. Now compare your predictions. After discussion, sketch your consensus prediction with a dashed line. Carry out the experiment. Sketch the result with a solid line. Mistake-catching lesson: If each student in the group made a correct prediction while working individually, skip this question. If someone made a mistake, try to figure out what went wrong. Specifically, if you made a mistake, write what you were thinking and how you can modify that thinking to avoid the mistake in the future. We ve found that your group can often help you with this process! If someone else made a mistake, it s your job to help them sort it out; and exam questions will reward you for being able to understand other students thinking. Sample answer: Here s a good response to this question from someone who drew a flat line instead of sloped line: I was thinking the graph shouldn t go up or down since the motion is steady; but even for steady motion, your distance from the clicker is increasing, so the graph should go up at a steady rate! The upward trend is what s steady. B. Medium fast, away. (Work individually) Predict the distance vs. time graph if you start 1 meter from the ranger and walk away from the detector medium fast and steadily. Sketch with a dotted line.
Compare/discuss. Sketch consensus with dashed line. Carry out the experiment. Remember to rotate who controls the computer and who does the walking. Sketch result with a solid line. Mistake-catching lesson: If someone made a mistake while working individually, try to figure out what went wrong. Specifically, if you made a mistake, write what you were thinking and how you can modify that thinking to avoid the mistake in the future. If someone else made a mistake, help them sort out why. C. Slow and steady, towards. (Work individually) Predict: distance vs. time graph if you start a few meters from the ranger and walk toward it slowly and steadily. Dotted line. Compare/discuss. Sketch consensus with dashed line. Carry out the experiment. Rotate who does what. Sketch result with a solid line. Mistake-catching lesson: If someone made a mistake while working individually, try to figure out what went wrong. Specifically, if you made a mistake, write what you were thinking and how you can modify that thinking to avoid the mistake in the future. If someone else made a mistake, help them sort out why. III. Working with distance graphs A. Briefly describe the difference between the graphs you made by walking slowly and the graphs you made by walking quickly. What feature of the distance vs. time graphs indicates your speed? B. Describe the difference between the graphs you made by walking toward the detector and the graphs you made by walking away from the detector. What feature of the distance vs. time graphs indicates your direction of motion? H. Test your knowledge (Work individually) Predict the distance graph if you walk away from the detector slowly and steadily for 4 seconds, then stop for 4 seconds, then walk toward the detector quickly. Sketch your prediction on the left graph below, using a dotted line. Keep in mind any mistake-catching strategies you wrote in part II above! Compare/discuss. Sketch your group consensus prediction on a graph using a dashed line. Do the experiment. When you are satisfied with your graph, sketch your group s final result. Mistake-catching lesson: If someone made a mistake while working individually, try to figure out what went wrong. Specifically, if you made a mistake, write what you were thinking and how you can modify that thinking to avoid the mistake in the future. If someone else made a mistake, help them sort out why. I. Could someone who just walked into the lab infer from the Final Result graph what your velocity was at different times during the motion? Hint: Look over your part A answer above. Watch the video (about 3 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: Blue 1-3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 S4: We have to consult with an instructor. TA: Consult with an instructor, OK. Uh, so, we re gonna flip back a couple pages to part three there. Um, you ve answered this question. Right here. Working with the distance graphs. So, I m a stupid person, I come in, I say I look at this graph and I is there a way that I could tell how fast you re going? And I don t, you know, I just look at your graph, can I tell when you re going faster or slower? S1: Yeah. TA: How? S1: By the slope. S3: By the slope, by the TA: So, again, I m stupid, I don t know what slope means. S4: Well, by the steepness of the line. TA: Steepness of the line. S4: So the less steeper it is, the slower you re going. S3: And the more steep it is, the faster you re going. S1: Right. TA: All right, cool. So that s pretty cool. So, what about could I tell what direction you re going? S1: Yes. TA: Like, if I look at the graph S3: Cause if it s moving up (S4: if you re moving up and going away) then you re moving in the positive direction and you re moving away from the detector. But if it s going down, then you re moving in a negative direction, well, you re moving towards the TA: So if it s going like this way, it means I m moving away from it. S3 and S4: Away from it. TA: All right, cool. So this is like sort of the main kind of physics content that we wanted to get out of this tutorial, which you ve just kind of articulated. S1: OK. TA: Now I m gonna ask you about, like, the reasoning strategies. So, were there any differences between what you predicted and what you saw, what your experiment 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 was? That you made a prediction, and then you looked at the graph and it was a little bit different? S1: Uh, maybe there would have been more roundedness on when it changed directions or something like that, or when you stopped. TA: So, were you able to reconcile that? How S1: Well, we just knew it was not gonna be an exact S3: Cause he paused for like S1: I m gonna pause, (S2: He paused for more than) I m gonna speed up to get to that speed. S4: And also our time was kind of like, there was more time there than four seconds. S2: Yeah, it wasn t exactly four seconds. S3: So that means he paused for more than four seconds, then. S1: Yeah right. TA: OK, so let me, let me for one second go back to this rounded issue here. Cause you were saying how did you make sense of that? S1: Uh, it s because I m not gonna be going like, I m not gonna stop almost immediately, I m just gonna slow down a little bit before I stop, cause I m not a machine, so S4: Right. TA: So, I think this is something cool, because your prediction said that look, it s just gonna be like this sharp, sharp line here and what you re seeing is that it s kind of rounded. But you have an explanation for that, you re saying Oh, it s not exactly rounded because, you know, it takes a little bit to stop and a little bit to start up. So I think that s cool, I think that s something that, I mean, you should include. You know, maybe it s not a mistake mistake, but you were thinking something in your head that really kind of rigid, and you saw something different, but you have an explanation for that, which is cool. S1: OK, all right, thanks.
The TA takes on the persona of a stupid person. You may or may not like his terminology, but in either case, what do you think he is trying to accomplish? Is it your feeling that all the students are actively engaged in the conversation with the TA? What does the TA do to promote engagement by all the students? Is there more he could be doing? Notice how this TA draws the students attention to both the physics content of the tutorial and the reasoning strategies. How do the students respond to the distinction he s making? Do they reflect on their reasoning strategies, or are they still answering in terms of the physics content? What is it that the TA is saying is so cool toward the end of the video? What s so cool about it? Did you notice anything about the TA s body language? What nonverbal messages does he send? What about the tone of how he talks? What are some key differences in the style of these two TAs?
Partner Exercise: Practice your questioning. (5 min) The students from the first video clearly still need some help. Review the transcript individually, and then brainstorm with a partner to think of questions that the TA could ask to help move the group towards a better understanding of the physics of this situation. Try to come up with as many different types of questions as you can.