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Due to technical difficulties, only a portion of lecture 1 is available for viewing
Welcome to Teaching College-Level Science and Engineering.
Now, the title contains the word "teaching," which may spark some questions in your mind.
For example, is teaching just an art? Or is it something that's just - something you're born with.
In which case, either you have it or you don't have it. Well, obviously I don't believe that
or I wouldn't be teaching a course on it.
What would be the point?
Or is it purely a science, where there's a set of equations and procedures to learn,
and then all of a sudden you'll be an excellent teacher?
Well, actually, it's neither and it's both. It's things that we're all born with,
on the one hand, and they're also procedures and techniques, and ways of thinking
that will improve how you teach, and that we can all learn.
So it's a happy mix, my favorite mix,
an art and a science. So, for example, another example that's an art and a science is book design.
So compared for example to just pure art, painting, say modern painting, very unconstrained
vs. say, biology procedures in the laboratory
you know, very very closely specified. It's somewhere in between there is an art but there is, of all
of the arts, of colors, of space, but they all have to
be used together to achieve a particular purpose. So, again, there are some beautifully designed books and
some not so beautifully designed books. And there are principles behind that that we can use to design good books.
Simiilarly, there are principles we can use to design good teaching.
So this is the whole point of this semester is to design good teaching and how you do that.
And rather than give you a big long theory about it,
because actually there isn't really theory
so much in the equivalent to say Einstein's theory of relativity,
but there's principles to learn.
The best way to learn those principles is
with an example.
So what we're gonna do today is
I'm going to do an example of teaching with you.
We're gonna do it slightly sped-up version of what we'd normally do
say if we were actually using this example in a class.
Then we're gonna analyze why it was done that way.
and from an analysis, general principles of teaching will come out
that will be address throughout the semester
and they'll be addressed in the context of particular tasks,
for example, how to make slides that are useful for teaching.
How to use a blackboard.
How to teach equations.
How to design a whole course.
How to make problems.
So all of those tasks will be the week-by-week subjects
and in each task, all the principles that we're gonna talk about now
will show up in those tasks and you'll see the principles illustrated repeatedly.
So, the problem. One of my favorites,
so these are two cones
one is -- has twice the dimensions of the other cones.
So let me show you how I made the cones.
So I printed out a circle and just cut out
one quarter of the circle
and then I taped this edge to that edge.
Or in mathematician speak, I identified the edges
which I now know means I taped the edges together.
and then you get a cone like that.
So this cone and the other cone were cut out of the same sheet of paper
except this one has twice the linear dimensions in its circle.
This circle was seven centimeters in radius and this is three and a half centimeters in radius.
Other than that, they're the same.
The question is which one has the higher terminal of velocity or are they more comparable.
So the question is this.
I'm gonna drop them and the question is
what is the ratio of their terminal velocities?
So the ratio of the big cone's terminal velocity to the small cone's terminal velocity
is equals to what and you get choices along this axis
So here is...
Okay, so those are the five regions to choose from.
So you have five choices for the ratio
roughly one quarter
some range here, because nothing's exact
and we're definitely not gonna do an exact experiment.
Roughly one half, roughly one, roughly two, or roughly four.
So does everyone understand the question?
You're gonna get to try it yourself.
Question about the question
I don't know if you could restate the question... actually there was a signing sheet going around... and I sorta lost it.
So, uh, yeah, can I restate the question, no problem.
So I'm gonna drop them
just like this no tricks,
I'm not gonna flip this one around or anything.
And the question is, what's the ratio of their terminal speeds.
So right away, as soon as you let go of them,
they come to a steady speed,
which is their terminal velocity.
And the question is how do the terminal speeds of the big one and the small one differ.
So in particular, the question is what's the ratio?
And there's five choices for them.
Okay.
That help?
-Yes, and what were the dimensions of them again.
-So this guy is -- he was cut out of a circle who was 7 centimeters in radius.
And this guy was cut out of a circle who was 3.5 centimeters in radius.
And then I was also very careful to use-- do this right?--
I used half the width of tape on the small guy as I did on the big guy
just to get it really very perfect scale.
Any questions about the question?
Okay, so think for yourself for about 30 seconds or so
just to induct yourself into the problem
and then we'll take a vote.
And then you'll have a chance to discuss it with each other.
Okay, let's just take a vote
so I understand I haven't given all of you enough time to come up with an exact answer or calculate anything.
So let's just get a straw poll and then you'll have a chance to argue about it with your neighbor.
So who votes for 1/4 which is--
so let's see-- 1, 2, 3, 4, 5, 6.
Who votes for 1/2?
[counts] 12
Who votes for C?
About 22.
Who votes for D?
No takers.
No takers for D.
How about E?
Okay, so
now find a neighbor or two,
one or two neighbors,
introduce yourself to your neighbor,
and also by the way, unless you're taking notes on your laptop,
if you could close your laptop, that would be very helpful for the purpose of discussion in this whole
course.
So find a neighbor or two, introduce yourself,
you'll be given a chance to meet graduate students from across te institute,
and try to convince them about your answer.
Especially if you have a different answer.
Or if you happen to share an answer, try to figure out why you're sure of it
or if you're not sure of it, settle...
So, discussion time.
And if you have any questions that come up as you're discussing,
raise your hand and I'll come and wonder over.
Okay, so meanwhile I also handed out
feedback sheets for the end of the session
which I'll ask you to spend a minute on at the end.
You'll notice one of the question is what's the most confusing thing?
So if anything really confusing comes up during the whole session,
you can just put it right there, you don't have to wait until the end,
or if there's something you really liked or hated,
that's question 2, you can put whenever to come up.
But, vote #2 and then we'll take some reasons...
so...
One quarter.
One, two, three.
Okay, four.
One half.
Halves don't have it.
There's one... okay great. 4, 5, 6.
Equall.
Let's call it 30.
Two
and four.
Okay, so
thanks for the votes.
Let's take reasons for any of them.
I'll take reasons for any of them, I'll put them up here.
You don't even have to agree with the reasons,
just something you guys discussed and something that was plausible.
-C...
-Oh....
-When you do these activities,
there's always some... [indistinct]
I want to know what you would do in that kind of situation.
-So, you're hmm...
[laughter] I'm not sure how to phrase this.
Uh...
Let me just take other comments.
[laughter]
I'll come to it afterwards.
Other comments
for any of the reasons.
So again, it doesn't have to be anything you necessarily believe
but things that are plausible
and that's actually more instructive than what you think is for sure right,
because you're trying to figure out what might be true and you're expanding
the ways you're thinking.
-C, because they have identical mass to certain...
-C, so mass-to-area ratio is the same.
Okay, can people think of plausible reasons against that argument?
Yes.
-I have no idea what the actual formula is.
-Right.
-There was a square there...
-Right, so I'll call this not C.
So supposedly, formual actually depended on the square root of A
or something like that.
You know maybe---- say, one chance out of three that it has A to the first power here.
It could have A to the 1/2 or 8 to the 2.
So, could be...
A to the k
M over A to the K for K not equal to one.
Okay, others.
4 against C, intuitive reasons, or for any of the others.
Okay, so hopefully that's...
-[indistinct]
...that air resistance goes with the area
and the gravitational force...
-Okay, so let's see.
F drag partial to area and weight.
So that's the argument for which choice?
For C, okay.
How do you know that the drab scales are the area.
Maybe the scales with the square root of area.
Any argument pro or con?
Okay, yeah.
-scales with the area...you can just break it up...
-Okay, so there's a ....
So for this, let's say there's a ... for subdividing
I'll just know that is subdividing.
Okay, yeah.
-Some weird shape... and then go to the rest of the pieces so...
-So it may depend on the division--I mean, the geometry,
so I'll put that here as geometry.
What else might it depend on?
For example, is air resistance say always proportional to area?
Hmm.
Yeah?
-...Depend on the material of the surface.
-Okay, so it might depend on the material
and it certainly does, which is actually why I was careful
to construct them out of the same piece of paper,
so let me put this.
Material...
So the surface roughness.
[indisctinct question]
-Okay, so whether they fall vertically or downward.
Yeah, that's true.
So it might depend on the way I drop them.
So to make us not have to worry about that,
I'll just drop them simultaniously, pointing downward.
So the fall configuration.
So there's all these other variables.
Okay, so let's do the experiment and then I'll come back to your question.
Okay, so let's do the experiement this way
so I'll stand on the table
and pray that I have matching socks on with is sort of 80% these days.
It's increased.
And I will drop them on the count of 3.
1--
Are they both, the points, about the same level?
They look sort of to me but
my depth perception is actually quite bad
so is that about equal?
Okay, so 1, 2, 3.
Simulateous.
Okay, so there you have choice C.
Interesting consequence of that.
So what that shows is that
drag in this case is proportional to area.
It turns out, that that's not always the case.
So drag very often,
well, not very often in everyday life,
but very easily can be proportional to...
proportional to size.
And you don't know ahead of time which one it's gonna be.
So it vari--- so it turns out at slow speeds,
low Reynold's number
this is true.
Turns out at high Reynold's number, this is true.
And this is the simplest experiment to show that.
So what this shows is that drag is proportional to area
so with the same velocity,
the extra weight is balanced by the extra drag force.
Exactly, four to one.
And what that shows now--the consequence--is that
I'm gonna replace the proportional with a twittle.
So it has an area in it,
so I'm gonna get something with the correct units in it.
So it has an area in it
and now you have left the play with
density, speed, and viscosity.
So now let's actually construct the drag force as a result of that.
So we know from the experiment, it's proportional to area.
And now among these,
so this here is the kinematic viscosity,
which is the one you may be more familiar with divided by row, the density.
So, we got to put some of these guys in, some of these guys in,
and some of these guys in.
And let the units come in as a force.
Well, one of them we can do right away.
There's how many powers of mass over on this side?
In a force, just one.
Right, and there's one here.
So we need to get one over on this side.
Now, among all these guys, which of them have mass in them?
Not this one, 'cause you divided them all out.
Not velocity,
only density.
And density is one power of mass,
so you have to put one density.
Question?
[indistinct question]
So this is a force.
Good question.
So drag is a force.
So this is just newtons or uh, mass legth per time square.
Does it help?
So it's just newtons.
In SI Newtons or in general, mass length per time squared.
So mass times an acceleration.
Okay, so now, we've matched the units of mass
and there's-- but we haven't matched the units of time yet.
So let's sort out the time.
There's no time here, there's not time there.
There's T to the minus 2 there.
Well -- what can we do about that?
We have to match -- We have to throw in some v and some nu (viscosity)
And the problem is we don't know how much
So the time doesn't helps us enough
Turns out, to make the time and the length work
The simultaneous constraint
The only way we can do it is that
Okay, making the same argument
Just to get the masses to match, the legths to match and the times to match
This is the only way to do it
So you don't have any viscosity
So actually that's the simplest experiment I know
To show that the drag at high speed, most flows are actually high speed,
High Reynolds number
Is independent from viscosity
So it's ro, A, v squared
And that is a great result because it tells you a lot of stuff
About everyday flows and everyday life
Like for example, why did people reduced speed
Speed limit on the highway back in the 70's,
To conserve gas
Well, on the highway
You're burning gasoline to fight drag
So if you reduce the speed
You reduce the drag,
You reduce the amount of gasoline
In particular, if reduce speed by 20%,
You reduce v squared by 40%
Which reduces drag by 40%
Decreased gas consumption by 40%
So you can these things right way, just by a simple formula
Which is a imediate consequence of this experiment
Now, turns out, this -- how do you get that to work?
This is the low Reynolds number limit
You can't deduce it from this experiment, but, if you know that this is true, you can make the same argument
And figure out, how the drag force varies for low Reynolds number
Okay, now let's just check wheter this formula here
That we deduced, works at all
So the folow up question is the following
Which is that I have -- 1, 2, 3, 4
Here on this side, I have 4 small cones
They're all identical to this small cone
So 1 small cone, 2 small cones, 3 small cones, 4 small cones
So I'm gonna stack all 4 small cones, into a thick small cone
And I'm gonna race it against one small cone
So the question is: what is the ratio of these guys' terminal speeds?
So let's call v4 and v1
So, 4...
Okay, so, what is the ratio of their terminal speeds?
1/4, 1/2, 1, 2 or 4?
So, talk to your neighboor for just a minute, we'll take a quick vote and we'll do the experiment
Okay, so let's take a vote and then we'll do the experiment
1/4?
Who votes for 1/4 ratio?
Who votes for 1/2?
1?
2?
It's about 35...
4?
Oh, 10
Okay, so, let's do the experiment
1, 2, 3, 4 of them
Okay so now let me drop them like --- that
Well it's kinda of hard to tell isn't it?
So that was actually not well designed experiment, right?
Because you actually have to get it out of timer and decide wich one is going faster
And measure how long it took
It would be nice if had a way that was just like the other experiment
What was nice about the other experiment is when I drop them,
You got the answer, by the fact that they hit simultaneously
So if we can make them hit simultaneously
Then that would be nice, now what do I have to do to do that?
Well I either have to -- Yeah -- I either have to switch their heights
4 to 1 or 2 to 1
So, let's try 4 to 1
Okay -- [laughter] -- Is that sort of 4 to 1?
No? What do I have to do?
This guy got go down
This is where my depth perception really fails me
So I only have a monocular vision. I can see with both eyes, but I don't binocular fuse
So I can't tell depth
[Indistinguishable suggestion from aluminum]
Oh that's true