Change in demand versus change in quantity demanded

WEBVTT
Kind: captions
Language: en

00:00:00.591 --> 00:00:02.189
- [Instructor] What we're
going to do in this video

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is a deep dive into the
difference between demand

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and quantity demanded.

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In particular, we're gonna
focus on change in demand

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versus change in quantity demanded.

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And so just as context, I
have price versus quantity

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here for brand X of
cars in a certain market

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and you see the demand
curve for brand X of cars

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and we see the it follows
the classic law of demand.

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At a high price, there is
a low quantity demanded,

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and so this is already trying
to draw the distinction.

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A quantity demanded,
so I'll call this qd1,

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is associated with a particular
point on the demand curve,

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it's not the whole curve itself.

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When people talk about demand,

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they're talking about the whole curve.

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But just following on of what I just said,

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following the law of
demand at a low price,

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this is associated with, if
we go to the demand curve,

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a high quantity demanded,
quantity demanded two.

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And so to be very particular about this,

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quantity demanded is associated
with a particular point

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on the demand curve while
the demand curve is the set

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of all of these points that
show how price and quantity

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are associated.

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So with that out of the way,
to make things more tangible,

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let's go through a bunch
of different circumstances

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and think about whether they would result

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in a change in demand versus
a change in quantity demanded.

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So in this first scenario
we say car dealerships

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slash prices by 10%.

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Would that result in a change in demand,

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which would involve
shifting our demand curve,

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or would it involve a
shift along the curve,

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a change in quantity demanded?

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Pause the video and try to figure it out.

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Well, there's a couple of
ways to think about it.

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In order to shift the demand curve itself

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the one way I think about
it is if you were to pick

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a given price, if you were
to pick a given price,

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does what's described here
in any way shift the quantity

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that would demanded at that price?

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Well, no, this is not
shifting how much consumers

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would want to buy at that price.

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This is just shifting the price itself.

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So this is going to be a
shift along the demand curve.

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So this would be a scenario where maybe

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the equilibrium price, and
we'll talk more about that

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in future videos, maybe
the equilibrium price

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and quantity demanded are
associated with that point

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right over here before car
dealers slashed their prices.

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So let's call this quantity demanded,

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let's call that quantity demanded three.

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But then when they slashed their prices,

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the prices go down, and so
we end up with this point

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on our demand curve, and so
this would be quantity demanded,

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quantity demanded four.

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So this would be a change

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in quantity demanded right over here,

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so change, I'll do delta for change in,

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change in quantity demanded.

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And in this case, the
quantity demanded would go up.

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What about the price
of gasoline increases?

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Pause this video.

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Think about what would happen.

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Would that change the
quantity demanded for the cars

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or would it shift the entire demand curve?

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Well, I'll do the same exercise.

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Pick a given price.

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Let's say we're at this
price right over here

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and this is the current quantity demanded,

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now if all of a sudden, actually
for any price that I pick,

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if the price of gasoline increases,

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consumers will just have
less money in their pocket,

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the cost of maintaining and
using a car at any price

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would go up, and so they
might be willing to buy

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less cars because the
operating cost has gone up.

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And this would be true at
any price, at any price.

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And so one way to think about it is

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the entire demand curve, the
way I've just phrased it,

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you could view for the entire
demand curve would shift.

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So if we call this D1
here, now this would be D2.

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So here we would say change in demand,

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and in this case, our change in demand,

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it would shift, it would go down.

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You could view it as shifting to the left.

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Actually, let me write that
as shifting to the left

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because that's what it
looks like on this graph.

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Let's do this third example,

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prices of public transportation goes down,

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what would happen?

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Is this a change in quantity demanded

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or would it be a shift
in the demand curve?

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Well, once again, for
any, for any given price

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that we are talking about,
whether we're talking about here

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or whether we're talking about here,

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the substitute or one of the substitutes,

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which is public transportation,

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is now looking more favorable.

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So you could imagine
people at a given price

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will just not demand, the
market will just not demand

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as much of a quantity.

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And so this, once again,

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would be a change in the demand curve.

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When something is true for any given price

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along the curve, then you
know that you're going to be

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shifting the curve.

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So our change in demand, and once again,

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we're going to shift to the left,

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so it's similar to bullet point two.

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Now, let's see, here
we say the state lowers

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vehicle registration fees.

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Pause the video and think about that.

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Well, once again, regardless
of where we might be sitting

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along the demand curve
now, if registration fees

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has gone down, now the
total cost of ownership

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of a car has gone down,
and so for any given price,

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people might be able to
demand a little bit more car.

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And so here we would have
a shift of the demand curve

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to the right.

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Shift of the demand curve to the right.

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We could call this D3 right over here.

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So we have a change in
the entire demand curve,

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not just quantity demanded,
and we are going to the right.

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Let's do this, what is
this, the fifth example.

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A recession leads to
falling household incomes.

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Pause this video and think about it.

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Well, falling household
incomes is actually

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analogous in some ways to the
price of gasoline increases

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because people are just
going to have less incomes

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regardless of what point
we are on the curve.

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People are just going
to be able to buy less.

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So that's going to shift the demand curve,

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the entire demand curve to the left.

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So it's a shift in demand
or a change in demand

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once again going to the left.

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Last but not least, consumers
expect new car prices

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to rise next year.

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What is that going to do to either,

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is that going to be a
change in demand or a change

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in quantity demanded?

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Pause the video and think about it.

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Well, once again, this
is something that applies

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regardless of where we happen to sit

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at a given moment on the curve,

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whatever the equilibrium price is,

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and we'll talk more about
that in other videos.

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This is generally going
to apply to any point

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that we are on the curve.

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If people expect prices to increase,

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if all of a sudden there's
a bulletin that says,

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Hey, car prices are going
to double next year,

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well then you can imagine
wherever we are on the curve,

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people are going to say, Oh, if car prices

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are going to double next year,

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I better buy more car right now,

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so our entire demand
curve is going to shift

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to the right, so it's a change
in the entire demand curve,

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and it is going to go to the right.

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So the big picture here,
if we're talking about

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a change in, well you could say a change

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in a particular price,
someone raises the price

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or lowers the price, well
that's going to change

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the quantity demanded.

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And later when we draw the supply curve

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and we see where they
intersect and you have

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an equilibrium price, when one
or both of the curves shift,

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their intersecting point
changes and so then you will,

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you could have a shift in the curves,

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which will then result in a
change in the quantity demanded.

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But if we're talking about
things that are generally

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true regardless of where
we are on the curve,

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that will just affect
people's general demand

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for something, that is going
to shift the entire curve,

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it's going to be a change in demand

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versus a change in quantity demanded.


Input approach to determining comparative advantage

WEBVTT
Kind: captions
Language: en

00:00:00.346 --> 00:00:01.580
- [Instructor] In other videos

00:00:01.580 --> 00:00:05.223
we have already looked at
production possibility curves

00:00:05.223 --> 00:00:08.071
and output tables in order to calculate

00:00:08.071 --> 00:00:11.974
opportunity costs of
producing a certain product

00:00:11.974 --> 00:00:13.641
in a certain country.

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And then we used that to think
about comparative advantage.

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We're going to do something
very similar in this video,

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but instead of thinking about,

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or instead of starting with output,

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we're gonna start with input.

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So right over here we have a table

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that shows us the worker
hours per item per country.

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So, instead of this being an output table

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where we say in a given country,

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how much of, say, toy cars can a worker

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in country A produce per day?

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Here we're saying, how
many hours does a worker

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in country A take to produce A toy car?

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In country A it is two hours.

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That labor, that two hours
of labor, this is the input.

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So we're not counting the
number of cars per day here.

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We're saying how many hours per car, A,

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we need to put in to produce it.

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Similarly, we have the
input required in country A

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to produce a belt.

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One hour of worker time.

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In country B, four hours of worker time

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produces a toy car.

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And in country B, three
hours of worker time

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produces a belt.

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So what we're gonna do
next is convert this

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into the world that you
might be more familiar with,

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of thinking in an output world.

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And to do that, we'll
just assume that there are

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eight working hours

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per day

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in either country.

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And so from this, can we
construct an output table?

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Let me put this right over here.

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Output table,

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where once again we're gonna think

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about the output in country A.

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We're gonna think about
the output in country B.

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And this is going to be in

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how many units of that
product can a worker produce

00:01:54.448 --> 00:01:56.757
per day in each of those countries?

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So once again, we're gonna
have toy cars in this row,

00:02:00.836 --> 00:02:03.958
and we're going to have belts

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in this row.

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And let me just draw
some lines so it's clear

00:02:07.164 --> 00:02:09.920
that we're dealing with a table here.

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So there we go.

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Then one more column.

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And so, see if you can fill these in.

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So how many toy cars per worker per day

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can we produce in country A?

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Then think about it for belts.

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Then think about both
of them for country B.

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Pause the video and
try to figure that out.

00:02:28.773 --> 00:02:31.238
Alright, now let's think about how many

00:02:31.238 --> 00:02:33.834
toy cars per worker per day.

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Let me make it very clear.

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We're thinking per worker

00:02:39.159 --> 00:02:40.242
per day here.

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Because if we can fill out
this output table from this,

00:02:43.819 --> 00:02:45.560
I guess you could call
this an input table,

00:02:45.560 --> 00:02:47.929
then we can think about opportunity cost

00:02:47.929 --> 00:02:49.127
in the traditional way.

00:02:49.127 --> 00:02:51.171
And then we could think
about in which country

00:02:51.171 --> 00:02:53.453
do we have a comparative advantage?

00:02:53.453 --> 00:02:54.733
So, let's see.

00:02:54.733 --> 00:02:56.590
Toy cars in country A.

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If it takes two hours
to produce one toy car

00:03:00.598 --> 00:03:02.099
in country A,

00:03:02.099 --> 00:03:04.299
and if you're working, if
the average, or if the worker

00:03:04.299 --> 00:03:06.486
is working eight hours per day,

00:03:06.486 --> 00:03:10.081
well then, a worker can produce four cars.

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Four cars times two hours is eight hours.

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So, an average worker per day in country A

00:03:16.797 --> 00:03:18.964
can produce four toy cars.

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Let me write than in that red color.

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Four toy cars.

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I just took eight hours and I divided

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by the number of hours it
takes to produce a toy car.

00:03:27.617 --> 00:03:29.414
Similarly for belts, if I have eight hours

00:03:29.414 --> 00:03:32.124
and it takes an hour for
a worker to make one belt,

00:03:32.124 --> 00:03:35.117
then per worker per day,
eight divided by one,

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I could produce eight belts.

00:03:37.552 --> 00:03:39.574
And we could do the same
thing for country B,

00:03:39.574 --> 00:03:40.576
and I encourage you to pause the video

00:03:40.576 --> 00:03:41.623
if you haven't done so already

00:03:41.623 --> 00:03:43.933
and try to fill this column out.

00:03:43.933 --> 00:03:46.478
Well, in country B, if it takes four hours

00:03:46.478 --> 00:03:49.287
to produce a toy car per worker,

00:03:49.287 --> 00:03:51.813
that means you take eight
hours divided by four hours

00:03:51.813 --> 00:03:55.919
that you could produce two
toy cars in a day per worker.

00:03:55.919 --> 00:03:58.977
If it takes three hours to produce a belt,

00:03:58.977 --> 00:04:01.045
well then you take your eight hours,

00:04:01.045 --> 00:04:03.426
divide it by three hours per belt,

00:04:03.426 --> 00:04:06.662
and you're gonna be able to make 8/3 belts

00:04:06.662 --> 00:04:08.054
per worker per day.

00:04:08.054 --> 00:04:11.471
This is the same thing as 2 2/3 belts

00:04:11.471 --> 00:04:13.061
per worker per day.

00:04:13.061 --> 00:04:15.333
So as you can see, we can easily translate

00:04:15.333 --> 00:04:18.801
between the input world
and the output world.

00:04:18.801 --> 00:04:21.961
And then we could use this to
calculate opportunity cost.

00:04:21.961 --> 00:04:22.907
So let's do that.

00:04:22.907 --> 00:04:25.407
Let me write opportunity cost.

00:04:30.059 --> 00:04:31.993
And I'll make another table here.

00:04:31.993 --> 00:04:33.076
So country A,

00:04:34.946 --> 00:04:35.779
country B,

00:04:37.350 --> 00:04:39.767
and then I have the toy cars,

00:04:42.655 --> 00:04:45.295
and then I have the belts.

00:04:45.295 --> 00:04:48.156
Let me do the belts in that orange color.

00:04:48.156 --> 00:04:49.573
I have the belts,

00:04:50.435 --> 00:04:53.102
and then let me set up my table.

00:04:54.179 --> 00:04:56.085
We're almost there.

00:04:56.085 --> 00:04:57.521
At any point in time,

00:04:57.521 --> 00:05:00.061
pause this video and see if you can figure

00:05:00.061 --> 00:05:02.128
out the opportunity cost
given the information

00:05:02.128 --> 00:05:03.479
that we already have.

00:05:03.479 --> 00:05:05.622
We took this table to
figure out this table,

00:05:05.622 --> 00:05:07.372
and now we could take

00:05:09.659 --> 00:05:12.046
this table to figure out this one.

00:05:12.046 --> 00:05:13.870
Well, let's do this together now.

00:05:13.870 --> 00:05:15.686
So, toy cars.

00:05:15.686 --> 00:05:18.217
What's the opportunity cost in country A?

00:05:18.217 --> 00:05:20.736
Well, one way to think
about it is in country A,

00:05:20.736 --> 00:05:23.319
the same energy to produce four

00:05:24.648 --> 00:05:28.448
toy cars, I'll call it four c, c for cars.

00:05:28.448 --> 00:05:32.637
We could also use that
to produce eight belts.

00:05:32.637 --> 00:05:36.368
So, if I were to divide
both sides by four,

00:05:36.368 --> 00:05:38.750
the energy to create one car is equal

00:05:38.750 --> 00:05:41.473
to the energy to create two belts.

00:05:41.473 --> 00:05:43.822
So my opportunity cost of a car

00:05:43.822 --> 00:05:45.423
is two belts.

00:05:45.423 --> 00:05:47.690
And if I start with this original equation

00:05:47.690 --> 00:05:50.093
and just divide both sides by eight,

00:05:50.093 --> 00:05:52.919
I would solve for the energy for a belt.

00:05:52.919 --> 00:05:54.925
And so that would be four over eight

00:05:54.925 --> 00:05:59.394
is 1/2 of the energy to make a car

00:05:59.394 --> 00:06:02.245
is equal to the energy to make a belt.

00:06:02.245 --> 00:06:05.813
And so the opportunity cost
of a belt is 1/2 a car.

00:06:05.813 --> 00:06:07.541
1/2 a car.

00:06:07.541 --> 00:06:08.374
And like always,

00:06:08.374 --> 00:06:10.543
this and this are
reciprocals of each other.

00:06:10.543 --> 00:06:13.735
And we could do this same
exercise for country B.

00:06:13.735 --> 00:06:14.900
And once again, I keep emphasizing,

00:06:14.900 --> 00:06:15.733
try to pause the video.

00:06:15.733 --> 00:06:16.846
If you do this on your own as opposed

00:06:16.846 --> 00:06:18.209
to just watching me do it,

00:06:18.209 --> 00:06:21.097
it'll stick a lot better in your brain.

00:06:21.097 --> 00:06:23.730
Alright, in country B, the same energy

00:06:23.730 --> 00:06:25.980
to make two cars, toy cars,

00:06:26.907 --> 00:06:31.074
with that same energy
I could make 8/3 belts.

00:06:32.687 --> 00:06:35.108
8/3 belts right over here.

00:06:35.108 --> 00:06:37.420
So the energy to make a car,

00:06:37.420 --> 00:06:39.268
divide both sides by two,

00:06:39.268 --> 00:06:43.435
is equal to, instead of one
car I can make 4/3 of a belt.

00:06:45.042 --> 00:06:49.209
And so I'll just write
this as 1 1/3 of a belt.

00:06:50.156 --> 00:06:51.766
And then if I start right over here

00:06:51.766 --> 00:06:54.069
and I multiply both sides by 3/8,

00:06:54.069 --> 00:06:55.114
actually, let me do that over here.

00:06:55.114 --> 00:06:57.819
So I have 3/8 times two c

00:06:57.819 --> 00:07:02.620
is equal to 8/3 b times 3/8.

00:07:02.620 --> 00:07:04.113
These cancel out.

00:07:04.113 --> 00:07:07.497
And over here I'm gonna have 6/8 c.

00:07:07.497 --> 00:07:11.947
6/8 c is the same thing
as 3/4 c is equal to b.

00:07:11.947 --> 00:07:13.807
So, instead of making one belt,

00:07:13.807 --> 00:07:18.626
I could take that same energy
and make 3/4 of a toy car.

00:07:18.626 --> 00:07:20.959
3/4 of a toy car.

00:07:21.873 --> 00:07:24.752
So given everything that we've just done,

00:07:24.752 --> 00:07:26.801
which country has the
comparative advantage

00:07:26.801 --> 00:07:27.801
in toy cars?

00:07:30.022 --> 00:07:31.343
Well, to figure that out,

00:07:31.343 --> 00:07:33.857
we just look at the
opportunity cost for toy cars

00:07:33.857 --> 00:07:35.511
and we compare them.

00:07:35.511 --> 00:07:39.998
In country A, the
opportunity cost is two belts

00:07:39.998 --> 00:07:42.445
while in country B it's only 1 1/3 belts.

00:07:42.445 --> 00:07:46.434
So country B has the comparative
advantage right over here.

00:07:46.434 --> 00:07:49.267
Comparative advantage in toy cars.

00:07:50.133 --> 00:07:51.371
And then in belts,

00:07:51.371 --> 00:07:56.202
1/2 of a car is less than 3/4 of a car.

00:07:56.202 --> 00:07:59.753
In belts, we see that country A has

00:07:59.753 --> 00:08:01.358
the comparative advantage.

00:08:01.358 --> 00:08:02.916
And now what's always interesting

00:08:02.916 --> 00:08:05.794
about thinking about this is notice,

00:08:05.794 --> 00:08:09.044
country B has the comparative advantage

00:08:09.900 --> 00:08:11.388
in toy cars.

00:08:11.388 --> 00:08:14.034
It has less of an
opportunity cost in toy cars.

00:08:14.034 --> 00:08:17.474
Even though country A has
the absolute advantage,

00:08:17.474 --> 00:08:20.258
its workers are more efficient
at producing toy cars.

00:08:20.258 --> 00:08:22.318
A worker can produce
four cars in country A

00:08:22.318 --> 00:08:23.854
versus two in country B.

00:08:23.854 --> 00:08:26.637
But despite that, because
of the opportunity cost,

00:08:26.637 --> 00:08:28.498
it would actually make sense for country B

00:08:28.498 --> 00:08:31.190
to focus on cars and for country A

00:08:31.190 --> 00:08:33.043
to focus on the belts.

00:08:33.043 --> 00:08:34.674
But the big picture here is

00:08:34.674 --> 00:08:36.323
we're thinking about
comparative advantage.

00:08:36.323 --> 00:08:39.440
And instead of thinking
about with an output lens

00:08:39.440 --> 00:08:41.786
from the beginning, we
started with an input lens,

00:08:41.786 --> 00:08:43.485
converted that to an output lens,

00:08:43.485 --> 00:08:45.151
calculated opportunity cost,

00:08:45.151 --> 00:08:46.438
and then was able to figure out

00:08:46.438 --> 00:08:48.753
which countries had a
comparative advantage

00:08:48.753 --> 00:08:50.253
in which products.


Production Possibilities Curve PPC as a model of a nation's output

WEBVTT
Kind: captions
Language: en

00:00:00.290 --> 00:00:01.552
- [Instructor] We are now going to study

00:00:01.552 --> 00:00:04.385
the magical republic of Fitlandia,

00:00:06.519 --> 00:00:09.117
and as we often do in economics,

00:00:09.117 --> 00:00:10.869
we're going to assume that Fitlandia,

00:00:10.869 --> 00:00:13.026
which of course does not
exist in the real world,

00:00:13.026 --> 00:00:15.468
is a very simple country.

00:00:15.468 --> 00:00:17.622
It helps us create a model for it.

00:00:17.622 --> 00:00:20.745
Let's say that Fitlandia is
capable of producing two goods.

00:00:20.745 --> 00:00:23.917
It can either produce dumbbells.

00:00:23.917 --> 00:00:26.482
That's my best picture of a
dumbbell right over there,

00:00:26.482 --> 00:00:29.461
or it can produce protein bars.

00:00:29.461 --> 00:00:33.294
So this right over here,
that is a protein bar

00:00:34.541 --> 00:00:36.986
or some combination of the two.

00:00:36.986 --> 00:00:41.324
So we can draw Fitlandia's
production possibilities curve.

00:00:41.324 --> 00:00:43.356
So let me write this, PPC,

00:00:43.356 --> 00:00:46.366
production possibilities
curve for Fitlandia.

00:00:46.366 --> 00:00:47.543
Sometimes this will be referred

00:00:47.543 --> 00:00:51.042
to as a production possibility frontier,

00:00:51.042 --> 00:00:53.196
and so let me draw two axes.

00:00:53.196 --> 00:00:57.302
One for dumbbells and
one for protein bars.

00:00:57.302 --> 00:00:59.833
So the vertical axis right over there,

00:00:59.833 --> 00:01:04.107
and then the horizontal
axis right over here,

00:01:04.107 --> 00:01:06.587
and we're going to assume
that everything we do,

00:01:06.587 --> 00:01:09.754
this is in thousands of tons per year,

00:01:15.422 --> 00:01:19.589
and so in the vertical axis,
we have one, two, three,

00:01:22.478 --> 00:01:26.471
four, and five, and the horizontal axis,

00:01:26.471 --> 00:01:30.013
one thousand tons per year,
two thousand tons per year,

00:01:30.013 --> 00:01:33.842
three thousand tons per year,
four thousand tons per year,

00:01:33.842 --> 00:01:36.376
and five thousand tons per year,

00:01:36.376 --> 00:01:40.245
and let's put dumbbells
in the vertical axis.

00:01:40.245 --> 00:01:42.883
Dumbbells right over here,

00:01:42.883 --> 00:01:47.689
and let's put our protein
bars in the horizontal axis,

00:01:47.689 --> 00:01:49.399
and let's say we know that,

00:01:49.399 --> 00:01:52.538
we're maybe the economics
minister for Fitlandia,

00:01:52.538 --> 00:01:55.144
or the secretary of commerce,
or something like that,

00:01:55.144 --> 00:01:58.889
and we know that if we put all
of our energy into dumbbells

00:01:58.889 --> 00:02:01.653
and optimally allocated our resources,

00:02:01.653 --> 00:02:04.139
we could produce five, actually,

00:02:04.139 --> 00:02:04.972
let's say we could produce

00:02:04.972 --> 00:02:08.472
four thousand tons of dumbbells in a year.

00:02:09.676 --> 00:02:11.588
We also know that well,

00:02:11.588 --> 00:02:14.194
if we wanted to produce some protein bars,

00:02:14.194 --> 00:02:15.746
we're going to have to
give up our production

00:02:15.746 --> 00:02:19.618
of some dumbbells, and so the
more protein bars we produce,

00:02:19.618 --> 00:02:24.096
we're going to produce
fewer and fewer dumbbells,

00:02:24.096 --> 00:02:26.490
and so we're going to sit on this curve

00:02:26.490 --> 00:02:28.889
if we're producing as
efficiently as possible

00:02:28.889 --> 00:02:30.394
given the resources we have,

00:02:30.394 --> 00:02:33.439
and if we put all of our
resources into protein bars,

00:02:33.439 --> 00:02:35.845
we could produce three thousand tons

00:02:35.845 --> 00:02:37.916
of protein bars per year.

00:02:37.916 --> 00:02:38.749
So this right over here

00:02:38.749 --> 00:02:41.409
is our production possibilities curve.

00:02:41.409 --> 00:02:44.576
If my country is operating efficiently

00:02:45.834 --> 00:02:47.957
and all the resources are being used.

00:02:47.957 --> 00:02:48.790
When I talk about resources,

00:02:48.790 --> 00:02:51.701
I'm talking about people's
time; so my labor.

00:02:51.701 --> 00:02:55.118
I'm talking about the factories
are being fully utilized,

00:02:55.118 --> 00:02:56.865
the land, the material.

00:02:56.865 --> 00:02:58.490
Then I would sit someplace

00:02:58.490 --> 00:03:00.562
on this production possibilities curve.

00:03:00.562 --> 00:03:01.538
Sometimes it's referred to as

00:03:01.538 --> 00:03:05.119
a productions possibility frontier

00:03:05.119 --> 00:03:09.645
because you can't go beyond
this unless something changes.

00:03:09.645 --> 00:03:12.206
We're gonna talk in a second
about why they change.

00:03:12.206 --> 00:03:14.249
So if you sit on this curve,

00:03:14.249 --> 00:03:16.849
if you sit someplace on this curve,

00:03:16.849 --> 00:03:19.085
and the country might choose
to sit at different points

00:03:19.085 --> 00:03:21.835
on this curve, this is efficient.

00:03:23.076 --> 00:03:26.164
Efficient use of the resources,

00:03:26.164 --> 00:03:28.287
and it's kind of a theoretical efficiency.

00:03:28.287 --> 00:03:31.696
In practice, almost no country can,

00:03:31.696 --> 00:03:34.828
or really no country can fully
utilize all of its resources

00:03:34.828 --> 00:03:37.024
where all of it's people are working

00:03:37.024 --> 00:03:39.382
absolutely all of the time,

00:03:39.382 --> 00:03:42.099
and so in reality a
country might actually sit

00:03:42.099 --> 00:03:45.763
a little bit below it's
production possibilities curve.

00:03:45.763 --> 00:03:47.958
So someplace behind it.

00:03:47.958 --> 00:03:50.238
Now what would happen, let's
say a country right over here,

00:03:50.238 --> 00:03:53.000
and this is a real, let's just
take the theoretical country

00:03:53.000 --> 00:03:55.807
that somehow is able to
operate super-efficiently,

00:03:55.807 --> 00:03:58.618
and it's sitting on it's
productions possibility curve,

00:03:58.618 --> 00:04:00.771
or it's production possibility frontier,

00:04:00.771 --> 00:04:04.802
and let's say it were to enter
into some type of recession,

00:04:04.802 --> 00:04:07.169
where all of a sudden
some of it's population

00:04:07.169 --> 00:04:10.306
isn't able to work, so the labor pool

00:04:10.306 --> 00:04:11.648
isn't being fully utilized,

00:04:11.648 --> 00:04:14.692
what would happen to it's production?

00:04:14.692 --> 00:04:18.859
Well, it's production would
then go off the curve,

00:04:20.834 --> 00:04:24.123
and it would go to down and to the left,

00:04:24.123 --> 00:04:26.559
and so it might end up right over here.

00:04:26.559 --> 00:04:29.892
So here maybe we have some unemployment.

00:04:31.319 --> 00:04:33.637
Unemployment right over here,

00:04:33.637 --> 00:04:37.493
and so this is an
inefficient use of resources.

00:04:37.493 --> 00:04:42.288
Maybe Fitlandia gets into a
war with some other country,

00:04:42.288 --> 00:04:45.295
and that other country destroys some

00:04:45.295 --> 00:04:48.556
of their productive capability;
some of the factories,

00:04:48.556 --> 00:04:50.796
or maybe some of the people of Fitlandia

00:04:50.796 --> 00:04:53.154
decide to move someplace else.

00:04:53.154 --> 00:04:54.699
Well the what would happen?

00:04:54.699 --> 00:04:57.463
Well then your production
possibilities frontier

00:04:57.463 --> 00:04:59.170
would actually contract.

00:04:59.170 --> 00:05:01.000
If you have fewer factories,

00:05:01.000 --> 00:05:02.793
or if you have a smaller population,

00:05:02.793 --> 00:05:05.395
or maybe you lose some
territory to another country,

00:05:05.395 --> 00:05:08.118
then you have fewer resources
with which to produce,

00:05:08.118 --> 00:05:10.398
and so you could end up in a scenario

00:05:10.398 --> 00:05:12.520
where your production
possibilities frontier

00:05:12.520 --> 00:05:16.687
contracts to something,
contracts to maybe something

00:05:17.978 --> 00:05:20.779
like this, and so this movement

00:05:20.779 --> 00:05:22.730
of the production possibilities curve,

00:05:22.730 --> 00:05:26.897
this would happen if you
have contracting resources,

00:05:31.016 --> 00:05:33.003
and likewise, most countries of course

00:05:33.003 --> 00:05:34.257
don't want to be in this situation;

00:05:34.257 --> 00:05:36.732
most countries want economic growth.

00:05:36.732 --> 00:05:40.351
An economic growth is when
you have expanding resources.

00:05:40.351 --> 00:05:42.059
So how can we get beyond this

00:05:42.059 --> 00:05:43.528
production possibilities frontier;

00:05:43.528 --> 00:05:46.536
maybe construct one that is further out?

00:05:46.536 --> 00:05:49.297
Let's say we want to get a
production possibilities frontier

00:05:49.297 --> 00:05:51.880
that looks something like this,

00:05:52.991 --> 00:05:53.824
and it doesn't have to increase

00:05:53.824 --> 00:05:55.826
both of the good proportionately.

00:05:55.826 --> 00:05:58.393
Maybe we want to get to a
production possibilities frontier

00:05:58.393 --> 00:05:59.448
that looks something like that?

00:05:59.448 --> 00:06:00.544
How could we get there?

00:06:00.544 --> 00:06:02.544
Well, there's a couple of mechanisms.

00:06:02.544 --> 00:06:05.461
One is you could have more capital.

00:06:06.615 --> 00:06:08.163
More capital.

00:06:08.163 --> 00:06:08.996
What do we mean by capital?

00:06:08.996 --> 00:06:12.140
Well, maybe we invest in
creating more factories

00:06:12.140 --> 00:06:13.559
or getting more technology.

00:06:13.559 --> 00:06:16.567
So computer-aided
things, robots, whatever,

00:06:16.567 --> 00:06:18.260
so that we could produce more

00:06:18.260 --> 00:06:21.760
either protein bars or dumbbells per year.

00:06:23.430 --> 00:06:27.241
Another possibility is
we have more population.

00:06:27.241 --> 00:06:30.046
More especially working population.

00:06:30.046 --> 00:06:31.842
More population.

00:06:31.842 --> 00:06:34.780
So the big takeaways here.

00:06:34.780 --> 00:06:36.401
The production possibilities curve

00:06:36.401 --> 00:06:39.409
or production possibilities
frontier for a country

00:06:39.409 --> 00:06:43.524
are the combinations of
goods that it can produce

00:06:43.524 --> 00:06:45.519
in a certain amount of time

00:06:45.519 --> 00:06:48.811
if it's using all of it's
resources completely efficiently.

00:06:48.811 --> 00:06:51.290
If it gets into some type of a recession

00:06:51.290 --> 00:06:53.610
or doesn't used it's
resources efficiently,

00:06:53.610 --> 00:06:56.502
then you're going to
have a production point;

00:06:56.502 --> 00:06:58.619
some kind of combination
of producing goods

00:06:58.619 --> 00:07:00.981
that sits under or behind

00:07:00.981 --> 00:07:02.857
your production possibilities frontier;

00:07:02.857 --> 00:07:05.137
maybe there, or there, or there,

00:07:05.137 --> 00:07:07.173
and maybe as you come out of
a recession you might get,

00:07:07.173 --> 00:07:10.834
again, closer to your production
possibilities frontier.

00:07:10.834 --> 00:07:14.865
Now, there's also ways you
can shift the entire frontier.

00:07:14.865 --> 00:07:17.796
The entire frontier, or the
production possibilities curve,

00:07:17.796 --> 00:07:20.768
can contract is you have
contracting resources,

00:07:20.768 --> 00:07:25.327
favorites that are bombed in
a war, net outward migration,

00:07:25.327 --> 00:07:28.830
or your production possibilities
frontier can expand.

00:07:28.830 --> 00:07:30.253
If you have more population,

00:07:30.253 --> 00:07:33.221
more people who could be there
to work to produce goods,

00:07:33.221 --> 00:07:35.738
more capital, more factories, more land,

00:07:35.738 --> 00:07:39.150
more material with which to produce goods,

00:07:39.150 --> 00:07:42.368
and so you can imagine most
countries want to do this,

00:07:42.368 --> 00:07:43.953
and this notion of expanding

00:07:43.953 --> 00:07:46.262
your production possibilities frontier,

00:07:46.262 --> 00:07:49.929
this is what we refer
to as economic growth.


Terms of Trade and the Gains from Trade

WEBVTT
Kind: captions
Language: en

00:00:00.283 --> 00:00:02.111
- [Instructor] Let's
imagine a very simple world,

00:00:02.111 --> 00:00:03.722
as we tend to do in economics,

00:00:03.722 --> 00:00:06.450
that has two countries that
are each capable of producing

00:00:06.450 --> 00:00:09.765
either pants or shirts,
or some combination.

00:00:09.765 --> 00:00:10.889
And so what we have here

00:00:10.889 --> 00:00:12.776
are the production possibility curves

00:00:12.776 --> 00:00:14.566
for each of those countries,

00:00:14.566 --> 00:00:16.694
and this is in per worker per day.

00:00:16.694 --> 00:00:19.475
So, for example, in country
A, per worker per day,

00:00:19.475 --> 00:00:21.428
they could, if they put all
of their energy into pants,

00:00:21.428 --> 00:00:22.506
they could produce 20.

00:00:22.506 --> 00:00:24.037
If they put all of their
energy into shirts,

00:00:24.037 --> 00:00:25.152
they could produce 10.

00:00:25.152 --> 00:00:26.574
Or there could be some combination

00:00:26.574 --> 00:00:28.304
that would sit on this line.

00:00:28.304 --> 00:00:31.379
Now, to help us digest the
production possibility curves

00:00:31.379 --> 00:00:32.657
for these two countries,

00:00:32.657 --> 00:00:35.105
let me construct an output table.

00:00:35.105 --> 00:00:36.076
So this will be,

00:00:36.076 --> 00:00:38.692
this column will be the
output for country A.

00:00:38.692 --> 00:00:41.893
This column will be the
output for country B.

00:00:41.893 --> 00:00:45.110
And we're gonna think about
the maximum number of pants,

00:00:45.110 --> 00:00:46.277
maximum pants,

00:00:47.472 --> 00:00:49.996
the maximum output of
pants per worker per day.

00:00:49.996 --> 00:00:52.023
The input is the worker per day.

00:00:52.023 --> 00:00:56.190
And then let's think about
the maximum number of shirts.

00:00:57.651 --> 00:01:00.047
So pause this video, and see
if you can fill this out.

00:01:00.047 --> 00:01:01.445
What are the max pants and shirts

00:01:01.445 --> 00:01:03.924
in country A and country B?

00:01:03.924 --> 00:01:05.468
Well, in country A, I
already talked about it,

00:01:05.468 --> 00:01:07.998
the maximum pants is 20,

00:01:07.998 --> 00:01:09.140
20 pants.

00:01:09.140 --> 00:01:10.384
And then the maximum shirts,

00:01:10.384 --> 00:01:13.316
if they didn't make any pants, are 10.

00:01:13.316 --> 00:01:15.061
And in country B,

00:01:15.061 --> 00:01:17.144
the maximum pants are 30,

00:01:18.449 --> 00:01:22.866
and the maximum shirts, it
looks like that is about 45.

00:01:22.866 --> 00:01:25.568
Now, from either of these
production possibility curves

00:01:25.568 --> 00:01:27.126
or from this output table,

00:01:27.126 --> 00:01:29.265
because we have a
constant opportunity cost,

00:01:29.265 --> 00:01:31.450
these production possibility curves

00:01:31.450 --> 00:01:33.821
are straight lines with a fixed slope,

00:01:33.821 --> 00:01:35.836
we can calculate the opportunity costs.

00:01:35.836 --> 00:01:37.572
So let's do that next.

00:01:37.572 --> 00:01:39.342
So this is country A,

00:01:39.342 --> 00:01:41.884
and then this is country B.

00:01:41.884 --> 00:01:46.869
And let me calculate the
opportunity cost of pants,

00:01:46.869 --> 00:01:51.623
and let's calculate the
opportunity cost of shirts.

00:01:51.623 --> 00:01:53.743
So pause this video, and see
if you can figure that out.

00:01:53.743 --> 00:01:55.612
What are the opportunity
costs of pants and shirts

00:01:55.612 --> 00:01:56.906
in countries A and B?

00:01:56.906 --> 00:01:59.238
And fill out this table.

00:01:59.238 --> 00:02:01.357
Well, one way to think about it,

00:02:01.357 --> 00:02:04.585
in country A, I could put
all of my energy into pants

00:02:04.585 --> 00:02:06.335
and produce 20 pants,

00:02:07.424 --> 00:02:09.709
or I could put all of
my energy into shirts

00:02:09.709 --> 00:02:11.571
and produce 10 shirts.

00:02:11.571 --> 00:02:14.186
10 shirts, s for shirts, p for pants.

00:02:14.186 --> 00:02:15.936
And so if I want the cost of pants,

00:02:15.936 --> 00:02:18.516
I could just divide both sides by 20,

00:02:18.516 --> 00:02:20.428
and I would get pants,

00:02:20.428 --> 00:02:23.747
the amount of energy per pant is equal to,

00:02:23.747 --> 00:02:27.690
well, 10 divided by 20 is 1/2 a shirt.

00:02:27.690 --> 00:02:30.337
So the energy for pant is 1/2 for,

00:02:30.337 --> 00:02:33.763
is the same as the energy for 1/2 a shirt.

00:02:33.763 --> 00:02:35.574
And so we could say the opportunity cost

00:02:35.574 --> 00:02:39.841
of producing a pant is 1/2 a shirt.

00:02:39.841 --> 00:02:42.073
If we want the opportunity
cost for shirts,

00:02:42.073 --> 00:02:44.733
we could take the
reciprocal of this number.

00:02:44.733 --> 00:02:47.249
We could say it's going
to be two over one pant.

00:02:47.249 --> 00:02:50.491
Or we could start with this
equation right over here,

00:02:50.491 --> 00:02:53.442
and instead of solving for
p, we could solve for s.

00:02:53.442 --> 00:02:55.522
How much energy, in terms of pants,

00:02:55.522 --> 00:02:57.866
does it take for us to produce one shirt?

00:02:57.866 --> 00:03:00.864
So if you divide both sides
of this equation by 10,

00:03:00.864 --> 00:03:02.031
you would get,

00:03:03.052 --> 00:03:06.533
you would get two p is equal to s.

00:03:06.533 --> 00:03:07.931
Or another way of thinking about it,

00:03:07.931 --> 00:03:10.109
the energy to create one shirt

00:03:10.109 --> 00:03:12.851
is equal to the energy
to create two pants.

00:03:12.851 --> 00:03:17.213
So the opportunity cost of
producing a shirt is two pants.

00:03:17.213 --> 00:03:18.535
With that same energy of the shirt,

00:03:18.535 --> 00:03:20.502
you could produce two pants.

00:03:20.502 --> 00:03:22.697
Now, let's also fill it out for country B.

00:03:22.697 --> 00:03:24.313
And if you haven't done so already,

00:03:24.313 --> 00:03:26.744
try to use the same method to fill this,

00:03:26.744 --> 00:03:30.084
the opportunity costs for
pants and shirts for country B.

00:03:30.084 --> 00:03:33.836
Well, in country B, I could
put all of my energy into pants

00:03:33.836 --> 00:03:35.283
and produce 30 pants

00:03:35.283 --> 00:03:39.311
or all of my energy into
shirts and produce 45 shirts.

00:03:39.311 --> 00:03:41.297
So the opportunity cost per pant,

00:03:41.297 --> 00:03:43.154
if I divide both sides by 30,

00:03:43.154 --> 00:03:47.438
it'd be 45 over 30,
which would be equal to,

00:03:47.438 --> 00:03:49.393
they're both divisible by 15,

00:03:49.393 --> 00:03:50.830
3/2 of a shirt.

00:03:50.830 --> 00:03:52.863
The energy for one pair of pants

00:03:52.863 --> 00:03:55.985
is the same as the
energy for 1 1/2 shirts,

00:03:55.985 --> 00:03:57.162
I guess I could say.

00:03:57.162 --> 00:03:58.569
So let me write it that way.

00:03:58.569 --> 00:04:01.664
So the opportunity cost of pants is,

00:04:01.664 --> 00:04:04.941
for each pair, I'm giving up 1 1/2 shirts.

00:04:04.941 --> 00:04:08.078
And then, in the
opportunity cost for shirts,

00:04:08.078 --> 00:04:09.893
well, I could just solve for s here.

00:04:09.893 --> 00:04:12.158
If I divide both sides by 45,

00:04:12.158 --> 00:04:16.325
I get the same energy for
one shirt would be 30/45

00:04:17.560 --> 00:04:18.992
of a pair of pants,

00:04:18.992 --> 00:04:23.705
which is the same thing
as 2/3 of a pair of pants.

00:04:23.705 --> 00:04:26.810
And so I could write that
as 2/3 of a pair of pants,

00:04:26.810 --> 00:04:29.360
or, if I want, oh, let me
just write it that way,

00:04:29.360 --> 00:04:32.193
2/3 of a pair of pants.

00:04:33.369 --> 00:04:35.720
So given the opportunity costs,

00:04:35.720 --> 00:04:38.564
what should each of
these countries focus on?

00:04:38.564 --> 00:04:41.537
Pause this video, and
try to figure that out.

00:04:41.537 --> 00:04:45.907
Well, let's first compare their
opportunity costs in pants.

00:04:45.907 --> 00:04:50.525
So let's first compare their
opportunity cost in pants.

00:04:50.525 --> 00:04:53.912
It is clear that country A
has a lower opportunity cost

00:04:53.912 --> 00:04:55.549
for producing a pair of pants.

00:04:55.549 --> 00:04:57.292
It's only giving up 1/2 a shirt

00:04:57.292 --> 00:05:00.845
while country B is giving up 1 1/2 shirts.

00:05:00.845 --> 00:05:05.097
So country A has the comparative
advantage right over here,

00:05:05.097 --> 00:05:07.180
so comparative advantage,

00:05:08.876 --> 00:05:10.822
right over here, in pants.

00:05:10.822 --> 00:05:13.002
And so it should focus all of its energy,

00:05:13.002 --> 00:05:15.089
according to the theory
of comparative advantage,

00:05:15.089 --> 00:05:19.472
it should focus all of
its energy on pants.

00:05:19.472 --> 00:05:21.079
And likewise, if we look at,

00:05:21.079 --> 00:05:23.126
so here we compared this to this,

00:05:23.126 --> 00:05:26.626
and likewise, if we try to look at shirts,

00:05:27.589 --> 00:05:29.431
right over here,

00:05:29.431 --> 00:05:32.046
if we look at their opportunity cost,

00:05:32.046 --> 00:05:34.740
country B is only giving
up 2/3 of a pair of pants

00:05:34.740 --> 00:05:37.870
while country A would be
giving up two pairs of pants.

00:05:37.870 --> 00:05:41.118
So country B has the
lower opportunity cost

00:05:41.118 --> 00:05:44.058
or the comparative advantage in shirts.

00:05:44.058 --> 00:05:48.225
So country B should put all
of their focus here on shirts.

00:05:49.823 --> 00:05:51.930
Now, I know what you might be thinking.

00:05:51.930 --> 00:05:55.490
People can't just walk
around wearing only shirts.

00:05:55.490 --> 00:05:58.012
People might get cold below their waist.

00:05:58.012 --> 00:05:59.853
Or people don't want to only wear pants.

00:05:59.853 --> 00:06:02.423
They might get cold above their waist.

00:06:02.423 --> 00:06:05.468
And so how can people in these countries

00:06:05.468 --> 00:06:08.188
get the other type of garment?

00:06:08.188 --> 00:06:11.489
Well, the obvious answer is,
if they focus in this way,

00:06:11.489 --> 00:06:13.233
they can trade.

00:06:13.233 --> 00:06:15.993
And what would be an
acceptable trading price,

00:06:15.993 --> 00:06:17.486
let's say, for pants?

00:06:17.486 --> 00:06:20.095
Let's focus on pants for a second.

00:06:20.095 --> 00:06:23.495
So if we're thinking about
the market for pants,

00:06:23.495 --> 00:06:25.100
so if you're country A,

00:06:25.100 --> 00:06:27.826
what would you be
willing to sell pants for

00:06:27.826 --> 00:06:29.409
in terms of shirts?

00:06:30.356 --> 00:06:32.958
Well, a good price, so to speak,

00:06:32.958 --> 00:06:36.014
would be something higher
than your opportunity cost.

00:06:36.014 --> 00:06:37.476
So A

00:06:37.476 --> 00:06:38.309
willing

00:06:39.655 --> 00:06:40.488
to sell,

00:06:42.059 --> 00:06:42.892
sell pants

00:06:45.644 --> 00:06:46.477
at price,

00:06:48.332 --> 00:06:49.929
I'll put that in quotes
'cause we're really thinking

00:06:49.929 --> 00:06:51.771
of price in terms of another good,

00:06:51.771 --> 00:06:54.929
at price greater than
their opportunity cost,

00:06:54.929 --> 00:06:58.179
greater than 1/2 of a shirt.

00:06:59.340 --> 00:07:02.839
And you could think of this
willing to trade or sell.

00:07:02.839 --> 00:07:03.672
I'll put that in quotes.

00:07:03.672 --> 00:07:05.962
They're really trading
in our everyday language,

00:07:05.962 --> 00:07:07.163
right over here.

00:07:07.163 --> 00:07:10.122
And likewise, what about country B?

00:07:10.122 --> 00:07:10.955
Well, B

00:07:11.885 --> 00:07:12.718
willing

00:07:14.243 --> 00:07:15.808
to buy pants,

00:07:15.808 --> 00:07:18.490
they need pants, otherwise they
would just be walking around

00:07:18.490 --> 00:07:19.916
with only shirts on,

00:07:19.916 --> 00:07:21.583
willing to buy pants

00:07:24.216 --> 00:07:25.133
at a price,

00:07:27.147 --> 00:07:31.883
at a price less than their
opportunity cost for pants.

00:07:31.883 --> 00:07:34.716
And so that would be less than 1.5

00:07:36.283 --> 00:07:37.820
of a shirt.

00:07:37.820 --> 00:07:42.780
So what would be a price that
is greater than 1/2 a shirt

00:07:42.780 --> 00:07:44.940
and less than 1 1/2 of a shirt?

00:07:44.940 --> 00:07:48.413
And really any price in between
these two values would work.

00:07:48.413 --> 00:07:49.892
Well, a nice round number is,

00:07:49.892 --> 00:07:54.467
well, they could trade at one
pair of pants for one shirt.

00:07:54.467 --> 00:07:56.911
So a clearing price,

00:07:56.911 --> 00:07:57.744
a price

00:07:59.321 --> 00:08:02.106
that would work could be

00:08:02.106 --> 00:08:02.939
one p,

00:08:03.819 --> 00:08:04.652
one pants,

00:08:06.077 --> 00:08:07.637
for

00:08:07.637 --> 00:08:08.470
one shirt.

00:08:09.452 --> 00:08:12.338
And now, let's appreciate
the gains from trade

00:08:12.338 --> 00:08:14.372
that they would both have here.

00:08:14.372 --> 00:08:16.700
So let's imagine this
world where country A

00:08:16.700 --> 00:08:20.804
is producing 20 pants per worker per day.

00:08:20.804 --> 00:08:23.596
But let's say they decide that they want,

00:08:23.596 --> 00:08:25.496
instead of those 20 pants,

00:08:25.496 --> 00:08:28.931
they would want to trade
15 of them away for shirts.

00:08:28.931 --> 00:08:30.780
And so they would get, at this price,

00:08:30.780 --> 00:08:32.435
they would get 15 shirts.

00:08:32.435 --> 00:08:35.210
So they're gonna give up 15 pants.

00:08:35.210 --> 00:08:36.597
They're giving up 15 pants,

00:08:36.597 --> 00:08:39.793
so they'll only have five
pants right over here.

00:08:39.793 --> 00:08:42.798
But they're going to get 15 shirts.

00:08:42.798 --> 00:08:44.718
So they're gonna get 15 shirts.

00:08:44.718 --> 00:08:47.162
And they're going to end right over here.

00:08:47.162 --> 00:08:49.598
This is where country
A is going to end up.

00:08:49.598 --> 00:08:51.137
And what's cool about this

00:08:51.137 --> 00:08:54.789
is we've gone beyond the
production possibilities curve.

00:08:54.789 --> 00:08:57.736
So you see, very clearly,
the gain from trade.

00:08:57.736 --> 00:09:00.998
Country A could not have gotten
to this point on its own.

00:09:00.998 --> 00:09:03.921
This is above the production
possibilities curve.

00:09:03.921 --> 00:09:06.281
Likewise, country B

00:09:06.281 --> 00:09:09.193
was over here, with 45 shirts.

00:09:09.193 --> 00:09:11.776
It gave up 15 of those shirts.

00:09:11.776 --> 00:09:13.308
It now has 30 shirts.

00:09:13.308 --> 00:09:15.796
But it now has 15 pants.

00:09:15.796 --> 00:09:17.229
At least some of the people in the country

00:09:17.229 --> 00:09:19.236
are going to be able to wear pants now.

00:09:19.236 --> 00:09:21.349
So it now has 15 pants.

00:09:21.349 --> 00:09:23.471
Once again, it, too, is in a point

00:09:23.471 --> 00:09:25.635
beyond its production possibilities curve.

00:09:25.635 --> 00:09:29.064
It would not have been able
to get here without the trade.

00:09:29.064 --> 00:09:31.474
So they are both better off.

00:09:31.474 --> 00:09:33.994
So the key thing, the key
takeaway from this video

00:09:33.994 --> 00:09:37.226
is we now appreciate why
comparative advantage is valuable,

00:09:37.226 --> 00:09:38.712
once again, making all the assumptions

00:09:38.712 --> 00:09:41.208
for these simplified economic models,

00:09:41.208 --> 00:09:44.309
because we can calculate
out opportunity cost

00:09:44.309 --> 00:09:45.908
from that comparative advantage.

00:09:45.908 --> 00:09:47.596
And then we could think
about what's a good price

00:09:47.596 --> 00:09:49.141
that they'd be willing to trade at

00:09:49.141 --> 00:09:50.739
and see that when they trade,

00:09:50.739 --> 00:09:52.543
they both are able to get beyond

00:09:52.543 --> 00:09:54.961
their production possibilities curve.


Identifying centripetal force for cars and satellites

WEBVTT
Kind: captions
Language: en

00:00:01.138 --> 00:00:04.221
- So here we have something
that you probably have done

00:00:04.221 --> 00:00:06.822
in the last, maybe in the last day.

00:00:06.822 --> 00:00:09.947
And if we're in a car and
we're just making a turn,

00:00:09.947 --> 00:00:13.517
let's say at a constant
speed, on a road that is flat.

00:00:13.517 --> 00:00:16.666
So it's not a banked race
track or anything like that.

00:00:16.666 --> 00:00:18.922
What is keeping the car from just

00:00:18.922 --> 00:00:21.136
veering off in a straight line?

00:00:21.136 --> 00:00:23.204
And this one's a little bit less intuitive

00:00:23.204 --> 00:00:25.516
because we don't have any string here

00:00:25.516 --> 00:00:28.683
that's tethering the car to the center

00:00:29.541 --> 00:00:32.379
of the curve of our road.

00:00:32.379 --> 00:00:35.644
So what's keeping it from
going in a straight line here?

00:00:35.644 --> 00:00:39.094
Pause the video and think about that.

00:00:39.094 --> 00:00:41.149
Well in this situation,
and we could think about

00:00:41.149 --> 00:00:43.150
other forces that are at play.

00:00:43.150 --> 00:00:45.148
And once again I'll
assume we're in a vacuum,

00:00:45.148 --> 00:00:47.186
although you could think
about air resistance as well

00:00:47.186 --> 00:00:49.723
and think about what is
counteracting the air resistance.

00:00:49.723 --> 00:00:51.696
It turns out that that's friction.

00:00:51.696 --> 00:00:53.974
But the other forces at play,

00:00:53.974 --> 00:00:55.811
you of course have the force of gravity

00:00:55.811 --> 00:00:59.356
pulling downward on the
car, force of gravity.

00:00:59.356 --> 00:01:03.333
And that's being counteracted
by the normal force,

00:01:03.333 --> 00:01:07.166
that's being counteracted
by the normal force.

00:01:09.193 --> 00:01:13.110
Force, the normal force
of the road on the car.

00:01:14.623 --> 00:01:16.344
But what's keeping the
car going in a circle?

00:01:16.344 --> 00:01:18.309
And actually let's just
do air resistance for fun.

00:01:18.309 --> 00:01:22.239
So the air resistance, the
force of the air on the car,

00:01:22.239 --> 00:01:25.167
that's gonna be pushing
in the direction opposite

00:01:25.167 --> 00:01:28.015
from the velocity of the car.

00:01:28.015 --> 00:01:32.174
So we could call that, let's
just call that force of air.

00:01:32.174 --> 00:01:35.412
You can't read that, let me do it this.

00:01:35.412 --> 00:01:38.687
So, force of the air, that
would be its magnitude.

00:01:38.687 --> 00:01:41.151
And then that's being counteracted by,

00:01:41.151 --> 00:01:42.567
and this is a little bit counterintuitive,

00:01:42.567 --> 00:01:44.067
and this will actually give us a clue

00:01:44.067 --> 00:01:48.885
on the centripital force,
that is this component,

00:01:48.885 --> 00:01:51.277
that is being counteracted
by this component

00:01:51.277 --> 00:01:54.444
of the friction, so force of friction,

00:01:56.213 --> 00:01:58.816
in the direction that the car is going.

00:01:58.816 --> 00:02:00.476
Think about it, if you didn't have--

00:02:00.476 --> 00:02:03.940
if this was ice on ice, if the
wheels didn't have traction,

00:02:03.940 --> 00:02:05.857
no matter how hard the engine went

00:02:05.857 --> 00:02:07.769
and no matter how fast the wheels sped,

00:02:07.769 --> 00:02:11.049
it wouldn't be able to
overcome the air resistance,

00:02:11.049 --> 00:02:13.460
and then the car would decelerate.

00:02:13.460 --> 00:02:16.185
But these are all the
forces that aren't acting

00:02:16.185 --> 00:02:19.677
in a radial direction,
that aren't keeping the car

00:02:19.677 --> 00:02:22.430
on the road, so to speak,
or keeping it going

00:02:22.430 --> 00:02:24.662
in that circular motion around the curve.

00:02:24.662 --> 00:02:28.829
The one there, is once
again, the force of friction.

00:02:29.981 --> 00:02:31.620
So this is another, I guess you could say,

00:02:31.620 --> 00:02:33.677
another component of
the force of friction.

00:02:33.677 --> 00:02:35.818
And that's happening where the tires,

00:02:35.818 --> 00:02:38.277
where the literally, the
rubber meets the road.

00:02:38.277 --> 00:02:41.407
But this right over here, you
have the force of friction,

00:02:41.407 --> 00:02:43.494
that is keeping, and maybe I'll call it

00:02:43.494 --> 00:02:46.577
force of friction radially, radially.

00:02:48.198 --> 00:02:49.483
We'll put it in parentheses.

00:02:49.483 --> 00:02:51.816
Force of friction, radially.

00:02:54.109 --> 00:02:57.363
That is keeping us going
in a circular direction.

00:02:57.363 --> 00:03:02.073
And so, in this situation,
that is our centripetal force.

00:03:02.073 --> 00:03:05.250
Let's do another example,
and let's keep going

00:03:05.250 --> 00:03:07.832
with the theme of cars now.

00:03:07.832 --> 00:03:10.332
So let's say a scenario where,

00:03:12.073 --> 00:03:14.031
we are on a loop-de-loop,

00:03:14.031 --> 00:03:16.196
which is always fun, and kind of scary.

00:03:16.196 --> 00:03:18.442
I have dreams where I have
to drive on loop-de-loop,

00:03:18.442 --> 00:03:21.784
for some reason, and I
find it intimidating.

00:03:21.784 --> 00:03:23.321
But let's think about the
car at different points

00:03:23.321 --> 00:03:25.981
of the loop-de-loop, and
think about what is--

00:03:25.981 --> 00:03:29.577
what is the centripetal
force at different points.

00:03:29.577 --> 00:03:33.100
So let's first think about
this point right over here.

00:03:33.100 --> 00:03:35.318
And, once again, we assume
that we are dealing,

00:03:35.318 --> 00:03:39.710
we're on a planet, and so you
have your force of gravity,

00:03:39.710 --> 00:03:42.500
right over here, force of gravity.

00:03:42.500 --> 00:03:46.000
And then, you also have your normal force.

00:03:47.440 --> 00:03:50.520
And I'm going to draw
it a little bit larger,

00:03:50.520 --> 00:03:52.890
because in order to be
moved, I guess you could say,

00:03:52.890 --> 00:03:55.738
upwards, to stay on the loop-de-loop,

00:03:55.738 --> 00:03:57.502
the normal force has to be larger,

00:03:57.502 --> 00:03:59.904
you have to have a net force inward.

00:03:59.904 --> 00:04:03.786
So this is "F," this is our normal force.

00:04:03.786 --> 00:04:07.877
And so, in this situation, the magnitude,

00:04:07.877 --> 00:04:10.286
the magnitude of our centripetal force,

00:04:10.286 --> 00:04:13.095
let me do this in a different color.

00:04:13.095 --> 00:04:16.523
The magnitude of our
centripetal force is going to be

00:04:16.523 --> 00:04:19.440
the net radial inward radial force,

00:04:20.288 --> 00:04:22.836
for the magnitude of the
net radial inward force.

00:04:22.836 --> 00:04:27.598
So this would be equal to the
magnitude of our normal force

00:04:27.598 --> 00:04:31.765
minus, minus the magnitude
of the force of gravity.

00:04:33.089 --> 00:04:36.486
If this wasn't net inward right over here,

00:04:36.486 --> 00:04:38.211
then you would not, this car would not

00:04:38.211 --> 00:04:40.666
be able to move in a circle.

00:04:40.666 --> 00:04:43.059
It would just, if this netted out to zero,

00:04:43.059 --> 00:04:45.241
it would go in a straight line that way.

00:04:45.241 --> 00:04:47.620
And if this netted out
so that it was negative

00:04:47.620 --> 00:04:50.058
it would accelerate downwards.

00:04:50.058 --> 00:04:52.149
So, let's go at this
point right over here.

00:04:52.149 --> 00:04:53.926
And we could also think about
things like air-resistance

00:04:53.926 --> 00:04:56.332
and friction, where
air-resistance is pushing back

00:04:56.332 --> 00:04:58.709
on the car, and friction is overcoming it,

00:04:58.709 --> 00:05:01.692
but we're going to focus
just on the things that are

00:05:01.692 --> 00:05:05.216
driving us centripetally
inward or outward right now.

00:05:05.216 --> 00:05:08.253
Now what about this point for the car?

00:05:08.253 --> 00:05:10.525
Well, we still have the force of gravity,

00:05:10.525 --> 00:05:13.234
you still have the force of gravity.

00:05:13.234 --> 00:05:15.859
And actually, I'll make
this a little bit bigger.

00:05:15.859 --> 00:05:18.263
We could-- eh, let me put
the air-resistance there,

00:05:18.263 --> 00:05:19.096
just to be complete.

00:05:19.096 --> 00:05:23.263
So this would be the air
resistance, force of the air,

00:05:24.822 --> 00:05:28.952
and then that's being
counteracted by force of friction,

00:05:28.952 --> 00:05:31.110
the traction that the
car has with the road.

00:05:31.110 --> 00:05:34.203
Over here, this orange
vector, this would now be

00:05:34.203 --> 00:05:37.206
the combination of the force of gravity.

00:05:37.206 --> 00:05:38.652
And actually, you could even consider it

00:05:38.652 --> 00:05:43.121
the force of gravity,
plus the, plus the force,

00:05:43.121 --> 00:05:47.166
the air resistance, plus
the force of the air

00:05:47.166 --> 00:05:50.147
pushing back on the car,
the pressure of the air.

00:05:50.147 --> 00:05:53.314
And then that is being counteracted by

00:05:55.096 --> 00:05:59.441
the force of friction,
so the force of friction

00:05:59.441 --> 00:06:01.721
of the tires of the
tires pushing, pushing--

00:06:01.721 --> 00:06:03.632
Or I guess, the force
of friction of the tire,

00:06:03.632 --> 00:06:05.711
between the tire and the road.

00:06:05.711 --> 00:06:08.396
But neither of these are
acting centripetally,

00:06:08.396 --> 00:06:10.109
acting radially inward.

00:06:10.109 --> 00:06:12.458
So, what's that going to be?

00:06:12.458 --> 00:06:16.433
Well, here you have the
normal force of the track.

00:06:16.433 --> 00:06:18.894
The track is what's keeping this car

00:06:18.894 --> 00:06:21.502
going in this circular direction.

00:06:21.502 --> 00:06:22.835
And so you have,

00:06:24.607 --> 00:06:26.126
so you have--

00:06:26.126 --> 00:06:30.806
Here, the inward force is
the normal force, F normal.

00:06:30.806 --> 00:06:33.878
So in this situation,
our centripetal force,

00:06:33.878 --> 00:06:36.163
the magnitude of our
centripetal force is equal to

00:06:36.163 --> 00:06:38.257
the magnitude of our normal force.

00:06:38.257 --> 00:06:40.747
And these, actually, are
even going to be the same,

00:06:40.747 --> 00:06:42.357
the exact same vectors.

00:06:42.357 --> 00:06:45.934
Now, let's consider one last scenario.

00:06:45.934 --> 00:06:48.557
When we are at the top
of the loop-de-loop.

00:06:48.557 --> 00:06:52.067
Pause the video, and see
if you can figure that out.

00:06:52.067 --> 00:06:54.913
Well, once again, we can do things like,

00:06:54.913 --> 00:06:57.728
we could say, hey look, there's
probably some air-resistance

00:06:57.728 --> 00:07:01.539
that is keeping us, that
is trying to decelerate us.

00:07:01.539 --> 00:07:04.257
So that, and then that's being,

00:07:04.257 --> 00:07:08.464
that's being netted out
by the force of friction.

00:07:08.464 --> 00:07:09.345
But let's think about what's going on

00:07:09.345 --> 00:07:11.085
in the vertical direction.

00:07:11.085 --> 00:07:13.668
So here, pushing down this way,

00:07:15.568 --> 00:07:18.753
you're going to have,
potentially several forces,

00:07:18.753 --> 00:07:20.197
and I want this to actually
be at the top of the

00:07:20.197 --> 00:07:22.767
loop-de-loop, although it
doesn't look quite like that,

00:07:22.767 --> 00:07:24.544
but actually let's just assume it is.

00:07:24.544 --> 00:07:26.765
We're at the top of the loop-de-loop.

00:07:26.765 --> 00:07:28.981
Pushing down, you're going
to have the force of gravity.

00:07:28.981 --> 00:07:30.685
But what else are you going to have?

00:07:30.685 --> 00:07:32.038
Assuming you're going fast enough,

00:07:32.038 --> 00:07:34.237
the track is also pushing down.

00:07:34.237 --> 00:07:37.954
The force of gravity
plus the normal force.

00:07:37.954 --> 00:07:39.959
The magnitude of this vector
would be the magnitude,

00:07:39.959 --> 00:07:41.519
it would be the sum of the magnitudes

00:07:41.519 --> 00:07:44.785
of the gravitational force
and the normal force.

00:07:44.785 --> 00:07:47.813
And that is what's providing
your centripetal force there.

00:07:47.813 --> 00:07:50.256
And so, in this scenario, we would say

00:07:50.256 --> 00:07:52.123
the magnitude of our centripetal force

00:07:52.123 --> 00:07:54.518
is equal to the magnitude
of our gravitational force

00:07:54.518 --> 00:07:57.178
plus the magnitude of our normal force.

00:07:57.178 --> 00:07:59.158
Or, we could even think
about it as vectors.

00:07:59.158 --> 00:08:01.490
We could say, hey look, if
we just add up these vectors,

00:08:01.490 --> 00:08:03.414
these two vectors, you're going to get

00:08:03.414 --> 00:08:05.401
your centripetal force vector.

00:08:05.401 --> 00:08:09.424
That's what keeps the car
going in that circular motion.

00:08:09.424 --> 00:08:13.468
Now let's just do one last
scenario, just for fun.

00:08:13.468 --> 00:08:17.651
Let's imagine that we
have an object in orbit.

00:08:17.651 --> 00:08:21.192
So, this is our planet,
or any planet really.

00:08:21.192 --> 00:08:23.472
And you have an object in
orbit, some type of a satellite.

00:08:23.472 --> 00:08:27.211
I'll draw what we normally
associate with as a satellite.

00:08:27.211 --> 00:08:29.582
But this could be even
a natural satellite,

00:08:29.582 --> 00:08:31.937
a moon for the planet,
and what I'm about to say

00:08:31.937 --> 00:08:33.741
applies to the moon as well.

00:08:33.741 --> 00:08:35.701
So here, we don't have air,

00:08:35.701 --> 00:08:37.952
we have very minimal air resistance,

00:08:37.952 --> 00:08:41.907
there might be a few molecules
every here and there.

00:08:41.907 --> 00:08:44.800
But for the most part,
this is in a vacuum,

00:08:44.800 --> 00:08:48.126
and it's in orbit, so what keeps--

00:08:48.126 --> 00:08:50.557
So it's in a uniform circular motion,

00:08:50.557 --> 00:08:52.578
it's moving in a circular
orbit around the planet.

00:08:52.578 --> 00:08:55.110
What keeps it going
off in a straight line?

00:08:55.110 --> 00:08:57.364
Pause the video and think about it.

00:08:57.364 --> 00:09:01.468
Well here, you have the force of gravity.

00:09:01.468 --> 00:09:04.988
You have the force of
gravity of the planet.

00:09:04.988 --> 00:09:07.914
So right there, you have
the force of gravity.

00:09:07.914 --> 00:09:09.614
And at first people
say, wait wait, gravity?

00:09:09.614 --> 00:09:11.446
I see these picture of astronauts

00:09:11.446 --> 00:09:12.869
floating when they're in orbit.

00:09:12.869 --> 00:09:14.335
Well, that's just because
they're in free-fall.

00:09:14.335 --> 00:09:17.272
But the gravity at that point,
if you're a few hundred miles

00:09:17.272 --> 00:09:19.560
above the surface of the
Earth, is not that different

00:09:19.560 --> 00:09:21.516
than the gravity on the
surface of the Earth.

00:09:21.516 --> 00:09:25.031
You just don't have air there,
and if you are in orbit,

00:09:25.031 --> 00:09:26.499
you're in constant free-fall,

00:09:26.499 --> 00:09:29.983
so it feels, to you,
like there is no gravity.

00:09:29.983 --> 00:09:33.927
But it's gravity that is
keeping you on the orbital path,

00:09:33.927 --> 00:09:36.430
on that circular path, and
keeps you from just going

00:09:36.430 --> 00:09:39.241
in a straight line out into space.


Identifying centripetal force for ball on string

WEBVTT
Kind: captions
Language: en

00:00:00.000 --> 00:00:01.239
- [Tutor] What we're
going to do in this video

00:00:01.239 --> 00:00:03.709
is try to look at as
many scenarios as we can,

00:00:03.709 --> 00:00:07.265
where an object is exhibiting
uniform circular motion,

00:00:07.265 --> 00:00:10.873
it's traveling around in a
circle at a constant speed

00:00:10.873 --> 00:00:13.262
and what we wanna do is think about

00:00:13.262 --> 00:00:15.085
why is it staying on the circle,

00:00:15.085 --> 00:00:17.972
what centripetal force
is keeping the object

00:00:17.972 --> 00:00:21.587
from just going off in a straight line?

00:00:21.587 --> 00:00:24.538
So in this first scenario,
I have some type of a wheel,

00:00:24.538 --> 00:00:27.441
maybe a ball attached to a string,

00:00:27.441 --> 00:00:30.653
that's attached to a peg
at the center of the table

00:00:30.653 --> 00:00:35.173
and this wheel is moving in
a circle at a constant speed,

00:00:35.173 --> 00:00:38.403
so it's moving in this
circle at a constant speed,

00:00:38.403 --> 00:00:40.934
so pause this video, think
about all of the forces

00:00:40.934 --> 00:00:44.868
that are acting on this wheel
and which of those forces,

00:00:44.868 --> 00:00:47.352
or maybe some combination of those forces,

00:00:47.352 --> 00:00:50.233
that are actually acting
as the centripetal force,

00:00:50.233 --> 00:00:54.006
that are keeping the wheel on the circle.

00:00:54.006 --> 00:00:56.835
Alright, now let's work
through this together,

00:00:56.835 --> 00:00:59.579
so there's a couple of
forces, that aren't impacting

00:00:59.579 --> 00:01:03.847
the wheels staying on the circle
so much, but they're there,

00:01:03.847 --> 00:01:05.310
for example, you're definitely gonna have

00:01:05.310 --> 00:01:06.213
the force of gravity,

00:01:06.213 --> 00:01:09.929
we're assuming we're dealing
with this wheel on a planet,

00:01:09.929 --> 00:01:12.346
so we'll denote its magnitude

00:01:14.036 --> 00:01:15.536
as capital F sub g

00:01:16.552 --> 00:01:19.391
and then this is its direction
with this orange arrow,

00:01:19.391 --> 00:01:21.097
so that's the force of gravity

00:01:21.097 --> 00:01:25.018
and the reason why the wheel
is not accelerating downward

00:01:25.018 --> 00:01:26.689
is that we have that table there

00:01:26.689 --> 00:01:29.837
and so the table is exerting

00:01:29.837 --> 00:01:31.223
a normal force on the wheel,

00:01:31.223 --> 00:01:34.090
that counteracts the gravitational force,

00:01:34.090 --> 00:01:38.070
so the magnitude there would
be the force, the normal force

00:01:38.070 --> 00:01:40.141
and these are going to
be the same magnitude,

00:01:40.141 --> 00:01:42.833
they're just going to be
in different directions,

00:01:42.833 --> 00:01:44.334
just let me see if I can draw this arrow

00:01:44.334 --> 00:01:48.824
a little bit taller, but
what else is going on?

00:01:48.824 --> 00:01:51.118
Well, as you can imagine,
if this string wasn't here,

00:01:51.118 --> 00:01:53.240
the wheel really would
go off in a straight line

00:01:53.240 --> 00:01:55.704
and eventually fall off of the table

00:01:55.704 --> 00:01:59.534
and so the string is
providing some inward force,

00:01:59.534 --> 00:02:02.701
that keeps the wheel going in a circle

00:02:04.061 --> 00:02:06.106
and that inward force, that pulling force,

00:02:06.106 --> 00:02:09.239
we would consider that
to be the tension force,

00:02:09.239 --> 00:02:11.725
so I'll just draw it like that

00:02:11.725 --> 00:02:14.597
and its magnitude is F sub T

00:02:14.597 --> 00:02:17.626
and in this situation, it is
providing that inward force,

00:02:17.626 --> 00:02:19.497
so that is the centripetal force,

00:02:19.497 --> 00:02:23.831
so we could say the
magnitude of the tension,

00:02:23.831 --> 00:02:26.055
the tension force, the pulling force,

00:02:26.055 --> 00:02:29.069
is going to be equal to
the centripetal force,

00:02:29.069 --> 00:02:32.304
in this case, they're actually
the exact same vector,

00:02:32.304 --> 00:02:34.167
so I can even write it like this,

00:02:34.167 --> 00:02:36.360
this is the centripetal force vector,

00:02:36.360 --> 00:02:38.480
it's the tension in that rope,

00:02:38.480 --> 00:02:40.893
that keeps us going in a circle.

00:02:40.893 --> 00:02:42.976
Let's do another example,

00:02:45.273 --> 00:02:47.510
so this one is similar,

00:02:47.510 --> 00:02:50.679
but I have a few more dimensions going on,

00:02:50.679 --> 00:02:53.117
here this is a classic
example from physics,

00:02:53.117 --> 00:02:55.900
I have a string attached to the ceiling

00:02:55.900 --> 00:02:58.546
and I have some type
of a ball or a pendulum

00:02:58.546 --> 00:03:02.404
and it's swinging in a
circular, in a circular motion

00:03:02.404 --> 00:03:05.541
right over here at a constant speed,

00:03:05.541 --> 00:03:09.324
so the center of its circle
would be right around there,

00:03:09.324 --> 00:03:10.568
so once again pause this video,

00:03:10.568 --> 00:03:13.151
think about all of the forces on that ball

00:03:13.151 --> 00:03:15.187
and we're not gonna talk too
much about air resistance,

00:03:15.187 --> 00:03:18.352
let's assume that these are
in vacuum chambers for now

00:03:18.352 --> 00:03:20.307
and then think about,
well, which of those forces

00:03:20.307 --> 00:03:23.224
is providing the centripetal force?

00:03:24.402 --> 00:03:25.834
Well, just like in the last video,

00:03:25.834 --> 00:03:28.275
there's definitely some force of gravity,

00:03:28.275 --> 00:03:32.122
so you have that vector right over there

00:03:32.122 --> 00:03:35.048
and so its magnitude is F sub g

00:03:35.048 --> 00:03:38.212
and you also have the
string holding up the ball

00:03:38.212 --> 00:03:41.843
and so you're gonna have its pulling force

00:03:41.843 --> 00:03:43.760
on, so this would be...

00:03:44.936 --> 00:03:46.997
the magnitude here would be F sub T,

00:03:46.997 --> 00:03:49.088
this is the tension force,

00:03:49.088 --> 00:03:50.876
but what's counteracting the gravity

00:03:50.876 --> 00:03:53.734
and what's keeping us going in a circle?

00:03:53.734 --> 00:03:55.690
Well, in this situation,
we can think about

00:03:55.690 --> 00:03:58.410
the different components of the tension,

00:03:58.410 --> 00:04:00.187
because this is going off at an angle,

00:04:00.187 --> 00:04:04.354
so if we break down that vector
in the vertical direction,

00:04:05.232 --> 00:04:07.969
so if we take the vertical component,

00:04:07.969 --> 00:04:11.087
or the y component of the tension force,

00:04:11.087 --> 00:04:12.551
it would look something like this,

00:04:12.551 --> 00:04:14.468
we could call that F Ty

00:04:16.390 --> 00:04:19.021
for the y component, this
would be its magnitude

00:04:19.021 --> 00:04:21.653
and that is what is
counteracting the gravity,

00:04:21.653 --> 00:04:24.213
why the ball is not accelerating downwards

00:04:24.213 --> 00:04:28.380
and if we think about the
x component of the tension,

00:04:29.741 --> 00:04:33.182
that would be this right over here,

00:04:33.182 --> 00:04:35.235
this is the x component of the tension,

00:04:35.235 --> 00:04:37.460
just to be clear where
I'm getting this from,

00:04:37.460 --> 00:04:40.375
so this would be F tension
in the x direction,

00:04:40.375 --> 00:04:42.263
that would be its magnitude

00:04:42.263 --> 00:04:45.339
and that is what is providing
the centripetal force

00:04:45.339 --> 00:04:49.506
or that is the centripetal
force, so in this situation,

00:04:50.566 --> 00:04:53.643
the component of our
tension in the x direction

00:04:53.643 --> 00:04:56.555
and let me just denote that as a vector,

00:04:56.555 --> 00:04:59.055
that is our centripetal force,

00:05:00.425 --> 00:05:01.947
that's what keeps the ball

00:05:01.947 --> 00:05:04.665
from just going straight off
in a direction like that.


Identifying force vectors for pendulum: Worked example

WEBVTT
Kind: captions
Language: en

00:00:00.377 --> 00:00:03.052
- [Lecturer] We're told that
a ball attached to a string

00:00:03.052 --> 00:00:06.676
swings in a horizontal
circle at constant speed

00:00:06.676 --> 00:00:08.114
as shown below.

00:00:08.114 --> 00:00:12.728
The string makes an angle
theta with the horizontal.

00:00:12.728 --> 00:00:16.478
Which arrows show all
the forces on the ball?

00:00:17.849 --> 00:00:22.832
So pause this video, and see
if you can figure that out.

00:00:22.832 --> 00:00:25.829
Okay, so let's work through this together.

00:00:25.829 --> 00:00:28.173
So this ball is attached to the string,

00:00:28.173 --> 00:00:29.409
and it's currently hanging down,

00:00:29.409 --> 00:00:31.279
and I think it's fair to say

00:00:31.279 --> 00:00:33.841
that we are on some type of a planet.

00:00:33.841 --> 00:00:36.474
And so, if we're on some type of planet,

00:00:36.474 --> 00:00:38.765
you're definitely gonna
have the force of gravity

00:00:38.765 --> 00:00:42.434
acting on the ball, so
let me draw that vector.

00:00:42.434 --> 00:00:45.353
So the force of gravity,
I'll do in orange.

00:00:45.353 --> 00:00:47.910
Let's say it looks something like that.

00:00:47.910 --> 00:00:51.485
Its magnitude, I'll denote as capital F

00:00:51.485 --> 00:00:54.247
with a sub g right over here.

00:00:54.247 --> 00:00:58.414
Now what's keeping that ball
from accelerating downwards?

00:00:59.820 --> 00:01:01.554
And also, what's keeping that ball

00:01:01.554 --> 00:01:04.393
in this uniform circular motion?

00:01:04.393 --> 00:01:06.659
And the answer to both of those questions

00:01:06.659 --> 00:01:09.501
is the tension in the rope.

00:01:09.501 --> 00:01:11.399
Remember, tension is a pulling force.

00:01:11.399 --> 00:01:13.459
The rope is pulling on this ball.

00:01:13.459 --> 00:01:15.959
And so, we could say the force

00:01:16.967 --> 00:01:21.134
of the tension, so it might
look something like this,

00:01:22.319 --> 00:01:24.986
the force, force of the tension.

00:01:27.385 --> 00:01:31.418
Now just with that, we have
constructed a free body diagram,

00:01:31.418 --> 00:01:33.688
and we can immediately
answer their question,

00:01:33.688 --> 00:01:35.821
what are the forces that
are acting on the ball,

00:01:35.821 --> 00:01:37.058
which arrows show it.

00:01:37.058 --> 00:01:38.217
So there is one downwards,

00:01:38.217 --> 00:01:41.102
and then there is one going in
the direction of the string,

00:01:41.102 --> 00:01:42.834
and if you look at these choices here,

00:01:42.834 --> 00:01:45.394
you would say it is that
one right over there.

00:01:45.394 --> 00:01:47.827
Now some of you might say,
"Wait, hold on a second.

00:01:47.827 --> 00:01:51.297
"Isn't there some type
of a centripetal force

00:01:51.297 --> 00:01:53.607
"that keeps the ball going in a circle,

00:01:53.607 --> 00:01:56.324
"that keeps it from
just going straight off?

00:01:56.324 --> 00:01:58.006
"And then isn't there some type of force

00:01:58.006 --> 00:02:01.094
"that counteracts the
actual force of gravity?"

00:02:01.094 --> 00:02:03.152
And the answer to the
question is yes, there is

00:02:03.152 --> 00:02:07.364
but those are really just
components of the tension.

00:02:07.364 --> 00:02:10.550
And so, if you look at the
X component of the tension,

00:02:10.550 --> 00:02:13.968
I'll do that in a blue
color right over here,

00:02:13.968 --> 00:02:16.354
this X component of the tension,

00:02:16.354 --> 00:02:20.521
so I'll call that F sub Tx,
that is our centripetal force,

00:02:22.484 --> 00:02:24.985
or that its magnitude of
the X component of tension

00:02:24.985 --> 00:02:29.152
is the same thing as the magnitude
of our centripetal force.

00:02:30.409 --> 00:02:34.833
If we look at the Y
component of our tension,

00:02:34.833 --> 00:02:36.688
the Y component of our tension,

00:02:36.688 --> 00:02:40.198
that's what counteracts
the force of gravity.

00:02:40.198 --> 00:02:44.940
So this right over here,
its magnitude is F sub Ty,

00:02:44.940 --> 00:02:48.306
and F sub Ty, this magnitude
is going to be the same thing

00:02:48.306 --> 00:02:51.075
as the magnitude of the force of gravity.

00:02:51.075 --> 00:02:52.848
But we already answered our question,

00:02:52.848 --> 00:02:54.128
and we just got a little
bit more intuition

00:02:54.128 --> 00:02:57.045
of what's going on right over here.


Introduction to centripetal force

WEBVTT
Kind: captions
Language: en

00:00:00.894 --> 00:00:01.855
- [Instructor] Just for kicks,

00:00:01.855 --> 00:00:05.168
let's imagine someone
spinning a flaming tennis ball

00:00:05.168 --> 00:00:08.446
attached to some type of a string or chain

00:00:08.446 --> 00:00:12.000
that they're spinning it
above their head like this

00:00:12.000 --> 00:00:14.929
and let's say they're spinning
it at a constant speed.

00:00:14.929 --> 00:00:17.423
We've already described
situations like this,

00:00:17.423 --> 00:00:20.409
maybe not with as much drama as this one

00:00:20.409 --> 00:00:23.919
but we can visualize the velocity vectors

00:00:23.919 --> 00:00:25.746
at different points for the ball.

00:00:25.746 --> 00:00:28.044
So, at this point, let's
say the velocity vector

00:00:28.044 --> 00:00:29.995
will look like this,

00:00:29.995 --> 00:00:33.699
the linear velocity vector
just to be super clear.

00:00:33.699 --> 00:00:34.731
So, the linear velocity vector

00:00:34.731 --> 00:00:36.335
might look something like that

00:00:36.335 --> 00:00:38.305
and it's going to have magnitude V,

00:00:38.305 --> 00:00:39.780
the magnitude of the velocity vector

00:00:39.780 --> 00:00:42.706
you could also view as its linear speed.

00:00:42.706 --> 00:00:45.428
Now, a few moments later,

00:00:45.428 --> 00:00:48.236
what is the ball going to be doing?

00:00:48.236 --> 00:00:49.566
Well, a few moments later

00:00:49.566 --> 00:00:52.521
the ball might be let's
say right over here,

00:00:52.521 --> 00:00:53.757
we don't wanna lose the drama,

00:00:53.757 --> 00:00:56.219
it's still flaming we're assuming,

00:00:56.219 --> 00:01:00.219
it's still attached to
our chain right over here

00:01:02.209 --> 00:01:04.804
but what would its velocity vector be?

00:01:04.804 --> 00:01:07.521
Well, we're assuming it
has a constant speed,

00:01:07.521 --> 00:01:09.253
a constant linear speed,

00:01:09.253 --> 00:01:11.410
so the magnitude is going to be the same

00:01:11.410 --> 00:01:14.343
but now the direction is
going to be tangential

00:01:14.343 --> 00:01:16.422
to the circular path at that point.

00:01:16.422 --> 00:01:19.744
So, our direction has changed.

00:01:19.744 --> 00:01:22.709
Now, one way to think about this change

00:01:22.709 --> 00:01:24.428
in direction of velocity,

00:01:24.428 --> 00:01:25.784
it's a little counterintuitive at first

00:01:25.784 --> 00:01:28.403
because when we first
think about acceleration,

00:01:28.403 --> 00:01:31.497
we tend to think in terms
of changing the magnitude

00:01:31.497 --> 00:01:35.120
of velocity but keeping
the magnitude the same,

00:01:35.120 --> 00:01:36.168
but changing the direction

00:01:36.168 --> 00:01:38.629
still involves an acceleration

00:01:38.629 --> 00:01:40.369
and at first, it's a
little counterintuitive

00:01:40.369 --> 00:01:42.181
the direction of that acceleration

00:01:42.181 --> 00:01:45.027
but if I were to take this
second velocity vector

00:01:45.027 --> 00:01:47.097
and if I were to shift it over here,

00:01:47.097 --> 00:01:50.824
and if I were to start it
at the exact same point,

00:01:50.824 --> 00:01:53.657
it would look something like this,

00:01:57.957 --> 00:01:59.926
actually, let me do it in
a slightly different color

00:01:59.926 --> 00:02:01.896
so it's a little bit more visible,

00:02:01.896 --> 00:02:04.979
so it would look something like this.

00:02:05.913 --> 00:02:07.963
This and this, they have the same length

00:02:07.963 --> 00:02:10.362
and they're parallel, so
they are the same vector

00:02:10.362 --> 00:02:11.814
and so, in some amount of time,

00:02:11.814 --> 00:02:14.293
if you wanna go from this velocity vector

00:02:14.293 --> 00:02:16.351
and actually this should
be a little bit longer,

00:02:16.351 --> 00:02:18.519
this should look like this,

00:02:18.519 --> 00:02:20.816
it should have the same
magnitude as this one,

00:02:20.816 --> 00:02:23.149
so it should look like this.

00:02:24.742 --> 00:02:25.787
So, if in some amount of time,

00:02:25.787 --> 00:02:27.860
this and this should
have the same magnitude.

00:02:27.860 --> 00:02:28.970
If in some amount of time

00:02:28.970 --> 00:02:30.026
you go from this velocity vector

00:02:30.026 --> 00:02:32.065
to this velocity vector,

00:02:32.065 --> 00:02:33.997
your net change in velocity

00:02:33.997 --> 00:02:36.624
is going radially inward.

00:02:36.624 --> 00:02:40.791
This right over here is
your net change in velocity

00:02:43.804 --> 00:02:45.097
and so, in other videos

00:02:45.097 --> 00:02:48.241
we talk about this notion
of centripetal acceleration.

00:02:48.241 --> 00:02:50.381
In order to keep something going

00:02:50.381 --> 00:02:52.520
in this uniform circular motion,

00:02:52.520 --> 00:02:55.117
in order to keep changing the direction

00:02:55.117 --> 00:02:56.394
of our velocity vector,

00:02:56.394 --> 00:03:00.532
you are accelerating it radially inward,

00:03:00.532 --> 00:03:03.471
centripetal acceleration,
inward acceleration

00:03:03.471 --> 00:03:05.246
and so, at all points in time,

00:03:05.246 --> 00:03:07.230
you have an inward acceleration

00:03:07.230 --> 00:03:09.278
which we denote, the magnitude,

00:03:09.278 --> 00:03:13.324
we usually say is A with a
C subscript for centripetal.

00:03:13.324 --> 00:03:17.443
Sometimes you'll see an A
with an R subscript for radial

00:03:17.443 --> 00:03:21.046
but in this context we
will use centripetal.

00:03:21.046 --> 00:03:23.898
Now, one question that you
might have been wondering

00:03:23.898 --> 00:03:25.140
this whole time that we talked

00:03:25.140 --> 00:03:26.807
about centripetal acceleration

00:03:26.807 --> 00:03:29.777
is Newton's First Law might be nagging.

00:03:29.777 --> 00:03:32.581
Newton's First Law tells
us that the velocity

00:03:32.581 --> 00:03:35.180
of an object both it's
magnitude and its direction

00:03:35.180 --> 00:03:39.252
will not change unless
there's some net force

00:03:39.252 --> 00:03:41.167
acting on the object

00:03:41.167 --> 00:03:42.590
and we clearly see here

00:03:42.590 --> 00:03:46.323
that the direction of our
velocity vector is changing,

00:03:46.323 --> 00:03:47.951
so Newton's First Law tells us

00:03:47.951 --> 00:03:51.360
that there must be some
net force acting on it

00:03:51.360 --> 00:03:54.243
and that net force is going to be acting

00:03:54.243 --> 00:03:58.187
in the same direction as our acceleration

00:03:58.187 --> 00:03:59.486
and so, what we're gonna do here

00:03:59.486 --> 00:04:02.986
is introduce an idea of centripetal force.

00:04:03.885 --> 00:04:04.810
So, centripetal force,

00:04:04.810 --> 00:04:08.070
if it's accelerating the object inwards

00:04:08.070 --> 00:04:10.681
in the inward direction,

00:04:10.681 --> 00:04:13.181
so we have a centripetal force

00:04:14.618 --> 00:04:18.368
that is causing our
centripetal acceleration.

00:04:19.619 --> 00:04:21.011
F sub C right over here,

00:04:21.011 --> 00:04:23.795
you can view that as the
magnitude of our centripetal force

00:04:23.795 --> 00:04:25.414
and the way that they would be connected

00:04:25.414 --> 00:04:27.151
comes straight out for
Newton's Second Law.

00:04:27.151 --> 00:04:29.982
This isn't some type of new,
different type of force,

00:04:29.982 --> 00:04:31.402
this is the same type of forces

00:04:31.402 --> 00:04:33.413
that we talk about throughout physics.

00:04:33.413 --> 00:04:37.134
We know that the magnitude
of our centripetal force

00:04:37.134 --> 00:04:41.336
is going to be equal to
the mass of our object

00:04:41.336 --> 00:04:45.503
times the magnitude of our
centripetal acceleration.

00:04:46.542 --> 00:04:50.242
If you want, you could put
vectors on top of this.

00:04:50.242 --> 00:04:52.451
You could say something like this

00:04:52.451 --> 00:04:57.125
but we know the direction
of the centripetal force

00:04:57.125 --> 00:04:59.666
and the centripetal
acceleration, it is inward.

00:04:59.666 --> 00:05:00.932
Now, what inward means,

00:05:00.932 --> 00:05:02.686
the exact arrow's going to be different

00:05:02.686 --> 00:05:05.476
at different points but for
any position for the ball

00:05:05.476 --> 00:05:07.183
we know at least conceptually

00:05:07.183 --> 00:05:09.557
what inward is going to be.

00:05:09.557 --> 00:05:11.989
So, this is just to appreciate the idea.

00:05:11.989 --> 00:05:15.097
Centripetal acceleration
in classical mechanics

00:05:15.097 --> 00:05:17.544
isn't just going to
show up out of nowhere.

00:05:17.544 --> 00:05:18.729
Newton's First Law tells us

00:05:18.729 --> 00:05:20.692
that if something is being accelerated,

00:05:20.692 --> 00:05:23.100
there must be a net force acting on it

00:05:23.100 --> 00:05:26.753
and if it's being accelerated inward

00:05:26.753 --> 00:05:30.328
in the centripetal direction
I guess you could say,

00:05:30.328 --> 00:05:33.817
then the force must also be acting inward

00:05:33.817 --> 00:05:36.606
and they would just be
related by F equals MA

00:05:36.606 --> 00:05:39.450
which we learn from Newton's Second Law.

00:05:39.450 --> 00:05:42.217
And to appreciate the intuition for this,

00:05:42.217 --> 00:05:43.664
just remember the last time

00:05:43.664 --> 00:05:47.647
that you were spinning or
rotating a flaming tennis ball

00:05:47.647 --> 00:05:50.395
attached to a chain above your head.

00:05:50.395 --> 00:05:53.566
In order to do that, in order
to keep the ball spinning

00:05:53.566 --> 00:05:55.953
and not just going and veering
off in a straight line,

00:05:55.953 --> 00:05:59.370
you can keep pulling inward on your chain

00:06:00.420 --> 00:06:03.212
so that the flaming tennis
ball doesn't go hit a wall

00:06:03.212 --> 00:06:05.207
and set things onto fire.

00:06:05.207 --> 00:06:08.273
And so, what you are providing
is that centripetal force

00:06:08.273 --> 00:06:10.323
to keep that flaming tennis ball

00:06:10.323 --> 00:06:12.990
in its uniform circular motion.