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Due to technical difficulties, only a portion of lecture 1 is available for viewing

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Welcome to Teaching College-Level Science and Engineering.

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Now, the title contains the word "teaching," which may spark some questions in your mind.

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For example, is teaching just an art? Or is it something that's just - something you're born with.

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In which case, either you have it or you don't have it. Well, obviously I don't believe that

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or I wouldn't be teaching a course on it.

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What would be the point?

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Or is it purely a science, where there's a set of equations and procedures to learn,

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and then all of a sudden you'll be an excellent teacher?

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Well, actually, it's neither and it's both. It's things that we're all born with,

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on the one hand, and they're also procedures and techniques, and ways of thinking

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that will improve how you teach, and that we can all learn.

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So it's a happy mix, my favorite mix,

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an art and a science. So, for example, another example that's an art and a science is book design.

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So compared for example to just pure art, painting, say modern painting, very unconstrained

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vs. say, biology procedures in the laboratory

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you know, very very closely specified. It's somewhere in between there is an art but there is, of all

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of the arts, of colors, of space, but they all have to

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be used together to achieve a particular purpose. So, again, there are some beautifully designed books and

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some not so beautifully designed books. And there are principles behind that that we can use to design good books.

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Simiilarly, there are principles we can use to design good teaching.

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So this is the whole point of this semester is to design good teaching and how you do that.

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And rather than give you a big long theory about it,

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because actually there isn't really theory

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so much in the equivalent to say Einstein's theory of relativity,

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but there's principles to learn.

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The best way to learn those principles is

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with an example.

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So what we're gonna do today is

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I'm going to do an example of teaching with you.

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We're gonna do it slightly sped-up version of what we'd normally do

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say if we were actually using this example in a class.

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Then we're gonna analyze why it was done that way.

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and from an analysis, general principles of teaching will come out

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that will be address throughout the semester

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and they'll be addressed in the context of particular tasks,

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for example, how to make slides that are useful for teaching.

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How to use a blackboard.

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How to teach equations.

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How to design a whole course.

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How to make problems.

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So all of those tasks will be the week-by-week subjects

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and in each task, all the principles that we're gonna talk about now

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will show up in those tasks and you'll see the principles illustrated repeatedly.

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So, the problem. One of my favorites,

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so these are two cones

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one is -- has twice the dimensions of the other cones.

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So let me show you how I made the cones.

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So I printed out a circle and just cut out

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one quarter of the circle

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and then I taped this edge to that edge.

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Or in mathematician speak, I identified the edges

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which I now know means I taped the edges together.

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and then you get a cone like that.

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So this cone and the other cone were cut out of the same sheet of paper

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except this one has twice the linear dimensions in its circle.

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This circle was seven centimeters in radius and this is three and a half centimeters in radius.

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Other than that, they're the same.

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The question is which one has the higher terminal of velocity or are they more comparable.

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So the question is this.

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I'm gonna drop them and the question is

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what is the ratio of their terminal velocities?

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So the ratio of the big cone's terminal velocity to the small cone's terminal velocity

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is equals to what and you get choices along this axis

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So here is...

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Okay, so those are the five regions to choose from.

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So you have five choices for the ratio

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roughly one quarter

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some range here, because nothing's exact

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and we're definitely not gonna do an exact experiment.

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Roughly one half, roughly one, roughly two, or roughly four.

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So does everyone understand the question?

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You're gonna get to try it yourself.

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Question about the question

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I don't know if you could restate the question... actually there was a signing sheet going around... and I sorta lost it.

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So, uh, yeah, can I restate the question, no problem.

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So I'm gonna drop them

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just like this no tricks,

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I'm not gonna flip this one around or anything.

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And the question is, what's the ratio of their terminal speeds.

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So right away, as soon as you let go of them,

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they come to a steady speed,

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which is their terminal velocity.

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And the question is how do the terminal speeds of the big one and the small one differ.

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So in particular, the question is what's the ratio?

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And there's five choices for them.

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Okay.

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That help?

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-Yes, and what were the dimensions of them again.

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-So this guy is -- he was cut out of a circle who was 7 centimeters in radius.

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And this guy was cut out of a circle who was 3.5 centimeters in radius.

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And then I was also very careful to use-- do this right?--

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I used half the width of tape on the small guy as I did on the big guy

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just to get it really very perfect scale.

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Any questions about the question?

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Okay, so think for yourself for about 30 seconds or so

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just to induct yourself into the problem

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and then we'll take a vote.

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And then you'll have a chance to discuss it with each other.

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Okay, let's just take a vote

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so I understand I haven't given all of you enough time to come up with an exact answer or calculate anything.

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So let's just get a straw poll and then you'll have a chance to argue about it with your neighbor.

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So who votes for 1/4 which is--

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so let's see-- 1, 2, 3, 4, 5, 6.

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Who votes for 1/2?

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[counts] 12

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Who votes for C?

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About 22.

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Who votes for D?

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No takers.

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No takers for D.

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How about E?

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Okay, so

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now find a neighbor or two,

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one or two neighbors,

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introduce yourself to your neighbor,

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and also by the way, unless you're taking notes on your laptop,

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if you could close your laptop, that would be very helpful for the purpose of discussion in this whole

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course.

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So find a neighbor or two, introduce yourself,

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you'll be given a chance to meet graduate students from across te institute,

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and try to convince them about your answer.

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Especially if you have a different answer.

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Or if you happen to share an answer, try to figure out why you're sure of it

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or if you're not sure of it, settle...

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So, discussion time.

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And if you have any questions that come up as you're discussing,

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raise your hand and I'll come and wonder over.

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Okay, so meanwhile I also handed out

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feedback sheets for the end of the session

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which I'll ask you to spend a minute on at the end.

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You'll notice one of the question is what's the most confusing thing?

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So if anything really confusing comes up during the whole session,

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you can just put it right there, you don't have to wait until the end,

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or if there's something you really liked or hated,

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that's question 2, you can put whenever to come up.

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But, vote #2 and then we'll take some reasons...

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so...

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One quarter.

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One, two, three.

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Okay, four.

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One half.

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Halves don't have it.

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There's one... okay great. 4, 5, 6.

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Equall.

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Let's call it 30.

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Two

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and four.

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Okay, so

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thanks for the votes.

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Let's take reasons for any of them.

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I'll take reasons for any of them, I'll put them up here.

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You don't even have to agree with the reasons,

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just something you guys discussed and something that was plausible.

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-C...

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-Oh....

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-When you do these activities,

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there's always some... [indistinct]

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I want to know what you would do in that kind of situation.

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-So, you're hmm...

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[laughter] I'm not sure how to phrase this.

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Uh...

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Let me just take other comments.

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[laughter]

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I'll come to it afterwards.

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Other comments

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for any of the reasons.

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So again, it doesn't have to be anything you necessarily believe

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but things that are plausible

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and that's actually more instructive than what you think is for sure right,

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because you're trying to figure out what might be true and you're expanding

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the ways you're thinking.

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-C, because they have identical mass to certain...

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-C, so mass-to-area ratio is the same.

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Okay, can people think of plausible reasons against that argument?

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Yes.

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-I have no idea what the actual formula is.

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-Right.

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-There was a square there...

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-Right, so I'll call this not C.

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So supposedly, formual actually depended on the square root of A

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or something like that.

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You know maybe---- say, one chance out of three that it has A to the first power here.

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It could have A to the 1/2 or 8 to the 2.

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So, could be...

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A to the k

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M over A to the K for K not equal to one.

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Okay, others.

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4 against C, intuitive reasons, or for any of the others.

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Okay, so hopefully that's...

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-[indistinct]

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...that air resistance goes with the area

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and the gravitational force...

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-Okay, so let's see.

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F drag partial to area and weight.

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So that's the argument for which choice?

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For C, okay.

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How do you know that the drab scales are the area.

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Maybe the scales with the square root of area.

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Any argument pro or con?

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Okay, yeah.

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-scales with the area...you can just break it up...

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-Okay, so there's a ....

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So for this, let's say there's a ... for subdividing

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I'll just know that is subdividing.

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Okay, yeah.

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-Some weird shape... and then go to the rest of the pieces so...

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-So it may depend on the division--I mean, the geometry,

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so I'll put that here as geometry.

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What else might it depend on?

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For example, is air resistance say always proportional to area?

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Hmm.

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Yeah?

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-...Depend on the material of the surface.

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-Okay, so it might depend on the material

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and it certainly does, which is actually why I was careful

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to construct them out of the same piece of paper,

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so let me put this.

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Material...

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So the surface roughness.

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[indisctinct question]

227
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-Okay, so whether they fall vertically or downward.

228
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Yeah, that's true.

229
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So it might depend on the way I drop them.

230
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So to make us not have to worry about that,

231
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I'll just drop them simultaniously, pointing downward.

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So the fall configuration.

233
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So there's all these other variables.

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Okay, so let's do the experiment and then I'll come back to your question.

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Okay, so let's do the experiement this way

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so I'll stand on the table

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and pray that I have matching socks on with is sort of 80% these days.

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It's increased.

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And I will drop them on the count of 3.

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1--

241
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Are they both, the points, about the same level?

242
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They look sort of to me but

243
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my depth perception is actually quite bad

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so is that about equal?

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Okay, so 1, 2, 3.

246
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Simulateous.

247
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Okay, so there you have choice C.

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Interesting consequence of that.

249
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So what that shows is that

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drag in this case is proportional to area.

251
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It turns out, that that's not always the case.

252
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So drag very often,

253
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well, not very often in everyday life,

254
00:17:10,260 --> 00:17:16,178
but very easily can be proportional to...

255
00:17:20,835 --> 00:17:23,125
proportional to size.

256
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And you don't know ahead of time which one it's gonna be.

257
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So it vari--- so it turns out at slow speeds,

258
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low Reynold's number

259
00:17:31,687 --> 00:17:32,679
this is true.

260
00:17:32,679 --> 00:17:34,953
Turns out at high Reynold's number, this is true.

261
00:17:34,969 --> 00:17:37,409
And this is the simplest experiment to show that.

262
00:17:37,409 --> 00:17:40,526
So what this shows is that drag is proportional to area

263
00:17:40,526 --> 00:17:42,895
so with the same velocity,

264
00:17:42,895 --> 00:17:50,055
the extra weight is balanced by the extra drag force.

265
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Exactly, four to one.

266
00:17:52,445 --> 00:18:00,349
And what that shows now--the consequence--is that

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I'm gonna replace the proportional with a twittle.

268
00:18:07,663 --> 00:18:09,286
So it has an area in it,

269
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so I'm gonna get something with the correct units in it.

270
00:18:12,057 --> 00:18:13,988
So it has an area in it

271
00:18:13,988 --> 00:18:16,440
and now you have left the play with

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00:18:16,440 --> 00:18:20,156
density, speed, and viscosity.

273
00:18:20,156 --> 00:18:23,814
So now let's actually construct the drag force as a result of that.

274
00:18:23,814 --> 00:18:27,499
So we know from the experiment, it's proportional to area.

275
00:18:28,392 --> 00:18:29,763
And now among these,

276
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so this here is the kinematic viscosity,

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which is the one you may be more familiar with divided by row, the density.

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00:18:39,887 --> 00:18:44,214
So, we got to put some of these guys in, some of these guys in,

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and some of these guys in.

280
00:18:46,022 --> 00:18:49,091
And let the units come in as a force.

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00:18:49,091 --> 00:18:51,842
Well, one of them we can do right away.

282
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There's how many powers of mass over on this side?

283
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In a force, just one.

284
00:18:58,842 --> 00:19:00,142
Right, and there's one here.

285
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So we need to get one over on this side.

286
00:19:02,694 --> 00:19:04,924
Now, among all these guys, which of them have mass in them?

287
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Not this one, 'cause you divided them all out.

288
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Not velocity,

289
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only density.

290
00:19:10,984 --> 00:19:12,095
And density is one power of mass,

291
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so you have to put one density.

292
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Question?

293
00:19:17,759 --> 00:19:19,244
[indistinct question]

294
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So this is a force.

295
00:19:21,555 --> 00:19:22,602
Good question.

296
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So drag is a force.

297
00:19:24,474 --> 00:19:32,583
So this is just newtons or uh, mass legth per time square.

298
00:19:32,583 --> 00:19:34,705
Does it help?

299
00:19:34,705 --> 00:19:38,250
So it's just newtons.

300
00:19:38,250 --> 00:19:41,720
In SI Newtons or in general, mass length per time squared.

301
00:19:41,720 --> 00:19:46,224
So mass times an acceleration.

302
00:19:46,224 --> 00:19:50,441
Okay, so now, we've matched the units of mass

303
00:19:50,441 --> 00:19:54,428
and there's-- but we haven't matched the units of time yet.

304
00:19:54,428 --> 00:19:56,165
So let's sort out the time.

305
00:19:56,165 --> 00:19:58,515
There's no time here, there's not time there.

306
00:20:00,190 --> 00:20:01,865
There's T to the minus 2 there.

307
99:59:59,999 --> 99:59:59,999
Well -- what can we do about that?

308
99:59:59,999 --> 99:59:59,999
We have to match -- We have to throw in some v and some nu (viscosity)

309
99:59:59,999 --> 99:59:59,999
And the problem is we don't know how much

310
99:59:59,999 --> 99:59:59,999
So the time doesn't helps us enough

311
99:59:59,999 --> 99:59:59,999
Turns out, to make the time and the length work

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The simultaneous constraint

313
99:59:59,999 --> 99:59:59,999
The only way we can do it is that

314
99:59:59,999 --> 99:59:59,999
Okay, making the same argument

315
99:59:59,999 --> 99:59:59,999
Just to get the masses to match, the legths to match and the times to match

316
99:59:59,999 --> 99:59:59,999
This is the only way to do it

317
99:59:59,999 --> 99:59:59,999
So you don't have any viscosity

318
99:59:59,999 --> 99:59:59,999
So actually that's the simplest experiment I know

319
99:59:59,999 --> 99:59:59,999
To show that the drag at high speed, most flows are actually high speed,

320
99:59:59,999 --> 99:59:59,999
High Reynolds number

321
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Is independent from viscosity

322
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So it's ro, A, v squared

323
99:59:59,999 --> 99:59:59,999
And that is a great result because it tells you a lot of stuff

324
99:59:59,999 --> 99:59:59,999
About everyday flows and everyday life

325
99:59:59,999 --> 99:59:59,999
Like for example, why did people reduced speed

326
99:59:59,999 --> 99:59:59,999
Speed limit on the highway back in the 70's,

327
99:59:59,999 --> 99:59:59,999
To conserve gas

328
99:59:59,999 --> 99:59:59,999
Well, on the highway

329
99:59:59,999 --> 99:59:59,999
You're burning gasoline to fight drag

330
99:59:59,999 --> 99:59:59,999
So if you reduce the speed

331
99:59:59,999 --> 99:59:59,999
You reduce the drag,

332
99:59:59,999 --> 99:59:59,999
You reduce the amount of gasoline

333
99:59:59,999 --> 99:59:59,999
In particular, if reduce speed by 20%,

334
99:59:59,999 --> 99:59:59,999
You reduce v squared by 40%

335
99:59:59,999 --> 99:59:59,999
Which reduces drag by 40%

336
99:59:59,999 --> 99:59:59,999
Decreased gas consumption by 40%

337
99:59:59,999 --> 99:59:59,999
So you can these things right way, just by a simple formula

338
99:59:59,999 --> 99:59:59,999
Which is a imediate consequence of this experiment

339
99:59:59,999 --> 99:59:59,999
Now, turns out, this -- how do you get that to work?

340
99:59:59,999 --> 99:59:59,999
This is the low Reynolds number limit

341
99:59:59,999 --> 99:59:59,999
You can't deduce it from this experiment, but, if you know that this is true, you can make the same argument

342
99:59:59,999 --> 99:59:59,999
And figure out, how the drag force varies for low Reynolds number

343
99:59:59,999 --> 99:59:59,999
Okay, now let's just check wheter this formula here

344
99:59:59,999 --> 99:59:59,999
That we deduced, works at all

345
99:59:59,999 --> 99:59:59,999
So the folow up question is the following

346
99:59:59,999 --> 99:59:59,999
Which is that I have -- 1, 2, 3, 4

347
99:59:59,999 --> 99:59:59,999
Here on this side, I have 4 small cones

348
99:59:59,999 --> 99:59:59,999
They're all identical to this small cone

349
99:59:59,999 --> 99:59:59,999
So 1 small cone, 2 small cones, 3 small cones, 4 small cones

350
99:59:59,999 --> 99:59:59,999
So I'm gonna stack all 4 small cones, into a thick small cone

351
99:59:59,999 --> 99:59:59,999
And I'm gonna race it against one small cone

352
99:59:59,999 --> 99:59:59,999
So the question is: what is the ratio of these guys' terminal speeds?

353
99:59:59,999 --> 99:59:59,999
So let's call v4 and v1

354
99:59:59,999 --> 99:59:59,999
So, 4...

355
99:59:59,999 --> 99:59:59,999
Okay, so, what is the ratio of their terminal speeds?

356
99:59:59,999 --> 99:59:59,999
1/4, 1/2, 1, 2 or 4?

357
99:59:59,999 --> 99:59:59,999
So, talk to your neighboor for just a minute, we'll take a quick vote and we'll do the experiment

358
99:59:59,999 --> 99:59:59,999
Okay, so let's take a vote and then we'll do the experiment

359
99:59:59,999 --> 99:59:59,999
1/4?

360
99:59:59,999 --> 99:59:59,999
Who votes for 1/4 ratio?

361
99:59:59,999 --> 99:59:59,999
Who votes for 1/2?

362
99:59:59,999 --> 99:59:59,999
1?

363
99:59:59,999 --> 99:59:59,999
2?

364
99:59:59,999 --> 99:59:59,999
It's about 35...

365
99:59:59,999 --> 99:59:59,999
4?

366
99:59:59,999 --> 99:59:59,999
Oh, 10

367
99:59:59,999 --> 99:59:59,999
Okay, so, let's do the experiment

368
99:59:59,999 --> 99:59:59,999
1, 2, 3, 4 of them

369
99:59:59,999 --> 99:59:59,999
Okay so now let me drop them like --- that

370
99:59:59,999 --> 99:59:59,999
Well it's kinda of hard to tell isn't it?

371
99:59:59,999 --> 99:59:59,999
So that was actually not well designed experiment, right?

372
99:59:59,999 --> 99:59:59,999
Because you actually have to get it out of timer and decide wich one is going faster

373
99:59:59,999 --> 99:59:59,999
And measure how long it took

374
99:59:59,999 --> 99:59:59,999
It would be nice if had a way that was just like the other experiment

375
99:59:59,999 --> 99:59:59,999
What was nice about the other experiment is when I drop them,

376
99:59:59,999 --> 99:59:59,999
You got the answer, by the fact that they hit simultaneously

377
99:59:59,999 --> 99:59:59,999
So if we can make them hit simultaneously

378
99:59:59,999 --> 99:59:59,999
Then that would be nice, now what do I have to do to do that?

379
99:59:59,999 --> 99:59:59,999
Well I either have to -- Yeah -- I either have to switch their heights

380
99:59:59,999 --> 99:59:59,999
4 to 1 or 2 to 1

381
99:59:59,999 --> 99:59:59,999
So, let's try 4 to 1

382
99:59:59,999 --> 99:59:59,999
Okay -- [laughter] -- Is that sort of 4 to 1?

383
99:59:59,999 --> 99:59:59,999
No? What do I have to do?

384
99:59:59,999 --> 99:59:59,999
This guy got go down

385
99:59:59,999 --> 99:59:59,999
This is where my depth perception really fails me

386
99:59:59,999 --> 99:59:59,999
So I only have a monocular vision. I can see with both eyes, but I don't binocular fuse

387
99:59:59,999 --> 99:59:59,999
So I can't tell depth

388
99:59:59,999 --> 99:59:59,999
[Indistinguishable suggestion from aluminum]

389
99:59:59,999 --> 99:59:59,999
Oh that's true