More on balance sheets and equity

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Language: en

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Welcome back.

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Where we left off in the last
video, I had just purchased a

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$1 million house.

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To do it, I went to the bank and
I said, bank, can you give

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me $750,000?

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They said, sure, Sal, you have
an excellent credit rating,

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and you look like an all
around great guy.

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So we'll give you $750,000.

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And so I took that $750,000 and
the $250,000 that I had

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saved up through a lifetime of
hard work, and I went and I

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bought that house.

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After that transaction, this is
what my personal -- well,

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this might not involve
everything, but it could be--

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my personal balance sheet.

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But it looks like my whole
world is this house.

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Which in a lot of cases, it
is, for a lot of people.

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So in this situation,
what are my assets?

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I have a $1 million house
on my balance sheet.

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I have one asset in the world.

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I guess you can't quantify
charisma and good looks.

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So the only real tangible
asset I have is

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a $1 million house.

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And what are my liabilities?

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Well I owe $750,000
to the bank.

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And so we learned in the last
video -- and you shouldn't

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view this as a formula.

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It should start to make a little
bit of intuitive sense

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-- that assets are equal to
liability plus equity.

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Or the other way to view it is,
assets minus liabilities

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is equal to equity, right?

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Subtract the liability
from both sides.

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And you know that if I have $1
million of assets, I owe

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$750,000, if I were to resolve
everything, what I'd have left

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over at the end is $250,000.

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And I could make that happen.

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I could sell the house for $1
million, hopefully, and then

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pay the bank back.

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And I would have
$250,000 left.

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So that's what equity is, just
what you have left after you

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resolve everything.

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Or another way -- and this
makes sense to you.

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If you talk about all the things
you own minus all the

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things you owe to other
people, equity

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is what's left over.

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Or that could be
owner's equity.

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So now let's play with some
scenarios of what happens,

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maybe, when the market value
of the house changes.

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So let's say, what happens when
-- oh, and one important

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thing to note, this bank,
they're not just going to give

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me $750,000 just to do
anything with it.

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They're not going to say, hey,
Sal, here's $750,000.

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I know you'll pay it back
to me, but you can go

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gamble it in Monaco.

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They want to know that they have
a good chance of getting

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at least the money that they
give, the loan amount, and

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that is often referred
to as the principal.

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They want to know that they're
going to be able to get that

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principal back one day.

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So what they say is, Sal, we're
only going to give you

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this loan, but this loan
has to be backed.

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Or it has to be collateralized
by some asset.

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And so what I say is, OK, well,
you know I'm taking this

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loan out to buy a house,
a $1 million house.

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If for whatever reason, I lose
my job, or I disappear

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somehow, or whatever happens.

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If I can't pay you the $750,000,
you get the house.

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You'll get this $1
million house.

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And right now that looks like
a pretty good deal to the

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bank, right?

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They almost hope that I'll
default, because

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they gave me $750,000.

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If after a day I just say, you
know what, bank, I can't pay

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this loan, I don't have the
income, or I lost my job, I

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can't afford the mortgage.

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They get a $1 million
house overnight.

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They would have made
$250,000, right?

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They would have essentially
gotten all my equity for free.

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So in that situation, the bank
works out pretty good.

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And that's why they make sure
that there's something that

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they can grab onto if you
can't pay the loan.

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And that's why, back in the good
old days, and I think the

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good old days are going to come
back again, and I think

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they already are -- that the
bank wants you to put some

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down payment in a house.

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Because there's a situation
where, let's

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say that I do this.

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I borrow the money, and
I buy the house.

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And I lose my job, or
you know, whatever.

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I just drink away all of
my money, whatever

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the case may be.

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And so the bank,
they foreclose.

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Foreclose means that Sal isn't
paying on his debt, so we're

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going to take the collateral
back that he

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gave for the loan.

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So in that situation, the bank
says, Sal can't pay, we're

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taking that house.

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Well when they take that house,
there's a situation

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where maybe they're not
going to get $1

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million for that house.

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They don't want to sit and wait
for months and months and

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months while a real estate
agent tries to sell it.

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So the bank might just auction
off the house.

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And when it auctions off the
house -- actually I think

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there are laws that it can't get
more than the mortgage, or

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anything more than the mortgage
it gets, it actually

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has to pay taxes, or -- we won't
go into all of that.

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But it will auction off the
house, and maybe it can only

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auction off the house
for $800,000.

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Right?

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So the $1 million asset
would really

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become an $800,000 asset.

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And so the bank keeps this
equity cushion, right?

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That if they loan $750,000 for
a $1 million house, and then

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the $1 million house only sells
for $800,000, the bank

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still gets all of their
money back.

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That's why, in the good old
days, the banks wanted you to

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put 20% or 25% down, because
they know even if the value of

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the house drops by 20%
or 25%, it'll all

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come from your equity.

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And maybe I should draw a
diagram to see that situation.

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Let's say that for whatever
reason, I have to sell this

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house in a fire sale.

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Or let's say I can't sell the
house and the bank is forcing

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me to liquidate my assets.

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The banks says well then,
I want that house back.

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So in that situation -- well
actually, that's not a good

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situation because the bank
will just -- I'll

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just get wiped out.

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Let's just do the situation
where let's say a neighbor's

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house sells for-- a neighbor's
house that is identical.

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An identical neighbor's house,
sells for $800,000, right?

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So in that situation, if I want
to be honest with myself,

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and if I want to be honest with
the balance sheet-- and

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actual real companies have to
do this-- I'll say, you know

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what, this asset, I have
to revalue it.

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I cannot in all honesty say that
this is now worth, that

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this is a $1 million asset.

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So I would revalue the asset.

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And this is actually called
marking to market.

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You probably heard
of this concept.

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Marking to market means I have
an asset, and every now and

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then, maybe every few months,
every quarter -- a quarter is

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just a fourth of a year -- I
have to figure out what that

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asset is worth.

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And the best way to figure out
what that asset is worth is to

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see what identical assets
like that are

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going for on the market.

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And very few houses are
completely identical.

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Well there are, in
a few suburbs.

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Very few assets are completely
identical.

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But let's just say that I know
for a fact that an identical

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house just sold for $800,000.

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So I have to be honest. And I
have to mark it to market, and

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then say that my assets are
now an $800,000 house.

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My same house.

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Nothing really happened, but the
market value has dropped

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by $200,000 for whatever
reason.

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Maybe the car factory nearby
has gone out of business.

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So in this situation,
what happens?

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What is my new balance sheet?

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Well has my liability changed,
because my neighbor's house

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sold for less?

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Well, no, as far as the bank
is concerned, I still owe

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$750,000 to the bank.

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This is a liability.

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I still owe $750,000.

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This is assets, of course.

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So what's leftover?

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What would be left over if I
were to liquidate at the

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market price, if I were
to sell the house

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at the market price?

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Well I would have $50,000
left over.

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Essentially when the market
price of my asset dropped, all

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of that value came
out of my equity.

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I'll do actually a whole other
video on the benefits and the

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risks of leverage, because
that's very relevant to what's

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happening in the world today.

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But I think you get a sense
of what's happening.

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Equity kind of takes
all of the risk.

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So in this situation, this is
why the bank wants you to put

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some down payment.

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Because the bank, if you can't
pay this loan right here,

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they're going to take
your house.

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And even in the situation where
the value of the house

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went down, if you can't pay the
loan, the bank will still

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be able to get its
$750,000, right?

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If you just leave town, or lose
your job, and you just

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tell the bank I can't pay
anymore, they're just going to

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take this house, sell it,
hopefully for $800,000,

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because that's what your
neighbor sold it for.

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And they're going to get the
money back for their loan.

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So that's why the bank wants you
to put some down payment.

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And then there's the other
situation, which is maybe a

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more positive situation.

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And this is what happened in
much of the world, and

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especially in areas like
California and Florida and

00:08:12.440 --> 00:08:15.580
Nevada over the last
five years or so.

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And I'll do a whole video
on why it happened.

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But let's say your neighbor's
house, a year later, didn't

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sell for $800,000.

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Let's say the identical
neighbor's house

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sold for $1.5 million.

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And you say, gee whiz.

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That's great.

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Now my house is also worth
$1.5 million because I'm

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marking to market.

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So now my asset -- nothing
has really changed.

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It's still the same house.

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But I guess, since someone else
sold it for $1.5 million,

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I guess I could, too.

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So my asset is now a
$1.5 million house.

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What are my liabilities?

00:08:45.920 --> 00:08:48.320
Well your liabilities still
haven't changed.

00:08:48.320 --> 00:08:55.810
I still owe $750,000 to bank.

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This is liabilities.

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So what's left over?

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What's my equity?

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Well, assets minus liability.

00:09:03.200 --> 00:09:06.860
So I have $750,000 of equity.

00:09:06.860 --> 00:09:08.200
That's awesome.

00:09:08.200 --> 00:09:10.820
Even though the house
appreciated by 50%, right?

00:09:10.820 --> 00:09:14.990
It went from $1 million to $1.5
million, my equity grew

00:09:14.990 --> 00:09:15.900
three-fold.

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It appreciated by 200%.

00:09:21.020 --> 00:09:23.650
I think you're starting to get
the benefits of what happens

00:09:23.650 --> 00:09:24.410
when you do leverage.

00:09:24.410 --> 00:09:27.750
Leverage is when you use
debt to buy an asset.

00:09:27.750 --> 00:09:31.840
But when you use leverage, the
return that you get on your

00:09:31.840 --> 00:09:34.550
asset gets multiplied when you
get the return on your equity.

00:09:34.550 --> 00:09:36.070
I hope I'm not confusing you.

00:09:36.070 --> 00:09:37.150
But in this situation,
all of a sudden I

00:09:37.150 --> 00:09:38.610
have a ton of equity.

00:09:38.610 --> 00:09:40.230
And I'm running out of time.

00:09:40.230 --> 00:09:41.760
But in the next video
I'm going to talk

00:09:41.760 --> 00:09:42.820
about how this happened.

00:09:42.820 --> 00:09:44.200
Because you saw it in a
lot of neighborhoods.

00:09:44.200 --> 00:09:50.370
A lot of houses appreciated
from about 2001 to 2005.

00:09:50.370 --> 00:09:52.830
And people, all of a sudden,
just sitting on their house,

00:09:52.830 --> 00:09:54.130
ended up with a lot of equity.

00:09:54.130 --> 00:09:57.380
And they felt that, wow, I just
went from having $250,000

00:09:57.380 --> 00:10:00.050
of net wealth to $750,000
of wealth,

00:10:00.050 --> 00:10:00.900
without doing anything.

00:10:00.900 --> 00:10:02.940
Just by my neighbor's house
selling for more.

00:10:02.940 --> 00:10:04.190
I'll see you in the next video.


Introduction to Balance Sheets

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Kind: captions
Language: en

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Welcome.

00:00:01.480 --> 00:00:04.160
Well there's been a lot of news
lately about what's going

00:00:04.160 --> 00:00:07.850
on with Bear Stearns and
Carlisle Capital.

00:00:07.850 --> 00:00:10.080
And I go to these parties, and
I start explaining to people

00:00:10.080 --> 00:00:11.000
because it's very exciting.

00:00:11.000 --> 00:00:13.520
It's actually very important,
to all of our collective

00:00:13.520 --> 00:00:15.890
futures and the whole health of
the financial system, and I

00:00:15.890 --> 00:00:18.790
feel like people's eyes
start to glaze over.

00:00:18.790 --> 00:00:21.330
So with that in mind, I decided
to take a little bit

00:00:21.330 --> 00:00:23.820
of a hiatus from the core math
and physics videos, and

00:00:23.820 --> 00:00:26.250
actually do some accounting
and finance videos.

00:00:26.250 --> 00:00:27.700
Because I think what's happening
in the world right

00:00:27.700 --> 00:00:30.560
now is extremely important.

00:00:30.560 --> 00:00:33.090
And I'm not just going to go
straight into what's going

00:00:33.090 --> 00:00:37.770
into Carlisle and Thornburg and
all of these characters.

00:00:37.770 --> 00:00:39.900
Because I think the newspapers
do that, but a lot of people

00:00:39.900 --> 00:00:41.650
don't understand the
basic accounting.

00:00:41.650 --> 00:00:43.490
What is a write-down, what does
it mean when you don't

00:00:43.490 --> 00:00:45.630
have liquidity, in really
tangible ways.

00:00:45.630 --> 00:00:48.500
So I'm going to use the same
Khan Academy techniques to

00:00:48.500 --> 00:00:50.130
hopefully explain
some of this.

00:00:50.130 --> 00:00:54.080
So I'm going to start with just
a very basic accounting

00:00:54.080 --> 00:00:55.470
concept of the balance sheet.

00:00:55.470 --> 00:00:57.210
You might have a sense
of what it is.

00:00:57.210 --> 00:00:57.980
So let's say a scenario.

00:00:57.980 --> 00:00:59.060
Let's say I want
to buy a house.

00:00:59.060 --> 00:01:01.780
So this is, let me
draw a house.

00:01:01.780 --> 00:01:05.650
So let's say this is the
house I want to buy.

00:01:05.650 --> 00:01:07.540
And the owner of this house
is asking for $1

00:01:07.540 --> 00:01:08.790
million for this house.

00:01:08.790 --> 00:01:11.420
And I like the house, and I
think that's a fair price.

00:01:11.420 --> 00:01:13.092
Other houses in the neighborhood
also went for $1

00:01:13.092 --> 00:01:14.180
million, whatever.

00:01:14.180 --> 00:01:15.230
Maybe they went for more,
so I think it's

00:01:15.230 --> 00:01:16.620
actually a good deal.

00:01:16.620 --> 00:01:30.320
But all I have in my pocket is,
let's say I have $250,000.

00:01:30.320 --> 00:01:33.680
So what I'm going to do is, I'm
going to create my balance

00:01:33.680 --> 00:01:35.520
sheet before I do anything.

00:01:35.520 --> 00:01:36.720
Before I go to try
to get the house.

00:01:36.720 --> 00:01:40.170
What is my before-house
balance sheet?

00:01:40.170 --> 00:01:42.290
What are my assets?

00:01:42.290 --> 00:01:43.540
I'm going to write
down Assets.

00:01:48.070 --> 00:01:49.700
Well before we know what my
assets are, let me tell you

00:01:49.700 --> 00:01:50.510
what an asset is.

00:01:50.510 --> 00:01:55.040
An asset is something that's
going to give you some future

00:01:55.040 --> 00:01:56.200
economic benefit.

00:01:56.200 --> 00:01:58.250
So for example, cash
is an asset.

00:01:58.250 --> 00:01:59.220
Why is cash an asset?

00:01:59.220 --> 00:02:03.720
Because in the future you can
use that cash to get stuff

00:02:03.720 --> 00:02:06.170
from people, or make them
do things, or buy stuff.

00:02:06.170 --> 00:02:08.570
You can, in a month from now,
you can use your cash.

00:02:08.570 --> 00:02:10.620
And you can make someone
dance for you.

00:02:10.620 --> 00:02:14.290
Or you can buy a car, or
you can go on vacation.

00:02:14.290 --> 00:02:16.430
So there's all sorts of
things you can do.

00:02:16.430 --> 00:02:18.010
I don't know if someone dancing
for you is an actual

00:02:18.010 --> 00:02:20.260
economic benefit, but
you get the idea.

00:02:20.260 --> 00:02:21.820
So cash could be an asset.

00:02:21.820 --> 00:02:25.020
A house could be an asset,
because the economic benefit

00:02:25.020 --> 00:02:26.730
you get in the future is, you
get to live in it, and not

00:02:26.730 --> 00:02:29.190
freeze when it's freezing
outside.

00:02:29.190 --> 00:02:30.690
So that's what an asset is.

00:02:30.690 --> 00:02:33.760
So what are my assets, before
I buy the house, or get a

00:02:33.760 --> 00:02:35.650
loan, or all of the things
that are about to happen?

00:02:35.650 --> 00:02:43.550
Well I have cash, I have
$250,000 worth of cash.

00:02:43.550 --> 00:02:47.000
What are my liabilities?

00:02:47.000 --> 00:02:47.980
I'm going to write the
liabilities on

00:02:47.980 --> 00:02:50.470
the left-hand side.

00:02:50.470 --> 00:02:52.180
I think that's the convention,
but I forget.

00:02:52.180 --> 00:02:53.460
It doesn't matter.

00:02:53.460 --> 00:02:55.270
What are my liabilities?

00:02:55.270 --> 00:03:00.320
Well, a liability is something
that's an economic obligation

00:03:00.320 --> 00:03:01.270
to someone else.

00:03:01.270 --> 00:03:04.370
So if I take a loan from
someone, I owe them interest,

00:03:04.370 --> 00:03:06.610
or I have to pay them back
the actual value of

00:03:06.610 --> 00:03:07.790
the loan one day.

00:03:07.790 --> 00:03:10.990
Say I have an IOU where I
promise to dance for someone

00:03:10.990 --> 00:03:11.880
in the future.

00:03:11.880 --> 00:03:13.250
That could be a liability.

00:03:13.250 --> 00:03:15.140
It'd be hard to value, but
that's something that I have

00:03:15.140 --> 00:03:16.550
to do in the future.

00:03:16.550 --> 00:03:17.690
But what are my liabilities
here?

00:03:17.690 --> 00:03:21.420
Well in the example I gave, I'm
just Sal, I have no debt,

00:03:21.420 --> 00:03:22.860
I paid off my college
loans, everything.

00:03:22.860 --> 00:03:26.850
And I have $250,000 in cash.

00:03:26.850 --> 00:03:29.440
So what are my liabilities
before I buy the house?

00:03:29.440 --> 00:03:30.290
Well, nothing.

00:03:30.290 --> 00:03:31.810
I don't have any liabilities.

00:03:31.810 --> 00:03:33.260
I don't owe anybody anything.

00:03:33.260 --> 00:03:35.320
And that's, actually,
that to me is the

00:03:35.320 --> 00:03:37.360
definition of freedom.

00:03:37.360 --> 00:03:40.580
So I have zero liability.

00:03:40.580 --> 00:03:43.630
So what is my equity?

00:03:43.630 --> 00:03:45.630
And you've probably heard this
word, people borrowing their

00:03:45.630 --> 00:03:47.010
equity, and all of
these things.

00:03:47.010 --> 00:03:48.510
So I'm going to give you a
little equation, actually,

00:03:48.510 --> 00:03:50.340
just to take a little
bit of a tangent.

00:03:50.340 --> 00:03:56.020
That assets, A for assets,
is equal to

00:03:56.020 --> 00:04:00.900
liabilities plus equity.

00:04:00.900 --> 00:04:05.890
So in this case, our assets
are $250,000.

00:04:05.890 --> 00:04:06.810
My liabilities are what?

00:04:06.810 --> 00:04:10.130
I owe nothing to nobody.

00:04:10.130 --> 00:04:11.510
I don't know if that was
correct, but anyway.

00:04:11.510 --> 00:04:13.200
I owe nothing to anyone.

00:04:13.200 --> 00:04:15.270
So my liabilities are zero.

00:04:15.270 --> 00:04:23.000
So my equity must be $250,000.

00:04:23.000 --> 00:04:25.450
So in this case, if I made a
balance sheet before I enter

00:04:25.450 --> 00:04:27.430
into any transactions -- let me
make it look a little bit

00:04:27.430 --> 00:04:30.380
like a balance sheet.

00:04:30.380 --> 00:04:32.100
My assets are $250,000.

00:04:32.100 --> 00:04:33.630
I have no liabilities.

00:04:33.630 --> 00:04:40.610
And then my equity would
be $250,000.

00:04:40.610 --> 00:04:42.380
And if I were to draw this
graphically-- actually, I

00:04:42.380 --> 00:04:43.210
should probably draw
it like this.

00:04:43.210 --> 00:04:43.770
I have no liabilities.

00:04:43.770 --> 00:04:47.180
So let me draw another little
mini balance sheet here.

00:04:47.180 --> 00:04:48.700
That's a neat square.

00:04:48.700 --> 00:04:50.200
You probably can't
see that square.

00:04:53.940 --> 00:04:57.270
So I put my assets on
the right-hand side.

00:04:57.270 --> 00:05:00.370
And I'll say, there, I have
$250,000 of cash.

00:05:00.370 --> 00:05:02.100
And on the left-hand side,
I have no liabilities.

00:05:02.100 --> 00:05:06.520
And I'll just say I have equity,
I have $250,000.

00:05:06.520 --> 00:05:08.510
Now, equity might not make a lot
of sense to you right now,

00:05:08.510 --> 00:05:11.010
because I'm just saying, well,
my equity is equal to my cash.

00:05:11.010 --> 00:05:14.060
in general, equity is
just what you own.

00:05:14.060 --> 00:05:16.890
After all of your assets and
liabilities are kind of

00:05:16.890 --> 00:05:19.190
resolved, or they're
cleared up, what do

00:05:19.190 --> 00:05:20.410
you have left over?

00:05:20.410 --> 00:05:21.270
That's equity.

00:05:21.270 --> 00:05:24.020
So in this situation, after I
pay off all of my debts, what

00:05:24.020 --> 00:05:24.860
do I have left over?

00:05:24.860 --> 00:05:28.080
Well I have no debts, so I have
$250,000 in cash, total.

00:05:28.080 --> 00:05:31.020
This will start to make sense
when I go to the bank now to

00:05:31.020 --> 00:05:33.060
get a loan to buy this house.

00:05:33.060 --> 00:05:36.190
So this house is a $1 million
house, right?

00:05:36.190 --> 00:05:37.770
So how much of a
loan do I need?

00:05:37.770 --> 00:05:41.780
Well, I have $250,000 cash, so
I'll go to the bank for a loan

00:05:41.780 --> 00:05:44.490
for the remainder,
for $750,000.

00:05:44.490 --> 00:05:49.650
So let me draw the bank.

00:05:49.650 --> 00:05:50.650
This is the bank.

00:05:50.650 --> 00:05:53.610
The big dollar sign is made out
of granite, to show you

00:05:53.610 --> 00:05:54.690
that it can never fail.

00:05:54.690 --> 00:05:57.700
It's going to be there forever,
even if they do silly

00:05:57.700 --> 00:06:00.890
things, like-- well I won't go
into all the silly things that

00:06:00.890 --> 00:06:02.410
they do, but they do
many silly things.

00:06:02.410 --> 00:06:03.570
We'll go into that later.

00:06:03.570 --> 00:06:12.380
But the bank is going to give
me another $750,000 in cash.

00:06:12.380 --> 00:06:17.700
And in return, I'm giving
them essentially an IOU.

00:06:17.700 --> 00:06:20.090
And I'm going to pay interest.
So they're going to hold this

00:06:20.090 --> 00:06:23.960
little security that says,
Sal owes me $750,000.

00:06:23.960 --> 00:06:27.290
And he has to give me 10%
interest every year.

00:06:27.290 --> 00:06:29.570
So $75,000 a year, or
something like that.

00:06:29.570 --> 00:06:32.280
And in return I get
$750,000 in cash.

00:06:32.280 --> 00:06:34.870
So what does my balance
sheet look like now?

00:06:34.870 --> 00:06:36.780
Well, let me draw it.

00:06:36.780 --> 00:06:41.130
Let me make sure my balance
sheet now looks, let me draw

00:06:41.130 --> 00:06:42.680
it like a square, because
I think the visual

00:06:42.680 --> 00:06:51.000
representation is helpful,
and then I will split it.

00:06:51.000 --> 00:06:53.060
So what are all my assets now?

00:06:53.060 --> 00:06:56.010
I had $250,000 and
I got another

00:06:56.010 --> 00:07:00.260
$750,000 from the bank.

00:07:00.260 --> 00:07:01.480
So now, what are my assets?

00:07:01.480 --> 00:07:03.740
Well, $250,000 plus $750,000.

00:07:03.740 --> 00:07:06.530
I now have cash of $1 million.

00:07:10.060 --> 00:07:11.820
What are my liabilities?

00:07:11.820 --> 00:07:15.460
Well, my liability, that's
something that I owe to

00:07:15.460 --> 00:07:16.000
someone else.

00:07:16.000 --> 00:07:19.700
I owe the bank $750,000.

00:07:19.700 --> 00:07:22.125
So liabilities, I'll just say L,
L for liabilities, because

00:07:22.125 --> 00:07:23.560
I'm running out of space.

00:07:23.560 --> 00:07:26.240
My wife was complaining that I
make these things very hard to

00:07:26.240 --> 00:07:28.060
read, but what can I do.

00:07:28.060 --> 00:07:28.390
Anyway.

00:07:28.390 --> 00:07:31.130
So my liabilities-- I owe
the bank $750,000.

00:07:31.130 --> 00:07:33.700
So that's a liability.

00:07:33.700 --> 00:07:37.140
And then the equity is,
essentially-- we would look at

00:07:37.140 --> 00:07:37.890
this formula.

00:07:37.890 --> 00:07:39.480
Assets equal liabilities
plus equity.

00:07:39.480 --> 00:07:41.170
This is $1 million,
this is $750,000.

00:07:41.170 --> 00:07:42.500
What do I have left over?

00:07:42.500 --> 00:07:44.670
Well, I have $250,000
left over.

00:07:44.670 --> 00:07:46.970
That's my equity.

00:07:46.970 --> 00:07:50.820
And I think hopefully the
concept of equity is starting

00:07:50.820 --> 00:07:53.300
to make a little more sense.

00:07:53.300 --> 00:07:58.320
Now we have-- I could say that
I have $1 million, and some

00:07:58.320 --> 00:07:59.120
people are like that.

00:07:59.120 --> 00:08:00.760
They think they're millionaires
when they have $1

00:08:00.760 --> 00:08:02.000
million in assets.

00:08:02.000 --> 00:08:04.580
But they don't consider, well
they might have $1 million of

00:08:04.580 --> 00:08:07.050
assets, but they might owe
other people $900,000.

00:08:07.050 --> 00:08:09.040
So I wouldn't consider that
person a millionaire.

00:08:09.040 --> 00:08:11.690
They're more of a hundred
thousand-aire.

00:08:11.690 --> 00:08:14.140
Your assets might be $1 million,
but you're not nearly

00:08:14.140 --> 00:08:15.620
a millionaire, because
you still owe

00:08:15.620 --> 00:08:17.810
other people $750,000.

00:08:17.810 --> 00:08:21.490
What you have left over, that
really is your net worth, or

00:08:21.490 --> 00:08:23.220
what you can have claim to.

00:08:23.220 --> 00:08:24.190
And that's your equity.

00:08:24.190 --> 00:08:25.810
Sometimes it's called
owners' equity.

00:08:25.810 --> 00:08:27.676
Or if there was a bunch of
people pitching together, it

00:08:27.676 --> 00:08:29.030
would be called shareholders'
equity.

00:08:29.030 --> 00:08:31.960
And maybe I'll do a little bit
more on that in the future.

00:08:31.960 --> 00:08:34.760
But hopefully now you can see
that the balance sheet is

00:08:34.760 --> 00:08:38.330
starting to seem a little
bit useful.

00:08:38.330 --> 00:08:42.620
I have the cash, and I took the
loan from the bank, but

00:08:42.620 --> 00:08:44.410
now I still haven't bought
the house yet.

00:08:44.410 --> 00:08:45.430
So what am I going to do?

00:08:45.430 --> 00:08:49.490
Well I'm going to give my cash
to the old owner of the house.

00:08:49.490 --> 00:08:52.450
Or maybe this Toll Brothers,
they just built this

00:08:52.450 --> 00:08:53.960
McMansion for me.

00:08:53.960 --> 00:08:58.060
So I give them $1 million, and
in return they give me the

00:08:58.060 --> 00:08:59.140
deed to the house.

00:08:59.140 --> 00:09:01.140
I could just say they
give me the house.

00:09:01.140 --> 00:09:03.270
The house is always there, but
you know it's really just a

00:09:03.270 --> 00:09:05.440
contract and all the legal
structure that I get around

00:09:05.440 --> 00:09:07.500
it, and all the property
rights and all of that.

00:09:07.500 --> 00:09:09.910
But that's getting too
philosophical.

00:09:09.910 --> 00:09:12.390
So now what does my balance
sheet look like?

00:09:12.390 --> 00:09:15.530
Instead of cash-- I think I'm
running out of space and time

00:09:15.530 --> 00:09:17.850
to draw another balance sheet--
I don't have cash

00:09:17.850 --> 00:09:19.460
worth $1 million.

00:09:19.460 --> 00:09:21.740
I now have a house
worth $1 million.

00:09:21.740 --> 00:09:24.200
Assuming that it really is worth
it, and that was the

00:09:24.200 --> 00:09:26.420
correct price, I didn't
overpay, whatever.

00:09:26.420 --> 00:09:30.120
I now have, my assets are
a $1 million house.

00:09:30.120 --> 00:09:33.500
And I owe the bank $750,000.

00:09:33.500 --> 00:09:39.000
So what's left over for me
is $250,000 of equity.

00:09:39.000 --> 00:09:40.260
I'm about to run out of time.

00:09:40.260 --> 00:09:42.280
So I'm going to leave
you from this video.

00:09:42.280 --> 00:09:43.830
In the next video, I'm going
to start explaining what

00:09:43.830 --> 00:09:46.330
happens if the value of the
house goes up or down, or you

00:09:46.330 --> 00:09:48.420
need cash, and all of these
interesting things.

00:09:48.420 --> 00:09:51.240
And we'll start to learn a
little bit more about what's

00:09:51.240 --> 00:09:52.210
going on in the world.

00:09:52.210 --> 00:09:53.640
See you soon.


Introduction to torque

WEBVTT
Kind: captions
Language: en

00:00:00.880 --> 00:00:03.300
Welcome to the presentation
on torque.

00:00:03.300 --> 00:00:06.060
So, if you watched the
presentation on the center of

00:00:06.060 --> 00:00:08.690
mass, which you should have, you
might have gotten a little

00:00:08.690 --> 00:00:11.850
bit of a glancing view
of what torque is.

00:00:11.850 --> 00:00:14.350
And now we'll do some
more in detail.

00:00:14.350 --> 00:00:19.680
So in general, from the center
of mass video, we learned, if

00:00:19.680 --> 00:00:23.745
this is a ruler and this is the
ruler's center of mass.

00:00:26.330 --> 00:00:32.259
And if I were to apply force at
the center of mass, I would

00:00:32.259 --> 00:00:35.820
accelerate the whole ruler in
the direction of the force.

00:00:35.820 --> 00:00:37.810
If I have the force applying at
the center of mass there,

00:00:37.810 --> 00:00:41.240
the whole ruler would accelerate
in that direction.

00:00:41.240 --> 00:00:43.510
And we'd figure it out by
taking the force we're

00:00:43.510 --> 00:00:46.000
applying to it and dividing
by the mass of the ruler.

00:00:46.000 --> 00:00:49.020
And in that center of mass
video, I imply-- well, what

00:00:49.020 --> 00:00:52.040
happens if the force
is applied here?

00:00:52.040 --> 00:00:54.050
Away from the center of mass?

00:00:54.050 --> 00:00:56.960
Well, in this situation, the
object, assuming it's a free

00:00:56.960 --> 00:00:59.750
floating object on the Space
Shuttle or something, it will

00:00:59.750 --> 00:01:02.450
rotate around the
center of mass.

00:01:02.450 --> 00:01:06.410
And that's also true, if we
didn't use the center of mass,

00:01:06.410 --> 00:01:07.810
but instead we fixed
the point.

00:01:07.810 --> 00:01:14.110
Let's say we had
another ruler.

00:01:14.110 --> 00:01:17.310
Although it has less height
than the previous one.

00:01:17.310 --> 00:01:19.160
Instead of worrying about its
center of mass, let's say that

00:01:19.160 --> 00:01:22.930
it's just fixed at
a point here.

00:01:22.930 --> 00:01:23.980
Let's say it's fixed here.

00:01:23.980 --> 00:01:28.450
So if this could be the hand
of a clock, and it's nailed

00:01:28.450 --> 00:01:30.510
down to the back of the
clock right there.

00:01:30.510 --> 00:01:33.160
So if we were trying to rotate
it, it would always rotate

00:01:33.160 --> 00:01:34.170
around this point.

00:01:34.170 --> 00:01:35.800
And the same thing
would happen.

00:01:35.800 --> 00:01:38.830
If I were to apply a force at
this point, maybe I could

00:01:38.830 --> 00:01:41.550
break the nail off the back of
the clock, or something, but I

00:01:41.550 --> 00:01:44.830
won't rotate this needle or
this ruler, or whatever you

00:01:44.830 --> 00:01:45.770
want to call it.

00:01:45.770 --> 00:01:51.440
But if I would apply a force
here, I would rotate the ruler

00:01:51.440 --> 00:01:53.440
around the pivot point.

00:01:53.440 --> 00:01:58.010
And this force that's applied a
distance away from the pivot

00:01:58.010 --> 00:02:01.080
point, or we could say from the
axis of rotation, or the

00:02:01.080 --> 00:02:02.190
center of mass.

00:02:02.190 --> 00:02:03.770
That's called torque.

00:02:03.770 --> 00:02:08.949
And torque, the letter for
torque is this Greek, I think

00:02:08.949 --> 00:02:11.860
that's tau, it's a curvy T.

00:02:11.860 --> 00:02:17.640
And torque is defined as
force times distance.

00:02:17.640 --> 00:02:19.560
And what force and what
distance is it?

00:02:19.560 --> 00:02:25.030
It's the force that's
perpendicular to the object.

00:02:25.030 --> 00:02:26.960
I guess you could say to
the distance vector.

00:02:26.960 --> 00:02:29.170
If this is the distance vector--
let me do it in a

00:02:29.170 --> 00:02:31.110
different color.

00:02:31.110 --> 00:02:37.790
If this is the distance vector,
the component of the

00:02:37.790 --> 00:02:40.750
force is perpendicular to
this distance vector.

00:02:40.750 --> 00:02:42.100
And this is torque.

00:02:42.100 --> 00:02:43.320
And so what are its units?

00:02:43.320 --> 00:02:46.810
Well, force is newtons, and
distance is meters, so this is

00:02:46.810 --> 00:02:48.570
newton meters.

00:02:48.570 --> 00:02:51.010
And you're saying, hey Sal,
newtons times meters, force

00:02:51.010 --> 00:02:54.440
times distance, that looks
an awful lot like work.

00:02:54.440 --> 00:02:56.840
And it's very important to
realize that this isn't work,

00:02:56.840 --> 00:02:59.300
and that's why we won't
call this joules.

00:02:59.300 --> 00:03:01.130
Because in work, what
are we doing?

00:03:01.130 --> 00:03:03.010
We are translating an object.

00:03:03.010 --> 00:03:06.960
If this is an object, and I'm
applying a force, I'm taking

00:03:06.960 --> 00:03:09.610
the force over the distance
in the same

00:03:09.610 --> 00:03:12.000
direction as the force.

00:03:12.000 --> 00:03:14.880
Here the distance and
the force are

00:03:14.880 --> 00:03:15.750
parallel to each other.

00:03:15.750 --> 00:03:17.910
You could say the distance
vector and the force vector

00:03:17.910 --> 00:03:20.850
are in the same direction.

00:03:20.850 --> 00:03:22.090
Of course, that's
translational.

00:03:22.090 --> 00:03:23.350
The whole object
is just moving.

00:03:23.350 --> 00:03:24.940
It's not rotating or anything.

00:03:24.940 --> 00:03:28.340
In the situation of torque,
let me switch colors.

00:03:28.340 --> 00:03:32.000
The distance vector, this is the
distance from the fulcrum

00:03:32.000 --> 00:03:33.770
or the pivot point of the center
of mass, to where I'm

00:03:33.770 --> 00:03:34.840
applying the force.

00:03:34.840 --> 00:03:38.640
This distance vector is
perpendicular to the force

00:03:38.640 --> 00:03:39.790
that's being applied.

00:03:39.790 --> 00:03:42.930
So torque and work are
fundamentally two different

00:03:42.930 --> 00:03:45.940
things, even though their
units are the same.

00:03:45.940 --> 00:03:48.660
And this is a little
bit of notational.

00:03:48.660 --> 00:03:53.610
This distance is often called
the moment arm distance.

00:03:53.610 --> 00:03:54.960
And I don't know where
that came from.

00:03:54.960 --> 00:03:57.250
Maybe one of you all can write
me a message saying where it

00:03:57.250 --> 00:03:58.180
did come from.

00:03:58.180 --> 00:04:01.200
And often in some of your
physics classes they'll often

00:04:01.200 --> 00:04:03.400
call torque as a moment.

00:04:03.400 --> 00:04:04.970
But we'll deal with
the term torque.

00:04:04.970 --> 00:04:08.280
And that's more fun, because
eventually we can understand

00:04:08.280 --> 00:04:11.630
concepts like torque
horsepower in cars.

00:04:11.630 --> 00:04:14.230
So let's do a little bit of
math, hopefully I've given you

00:04:14.230 --> 00:04:16.930
a little bit of intuition.

00:04:16.930 --> 00:04:23.510
So let's say I had this ruler.

00:04:23.510 --> 00:04:28.780
And let's say that this is its
pivot point right here.

00:04:28.780 --> 00:04:29.960
So it would rotate around
that point.

00:04:29.960 --> 00:04:32.220
It's nailed to the wall
or something.

00:04:32.220 --> 00:04:37.990
And let's say that I apply a
force-- Let's say the moment

00:04:37.990 --> 00:04:39.760
arm distance.

00:04:39.760 --> 00:04:41.532
So let's say this distance,
let me do it

00:04:41.532 --> 00:04:43.690
in different color.

00:04:43.690 --> 00:04:49.740
Let's say that this distance
right here is 10 meters.

00:04:49.740 --> 00:04:57.300
And I were to apply a force of 5
newtons perpendicular to the

00:04:57.300 --> 00:05:00.710
distance vector, or to dimension
of the moment arm,

00:05:00.710 --> 00:05:02.040
you could view it either way.

00:05:02.040 --> 00:05:04.300
So torque is pretty easy
in this situation.

00:05:04.300 --> 00:05:11.580
Torque is going to be equal to
the force, 5 newtons, times

00:05:11.580 --> 00:05:13.010
the distance, 10.

00:05:13.010 --> 00:05:16.816
So it would be 50
newton meters.

00:05:16.816 --> 00:05:18.910
And you're probably saying,
well, Sal, how do I know if

00:05:18.910 --> 00:05:20.490
this torque is going to be
positive or negative?

00:05:20.490 --> 00:05:22.880
And this is where there's just a
general arbitrary convention

00:05:22.880 --> 00:05:23.550
in physics.

00:05:23.550 --> 00:05:25.190
And it's good to know.

00:05:25.190 --> 00:05:30.150
If you're rotating clockwise
torque is negative.

00:05:30.150 --> 00:05:30.990
Let me go the other way.

00:05:30.990 --> 00:05:32.930
If you were rotating
counterclockwise, like we were

00:05:32.930 --> 00:05:35.650
in this example, rotating
counterclockwise, the opposite

00:05:35.650 --> 00:05:38.250
direction of which a clock
would move in.

00:05:38.250 --> 00:05:39.560
Torque is positive.

00:05:39.560 --> 00:05:42.540
And if you rotate clockwise
the other

00:05:42.540 --> 00:05:44.250
way, torque is negative.

00:05:44.250 --> 00:05:45.680
So clockwise is negative.

00:05:45.680 --> 00:05:50.390
And I'm not going to go into
the whole cross product and

00:05:50.390 --> 00:05:52.210
the linear algebra of torque
right now, because I think

00:05:52.210 --> 00:05:53.790
that's a little bit
beyond the scope.

00:05:53.790 --> 00:05:55.450
But we'll do that
once we do more

00:05:55.450 --> 00:05:58.160
mathematically intensive physics.

00:05:58.160 --> 00:06:00.190
But, so, good enough.

00:06:00.190 --> 00:06:02.790
There's a torque of
50 newton meters.

00:06:02.790 --> 00:06:04.390
And that's all of the torque
that is acting

00:06:04.390 --> 00:06:05.040
on this object .

00:06:05.040 --> 00:06:06.330
So it's going to rotate
in this direction.

00:06:06.330 --> 00:06:09.910
And we don't have the tools yet
to figure out how quickly

00:06:09.910 --> 00:06:10.660
it will rotate.

00:06:10.660 --> 00:06:12.010
But we know it will rotate.

00:06:12.010 --> 00:06:14.510
And that's vaguely useful.

00:06:14.510 --> 00:06:17.100
But what if I said that the
object is not rotating?

00:06:17.100 --> 00:06:24.940
And that I have another
force acting here?

00:06:24.940 --> 00:06:35.180
And let's say that that force
is-- I don't know, let me make

00:06:35.180 --> 00:06:37.570
up something, that's 5
meters to the left

00:06:37.570 --> 00:06:38.820
of the pivot point.

00:06:44.000 --> 00:06:48.130
If I were tell you that this
object does not rotate.

00:06:48.130 --> 00:06:50.610
So if I tell you that the object
is not rotating, that

00:06:50.610 --> 00:06:56.340
means the net torque on this
ruler must be 0, because it's

00:06:56.340 --> 00:07:00.380
not-- its rate of change of
rotation is not changing.

00:07:00.380 --> 00:07:01.860
I should be a little exact.

00:07:01.860 --> 00:07:07.600
If I'm applying some force here,
and still not rotating,

00:07:07.600 --> 00:07:12.020
then we know that the net torque
on this object is 0.

00:07:12.020 --> 00:07:14.730
So what is the force
being applied here?

00:07:14.730 --> 00:07:16.750
Well, what is the net torque?

00:07:16.750 --> 00:07:19.170
Well, it's this torque, which
we already figured out.

00:07:19.170 --> 00:07:20.740
It's going in the clockwise
direction.

00:07:20.740 --> 00:07:24.340
So it's 5-- Let me do it
in a brighter color.

00:07:24.340 --> 00:07:27.480
5 times 10.

00:07:27.480 --> 00:07:28.960
And then the net torque.

00:07:28.960 --> 00:07:31.580
The sum of all the torques
have to be equal to 0.

00:07:31.580 --> 00:07:32.510
So what's this torque?

00:07:32.510 --> 00:07:34.480
So let's call this f.

00:07:34.480 --> 00:07:35.750
This is the force.

00:07:35.750 --> 00:07:40.790
So, plus-- Well, this force is
acting in what direction?

00:07:40.790 --> 00:07:43.110
Clockwise or counterclockwise?

00:07:43.110 --> 00:07:44.810
Well, it's acting in the
clockwise direction.

00:07:44.810 --> 00:07:47.710
This force wants to make the
ruler rotate this way.

00:07:47.710 --> 00:07:50.040
So this is actually going
to be a negative torque.

00:07:50.040 --> 00:07:55.570
So let's say, put a negative
number here times f, times its

00:07:55.570 --> 00:07:59.630
moment arm distance, times
5, and all of this

00:07:59.630 --> 00:08:00.930
has to equal 0.

00:08:00.930 --> 00:08:05.300
The net torque is 0, because the
object's rate of change of

00:08:05.300 --> 00:08:07.990
rotation isn't changing, or if
it started off not rotating,

00:08:07.990 --> 00:08:09.660
it's still not rotating.

00:08:09.660 --> 00:08:16.300
So here we get 50 minus
5 f is equal to 0.

00:08:16.300 --> 00:08:20.440
That's 50 is equal to 5 f.

00:08:20.440 --> 00:08:22.290
f is equal to 10.

00:08:22.290 --> 00:08:25.700
If we follow the units all the
way through, we would get that

00:08:25.700 --> 00:08:28.460
f is equal to 10 newtons.

00:08:28.460 --> 00:08:30.220
So that's interesting.

00:08:30.220 --> 00:08:34.289
I applied double the force
at half the distance.

00:08:34.289 --> 00:08:38.409
And it offsetted half the force
at twice the distance.

00:08:38.409 --> 00:08:41.059
And that should all connect, or
start to connect, with what

00:08:41.059 --> 00:08:43.309
we talked about with mechanical
advantage.

00:08:43.309 --> 00:08:45.270
You could view it
the other way.

00:08:45.270 --> 00:08:48.160
Let's say these are people
applying these forces.

00:08:48.160 --> 00:08:50.430
Say this guy over here is
applying 10 newtons.

00:08:50.430 --> 00:08:51.410
He's much stronger.

00:08:51.410 --> 00:08:53.240
He's twice as strong as
this guy over here.

00:08:53.240 --> 00:08:57.310
But because this guy is twice
as far away from the pivot

00:08:57.310 --> 00:08:59.820
point, he balances
the other guy.

00:08:59.820 --> 00:09:01.810
So you can kind of view it
as this guy having some

00:09:01.810 --> 00:09:04.340
mechanical advantage or having
a mechanical advantage of 2.

00:09:04.340 --> 00:09:06.330
And watch the mechanical
advantage videos if that

00:09:06.330 --> 00:09:07.910
confuses you a little bit.

00:09:07.910 --> 00:09:09.550
But this is where to
torque is useful.

00:09:09.550 --> 00:09:13.600
Because if an object's rate of
rotation is not changing, you

00:09:13.600 --> 00:09:16.200
know that the net torque
on that object is 0.

00:09:16.200 --> 00:09:19.910
And you can solve for the
forces or the distances.

00:09:19.910 --> 00:09:21.460
I'm about to run out of
time, so I will see

00:09:21.460 --> 00:09:23.380
you in the next video.


Center of mass

WEBVTT
Kind: captions
Language: en

00:00:02.550 --> 00:00:05.840
I will now do a presentation
on the center of mass.

00:00:05.840 --> 00:00:09.110
And the center mass, hopefully,
is something that

00:00:09.110 --> 00:00:12.130
will be a little bit intuitive
to you, and it actually has

00:00:12.130 --> 00:00:14.300
some very neat applications.

00:00:14.300 --> 00:00:18.530
So in very simple terms, the
center of mass is a point.

00:00:18.530 --> 00:00:21.850
Let me draw an object.

00:00:21.850 --> 00:00:25.520
Let's say that this
is my object.

00:00:25.520 --> 00:00:26.770
Let's say it's a ruler.

00:00:30.800 --> 00:00:33.270
This ruler, it exists,
so it has some mass.

00:00:33.270 --> 00:00:35.310
And my question to you is
what is the center mass?

00:00:35.310 --> 00:00:37.240
And you say, Sal, well, in order
to know figure out the

00:00:37.240 --> 00:00:39.910
center mass, you have to tell me
what the center of mass is.

00:00:39.910 --> 00:00:43.340
And what I tell you is the
center mass is a point, and it

00:00:43.340 --> 00:00:46.750
actually doesn't have to even
be a point in the object.

00:00:46.750 --> 00:00:48.850
I'll do an example soon
where it won't be.

00:00:48.850 --> 00:00:49.820
But it's a point.

00:00:49.820 --> 00:00:53.705
And at that point, for dealing
with this object as a whole or

00:00:53.705 --> 00:00:57.040
the mass of the object as a
whole, we can pretend that the

00:00:57.040 --> 00:00:59.550
entire mass exists
at that point.

00:00:59.550 --> 00:01:01.420
And what do I mean
by saying that?

00:01:01.420 --> 00:01:05.540
Well, let's say that the
center of mass is here.

00:01:05.540 --> 00:01:06.890
And I'll tell you why
I picked this point.

00:01:06.890 --> 00:01:08.200
Because that is pretty close
to where the center

00:01:08.200 --> 00:01:09.970
of mass will be.

00:01:09.970 --> 00:01:12.980
If the center of mass is there,
and let's say the mass

00:01:12.980 --> 00:01:18.110
of this entire ruler is, I don't
know, 10 kilograms. This

00:01:18.110 --> 00:01:25.820
ruler, if a force is applied at
the center of mass, let's

00:01:25.820 --> 00:01:30.950
say 10 Newtons, so the mass
of the whole ruler is 10

00:01:30.950 --> 00:01:37.430
kilograms. If a force is applied
at the center of mass,

00:01:37.430 --> 00:01:42.250
this ruler will accelerate the
same exact way as would a

00:01:42.250 --> 00:01:43.950
point mass.

00:01:43.950 --> 00:01:46.180
Let's say that we just had a
little dot, but that little

00:01:46.180 --> 00:01:51.870
dot had the same mass, 10
kilograms, and we were to push

00:01:51.870 --> 00:01:54.500
on that dot with 10 Newtons.

00:01:54.500 --> 00:01:57.960
In either case, in the case of
the ruler, we would accelerate

00:01:57.960 --> 00:01:58.860
upwards at what?

00:01:58.860 --> 00:02:02.460
Force divided by mass, so we
would accelerate upwards at 1

00:02:02.460 --> 00:02:04.580
meter per second squared.

00:02:04.580 --> 00:02:07.580
And in this case of this
point mass, we would

00:02:07.580 --> 00:02:09.009
accelerate that point.

00:02:09.009 --> 00:02:10.665
When I say point mass, I'm just
saying something really,

00:02:10.665 --> 00:02:13.500
really small, but it has a mass
of 10 kilograms, so it's

00:02:13.500 --> 00:02:15.470
much smaller, but it has the
same mass as this ruler.

00:02:15.470 --> 00:02:20.270
This would also accelerate
upwards with a magnitude of 1

00:02:20.270 --> 00:02:21.870
meters per second squared.

00:02:24.550 --> 00:02:26.660
So why is this useful to us?

00:02:26.660 --> 00:02:29.850
Well, sometimes we have some
really crazy objects and we

00:02:29.850 --> 00:02:31.550
want to figure out exactly
what it does.

00:02:31.550 --> 00:02:35.370
If we know its center of mass
first, we can know how that

00:02:35.370 --> 00:02:37.440
object will behave without
having to worry about the

00:02:37.440 --> 00:02:38.850
shape of that object.

00:02:38.850 --> 00:02:41.730
And I'll give you a really easy
way of realizing where

00:02:41.730 --> 00:02:43.270
the center of mass is.

00:02:43.270 --> 00:02:47.710
If the object has a uniform
distribution-- when I say

00:02:47.710 --> 00:02:51.160
that, it means, for simple
purposes, if it's made out of

00:02:51.160 --> 00:02:53.710
the same thing and that thing
that it's made out of, its

00:02:53.710 --> 00:02:56.970
density, doesn't really change
throughout the object, the

00:02:56.970 --> 00:03:03.490
center of mass will be the
object's geometric center.

00:03:03.490 --> 00:03:05.700
So in this case, this
ruler's almost a

00:03:05.700 --> 00:03:06.660
one-dimensional object.

00:03:06.660 --> 00:03:07.840
We just went halfway.

00:03:07.840 --> 00:03:09.670
The distance from here to here
and the distance from here to

00:03:09.670 --> 00:03:10.230
here are the same.

00:03:10.230 --> 00:03:11.240
This is the center of mass.

00:03:11.240 --> 00:03:13.900
If we had a two-dimensional
object, let's say we had this

00:03:13.900 --> 00:03:18.080
triangle and we want to figure
out its center of mass, it'll

00:03:18.080 --> 00:03:20.070
be the center in
two dimensions.

00:03:20.070 --> 00:03:22.370
So it'll be something
like that.

00:03:22.370 --> 00:03:28.730
Now, if I had another situation,
let's say I have

00:03:28.730 --> 00:03:32.340
this square.

00:03:32.340 --> 00:03:34.800
I don't know if that's big
enough for you to see.

00:03:34.800 --> 00:03:36.550
I need to draw it a
little thicker.

00:03:36.550 --> 00:03:40.890
Let's say I have this square,
but let's say that half of

00:03:40.890 --> 00:03:49.945
this square is made from lead.

00:03:55.780 --> 00:03:59.630
And let's say the other half
of the square is made from

00:03:59.630 --> 00:04:01.120
something lighter than lead.

00:04:01.120 --> 00:04:02.920
It's made of styrofoam.

00:04:02.920 --> 00:04:05.450
That is lighter than lead.

00:04:05.450 --> 00:04:07.680
So in this situation, the center
of mass isn't going to

00:04:07.680 --> 00:04:08.770
be the geographic center.

00:04:08.770 --> 00:04:12.080
I don't know how much denser
lead is than styrofoam, but

00:04:12.080 --> 00:04:16.360
the center of mass is going to
be someplace closer to the

00:04:16.360 --> 00:04:20.930
right because this object does
not have a uniform density.

00:04:20.930 --> 00:04:25.065
It'll actually depend on how
much denser the lead is than

00:04:25.065 --> 00:04:26.730
the styrofoam, which
I don't know.

00:04:26.730 --> 00:04:29.100
But hopefully, that gives you a
little intuition of what the

00:04:29.100 --> 00:04:31.100
center of mass is.

00:04:31.100 --> 00:04:34.130
And now I'll tell you something
a little more

00:04:34.130 --> 00:04:35.650
interesting.

00:04:35.650 --> 00:04:40.530
Every problem we have done so
far, we actually made the

00:04:40.530 --> 00:04:43.360
simplifying assumption that
the force acts on

00:04:43.360 --> 00:04:44.930
the center of mass.

00:04:44.930 --> 00:04:48.510
So if I have an object, let's
say the object that

00:04:48.510 --> 00:04:49.760
looks like a horse.

00:04:53.620 --> 00:04:55.590
Let's say that object.

00:04:55.590 --> 00:04:58.210
If this is the object's center
of mass, I don't know where

00:04:58.210 --> 00:05:01.100
the horse's center of mass
normally is, but let's say a

00:05:01.100 --> 00:05:03.810
horse's center of
mass is here.

00:05:03.810 --> 00:05:10.990
If I apply a force directly on
that center of mass, then the

00:05:10.990 --> 00:05:14.310
object will move in the
direction of that force with

00:05:14.310 --> 00:05:15.660
the appropriate acceleration.

00:05:15.660 --> 00:05:19.390
We could divide the force by the
mass of the entire horse

00:05:19.390 --> 00:05:19.990
and we would figure out the

00:05:19.990 --> 00:05:23.080
acceleration in that direction.

00:05:23.080 --> 00:05:25.480
But now I will throw in a twist.
And actually, every

00:05:25.480 --> 00:05:28.200
problem we did, all of these
Newton's Law's problems, we

00:05:28.200 --> 00:05:32.140
assumed that the force acted
at the center of mass.

00:05:32.140 --> 00:05:35.820
But something more interesting
happens if the force acts away

00:05:35.820 --> 00:05:37.070
from the center of mass.

00:05:40.350 --> 00:05:42.190
Let me actually take
that ruler example.

00:05:42.190 --> 00:05:45.210
I don't know why I even
drew the horse.

00:05:45.210 --> 00:05:52.570
If I have this ruler again and
this is the center of mass, as

00:05:52.570 --> 00:05:56.120
we said, any force that we act
on the center of mass, the

00:05:56.120 --> 00:05:59.040
whole object will move in the
direction of the force.

00:05:59.040 --> 00:06:01.800
It'll be shifted by the
force, essentially.

00:06:01.800 --> 00:06:02.810
Now, this is what's
interesting.

00:06:02.810 --> 00:06:06.900
If that's the center of mass and
if I were to apply a force

00:06:06.900 --> 00:06:11.736
someplace else away from the
center of mass, let' say I

00:06:11.736 --> 00:06:15.880
apply a force here, I want you
to think about for a second

00:06:15.880 --> 00:06:18.750
what will probably happen
to the object.

00:06:18.750 --> 00:06:21.220
Well, it turns out that the
object will rotate.

00:06:21.220 --> 00:06:23.240
And so think about if we're on
the space shuttle or we're in

00:06:23.240 --> 00:06:25.540
deep space or something, and
if I have a ruler, and if I

00:06:25.540 --> 00:06:27.980
just push at one end of the
ruler, what's going to happen?

00:06:27.980 --> 00:06:30.240
Am I just going to push the
whole ruler or is the whole

00:06:30.240 --> 00:06:31.300
ruler is going to rotate?

00:06:31.300 --> 00:06:33.430
And hopefully, your intuition
is correct.

00:06:33.430 --> 00:06:36.770
The whole ruler will rotate
around the center of mass.

00:06:36.770 --> 00:06:42.010
And in general, if you were to
throw a monkey wrench at

00:06:42.010 --> 00:06:45.680
someone, and I don't recommend
that you do, but if you did,

00:06:45.680 --> 00:06:48.890
and while the monkey wrench is
spinning in the air, it's

00:06:48.890 --> 00:06:51.480
spinning around its
center of mass.

00:06:51.480 --> 00:06:52.940
Same for a knife.

00:06:52.940 --> 00:06:54.900
If you're a knife catcher,
that's something you should

00:06:54.900 --> 00:07:00.280
think about, that the object,
when it's free, when it's not

00:07:00.280 --> 00:07:03.580
fixed to any point, it rotates
around its center of mass, and

00:07:03.580 --> 00:07:04.570
that's very interesting.

00:07:04.570 --> 00:07:07.650
So you can actually throw random
objects, and that point

00:07:07.650 --> 00:07:09.330
at which it rotates
around, that's the

00:07:09.330 --> 00:07:10.340
object's center of mass.

00:07:10.340 --> 00:07:13.630
That's an experiment that you
should do in an open field

00:07:13.630 --> 00:07:15.690
around no one else.

00:07:15.690 --> 00:07:18.970
Now, with all of this, and
I'll actually in the next

00:07:18.970 --> 00:07:20.290
video tell you what this is.

00:07:20.290 --> 00:07:23.130
When you have a force that
causes rotational motion as

00:07:23.130 --> 00:07:25.970
opposed to a shifting motion,
that's torque, but we'll do

00:07:25.970 --> 00:07:26.850
that in the next video.

00:07:26.850 --> 00:07:30.610
But now I'll show you just a
cool example of how the center

00:07:30.610 --> 00:07:34.880
of mass is relevant in everyday
applications, like

00:07:34.880 --> 00:07:36.890
high jumping.

00:07:36.890 --> 00:07:40.340
So in general, let's say
that this is a bar.

00:07:40.340 --> 00:07:42.690
This is a side view of a
bar, and this is the

00:07:42.690 --> 00:07:43.530
thing holding the bar.

00:07:43.530 --> 00:07:45.440
And a guy wants to jump
over the bar.

00:07:48.810 --> 00:07:51.880
His center of mass is-- most
people's center of mass is

00:07:51.880 --> 00:07:53.170
around their gut.

00:07:53.170 --> 00:07:55.380
I think evolutionarily that's
why our gut is there, because

00:07:55.380 --> 00:07:56.870
it's close to our
center of mass.

00:07:56.870 --> 00:07:58.460
So there's two ways to jump.

00:07:58.460 --> 00:08:01.500
You could just jump straight
over the bar, like a hurdle

00:08:01.500 --> 00:08:06.130
jump, in which case your center
of mass would have to

00:08:06.130 --> 00:08:07.500
cross over the bar.

00:08:07.500 --> 00:08:09.510
And we could figure out this
mass, and we can figure out

00:08:09.510 --> 00:08:12.657
how much energy and how much
force is required to propel a

00:08:12.657 --> 00:08:16.630
mass that high because we know
projectile motion and we know

00:08:16.630 --> 00:08:18.270
all of Newton's laws.

00:08:18.270 --> 00:08:21.410
But what you see a lot in the
Olympics is people doing a

00:08:21.410 --> 00:08:24.810
very strange type of jump,
where, when they're going over

00:08:24.810 --> 00:08:28.430
the bar, they look something
like this.

00:08:28.430 --> 00:08:30.700
Their backs are arched
over the bar.

00:08:34.600 --> 00:08:36.000
Not a good picture.

00:08:36.000 --> 00:08:38.520
But what happens when someone
arches their back over

00:08:38.520 --> 00:08:39.340
the bar like this?

00:08:39.340 --> 00:08:40.370
I hope you get the point.

00:08:40.370 --> 00:08:42.440
This is the bar right here.

00:08:42.440 --> 00:08:44.350
Well, it's interesting.

00:08:44.350 --> 00:08:46.390
If you took the average of
this person's density and

00:08:46.390 --> 00:08:48.940
figured out his geometric center
and all of that, the

00:08:48.940 --> 00:08:51.500
center of mass in this
situation, if someone jumps

00:08:51.500 --> 00:08:54.940
like that, actually travels
below the bar.

00:08:54.940 --> 00:08:57.750
Because the person arches their
back so much, if you

00:08:57.750 --> 00:09:00.590
took the average of the total
mass of where the person is,

00:09:00.590 --> 00:09:03.770
their center of mass actually
goes below the bar.

00:09:03.770 --> 00:09:06.320
And because of that, you can
clear a bar without having

00:09:06.320 --> 00:09:08.820
your center of mass go as high
as the bar and so you need

00:09:08.820 --> 00:09:09.960
less force to do it.

00:09:09.960 --> 00:09:13.370
Or another way to say it, with
the same force, you could

00:09:13.370 --> 00:09:14.723
clear a higher bar.

00:09:14.723 --> 00:09:15.530
,

00:09:15.530 --> 00:09:18.720
Hopefully, I didn't confuse you,
but that's exactly why

00:09:18.720 --> 00:09:23.037
these high jumpers arch their
back, so that their center of

00:09:23.037 --> 00:09:26.910
mass is actually below the bar
and they don't have to exert

00:09:26.910 --> 00:09:27.810
as much force.

00:09:27.810 --> 00:09:30.430
Anyway, hopefully you found that
to be a vaguely useful

00:09:30.430 --> 00:09:32.610
introduction to the center of
mass, and I'll see you in the

00:09:32.610 --> 00:09:35.100
next video on torque.


Mechanical advantage (part 3)

WEBVTT
Kind: captions
Language: en

00:00:01.020 --> 00:00:02.000
Welcome back.

00:00:02.000 --> 00:00:04.050
Now let's do some more
mechanical advantage problems.

00:00:04.050 --> 00:00:06.410
And in this video, we'll focus
on pulleys, which is another

00:00:06.410 --> 00:00:08.260
form of a simple machine.

00:00:08.260 --> 00:00:10.105
And we've done some pulley
problems in the past, but now

00:00:10.105 --> 00:00:12.200
we'll actually understand what
the mechanical advantage

00:00:12.200 --> 00:00:14.350
inherent in these
machines are.

00:00:14.350 --> 00:00:17.370
So let me start with a
very simple pulley.

00:00:17.370 --> 00:00:19.190
So this is the ceiling
up here.

00:00:23.000 --> 00:00:24.780
I don't know what they call
that part of the pulley.

00:00:24.780 --> 00:00:26.540
I should learn my actual
terminology.

00:00:26.540 --> 00:00:29.840
But let's say I have that little
disk where the rope

00:00:29.840 --> 00:00:34.170
goes over and it rolls so that
the rope can go over it and

00:00:34.170 --> 00:00:36.120
move without having
a lot of friction.

00:00:36.120 --> 00:00:38.520
And let's say I have a rope
going over that pulley.

00:00:42.600 --> 00:00:44.610
That's my rope.

00:00:44.610 --> 00:00:51.740
And at this end, let's say I
have a weight, a 10-Newton

00:00:51.740 --> 00:00:57.730
weight, and I'm going to pull
down on this end to make the

00:00:57.730 --> 00:00:59.160
weight to go up.

00:00:59.160 --> 00:01:01.410
So my question to you is what is
the mechanical advantage of

00:01:01.410 --> 00:01:02.480
this system?

00:01:02.480 --> 00:01:05.740
What is the force that I have to
pull down in order to lift

00:01:05.740 --> 00:01:09.770
this weight, this 10-Newton
weight in order to produce 10

00:01:09.770 --> 00:01:11.620
Newtons of force upwards?

00:01:11.620 --> 00:01:14.985
Well, in any pulley situation--
and I don't know

00:01:14.985 --> 00:01:17.380
if textbooks cover it this way,
but this is how I think

00:01:17.380 --> 00:01:19.610
about it, because you don't
have to memorize formulas.

00:01:19.610 --> 00:01:21.920
I just think about, well,
what happens to

00:01:21.920 --> 00:01:23.150
the lengths of rope?

00:01:23.150 --> 00:01:25.760
Or what is the total distance
that the object you're trying

00:01:25.760 --> 00:01:27.000
to move travels?

00:01:27.000 --> 00:01:29.310
And if you know the distance
that it travels versus the

00:01:29.310 --> 00:01:31.040
distance that you have
to pull, you know

00:01:31.040 --> 00:01:32.590
the mechanical advantage.

00:01:32.590 --> 00:01:36.880
So in this situation, if I were
to hold the rope at that

00:01:36.880 --> 00:01:41.670
point, and if I were to pull
it down 10 feet or some

00:01:41.670 --> 00:01:44.350
arbitrary distance, what
happens over here?

00:01:44.350 --> 00:01:46.300
Well, this weight is
going to move up

00:01:46.300 --> 00:01:49.560
exactly the same amount.

00:01:49.560 --> 00:01:53.250
Whatever I pull, if I pull a
foot down here, this weight

00:01:53.250 --> 00:01:57.360
will move up by a foot, so the
distance that I pull here is

00:01:57.360 --> 00:02:00.130
equivalent to the distance
that it pulls up here.

00:02:00.130 --> 00:02:02.880
And since we know that the work
in has to equal the work

00:02:02.880 --> 00:02:06.670
out, we know that the force I'm
pulling down has to be the

00:02:06.670 --> 00:02:10.080
same as the force or the tension
that the rope is

00:02:10.080 --> 00:02:11.530
pulling up here.

00:02:11.530 --> 00:02:14.920
And we could have done that when
we learned about tension,

00:02:14.920 --> 00:02:16.740
that the tension in the
rope is constant.

00:02:16.740 --> 00:02:19.850
I'm producing tension in the
rope when I pull here and

00:02:19.850 --> 00:02:22.480
that's the same pulling force of
the tension on the weight.

00:02:22.480 --> 00:02:25.180
So this isn't too interesting
of a machine.

00:02:25.180 --> 00:02:29.920
All it's doing is I pull down
with a force of 10 Newtons and

00:02:29.920 --> 00:02:32.480
it will pull up with a force
of 10 Newtons, and so the

00:02:32.480 --> 00:02:36.550
mechanical advantage is 1, no
real mechanical advantage,

00:02:36.550 --> 00:02:37.940
although this could be useful.

00:02:37.940 --> 00:02:39.590
Maybe it's easier for
me to pull down than

00:02:39.590 --> 00:02:40.880
for me to pull up.

00:02:40.880 --> 00:02:43.810
Or at some point, maybe I can't
reach up here, so it's

00:02:43.810 --> 00:02:45.930
nice for me to pull down here
where I can reach and the

00:02:45.930 --> 00:02:48.260
object will keep going up
like in a flag pole or

00:02:48.260 --> 00:02:49.160
something like that.

00:02:49.160 --> 00:02:51.820
So this could still be useful
even though its mechanical

00:02:51.820 --> 00:02:54.220
advantage is only 1.

00:02:54.220 --> 00:02:58.270
So let's see if we can construct
a pulley situation

00:02:58.270 --> 00:03:03.170
where the mechanical advantage
is more than 1.

00:03:03.170 --> 00:03:09.810
So let's say over here at the
top, I still have the same

00:03:09.810 --> 00:03:14.080
pulley that's attached to the
ceiling, but I'm going to add

00:03:14.080 --> 00:03:16.766
slight variation here.

00:03:16.766 --> 00:03:19.700
I have another pulley here.

00:03:19.700 --> 00:03:32.315
And now let me do the other
pulley down here.

00:03:36.790 --> 00:03:40.470
And then let me see if I can
draw my rope in a good way.

00:03:40.470 --> 00:03:46.010
So my rope starts up going up
like that, then it comes back

00:03:46.010 --> 00:03:50.820
down, comes around the second
pulley, and now this is

00:03:50.820 --> 00:03:54.330
attached to the ceiling
up here.

00:03:54.330 --> 00:03:56.280
The second pulley is
actually where the

00:03:56.280 --> 00:03:58.660
weight is attached to.

00:03:58.660 --> 00:04:00.750
And let's just call it a
10-Newton weight again,

00:04:00.750 --> 00:04:02.610
although it doesn't really
matter what the weight is.

00:04:02.610 --> 00:04:05.030
Let's figure out what the
mechanical advantage is.

00:04:05.030 --> 00:04:06.430
So the same question.

00:04:06.430 --> 00:04:07.930
And this is really the question
you always have to

00:04:07.930 --> 00:04:08.850
ask yourself.

00:04:08.850 --> 00:04:15.150
If I were take a point on this
rope and if I were to pull it

00:04:15.150 --> 00:04:18.399
2 feet down, so let's see I take
this point and I move it

00:04:18.399 --> 00:04:23.970
2 feet down, what essentially
happens to the rope?

00:04:23.970 --> 00:04:26.480
Well, every point on the
rope's going to move

00:04:26.480 --> 00:04:29.720
2 feet to the right.

00:04:29.720 --> 00:04:31.640
I guess you can view it this way
if you view that motion is

00:04:31.640 --> 00:04:33.330
to the right.

00:04:33.330 --> 00:04:37.780
But if this length of rope is
getting 2 feet shorter, what

00:04:37.780 --> 00:04:39.740
is this length of
rope getting?

00:04:39.740 --> 00:04:42.410
Well, this entire length of rope
is also going to get 2

00:04:42.410 --> 00:04:46.530
feet shorter, this entire length
of rope right here.

00:04:46.530 --> 00:04:49.940
But this entire length of rope
is split between this side--

00:04:49.940 --> 00:04:53.882
let me do it in different
color-- between this

00:04:53.882 --> 00:04:58.050
side and this side.

00:04:58.050 --> 00:05:02.420
So if I make this side of the
rope shorter-- I mean, the

00:05:02.420 --> 00:05:05.660
rope goes through the whole
thing, but if I take this side

00:05:05.660 --> 00:05:08.080
of the rope and I pull
down by 2 feet,

00:05:08.080 --> 00:05:10.080
what is going to happen?

00:05:10.080 --> 00:05:13.590
Well, this is going to
get 1 foot shorter.

00:05:13.590 --> 00:05:15.840
This rope is going to
get 1 foot shorter.

00:05:15.840 --> 00:05:18.960
This is going to go 1 foot
shorter and this length of the

00:05:18.960 --> 00:05:20.590
rope is going to get
1 foot shorter.

00:05:20.590 --> 00:05:21.440
And how do I know that?

00:05:21.440 --> 00:05:23.070
Well, this is all
the same rope.

00:05:23.070 --> 00:05:25.070
And if this is getting 1 foot
shorter, and this is one

00:05:25.070 --> 00:05:26.950
getting 1 foot shorter, it makes
sense this whole thing

00:05:26.950 --> 00:05:28.510
is getting 2 feet shorter.

00:05:28.510 --> 00:05:30.520
But the important thing to
realize, if each of these are

00:05:30.520 --> 00:05:33.200
getting 1 foot shorter,
then this weight is

00:05:33.200 --> 00:05:35.110
only moving up 1 foot.

00:05:38.050 --> 00:05:42.440
So when I pull the rope down 2
feet here, this weight only

00:05:42.440 --> 00:05:43.850
moves up 1 foot.

00:05:43.850 --> 00:05:46.320
So what is the work
that I'm doing?

00:05:46.320 --> 00:05:48.560
Well, the work in is the same
as the work out, and we know

00:05:48.560 --> 00:05:49.960
what the work out is.

00:05:49.960 --> 00:05:53.100
The work out is going to
be the force that this

00:05:53.100 --> 00:05:55.530
contraption or this machine is
pulling upwards with, and

00:05:55.530 --> 00:06:01.070
that's 10 Newtons, so the
workout is equal to 10 Newtons

00:06:01.070 --> 00:06:03.255
times the distance
that the force is

00:06:03.255 --> 00:06:05.730
pulling in, times 1 foot.

00:06:05.730 --> 00:06:06.750
Oh, why did I do feet?

00:06:06.750 --> 00:06:08.000
I should do meters.

00:06:10.920 --> 00:06:12.565
That's not a good thing
for me to do.

00:06:12.565 --> 00:06:15.170
That should be meters.

00:06:15.170 --> 00:06:17.360
I shouldn't mix English
and metric system.

00:06:17.360 --> 00:06:23.840
So 10 Newtons times 1 meter,
so it equals 10 joules.

00:06:23.840 --> 00:06:25.310
And this has to be the
work that I've put

00:06:25.310 --> 00:06:26.330
into it, too, right?

00:06:26.330 --> 00:06:32.350
So the work in also has
to be 10 joules.

00:06:32.350 --> 00:06:33.890
Well, I know the distance
that I pulled down.

00:06:33.890 --> 00:06:36.280
I know I pulled down 2 meters.

00:06:36.280 --> 00:06:39.100
So I pulled down 2 meters, so
this has to equal the force

00:06:39.100 --> 00:06:39.890
times the distance.

00:06:39.890 --> 00:06:42.360
So the force, which I don't
know, times the distance,

00:06:42.360 --> 00:06:45.420
which is 2 meters, is
equal to 10 joules.

00:06:45.420 --> 00:06:48.090
So divide both sides by 2, so
the force that I pulled down

00:06:48.090 --> 00:06:51.270
with is 5 Newtons.

00:06:51.270 --> 00:06:54.940
So I pulled down 5 Newtons for
2 meters, and it pulls up a

00:06:54.940 --> 00:06:57.100
10-Newton weight for 1 meter.

00:06:57.100 --> 00:06:59.780
Force times distance is equal
to force times distance.

00:06:59.780 --> 00:07:01.800
So what was the input force?

00:07:01.800 --> 00:07:07.050
The input force is equal to 5
Newtons and the output force

00:07:07.050 --> 00:07:09.280
of this machine is equal
to 10 Newtons.

00:07:09.280 --> 00:07:12.650
Mechanical advantage is the
output over the input, so the

00:07:12.650 --> 00:07:16.110
mechanical advantage is equal
to the force output by the

00:07:16.110 --> 00:07:20.400
force input, which equals
10/5, which equals 2.

00:07:20.400 --> 00:07:23.970
And that makes sense, because
I have to pull twice as much

00:07:23.970 --> 00:07:32.280
for this thing to move up
half of that distance.

00:07:32.280 --> 00:07:36.520
Let's see if we can do another
mechanical advantage problem.

00:07:36.520 --> 00:07:39.410
Actually, let's do a really
simple one that we've really

00:07:39.410 --> 00:07:41.690
been working with a long time.

00:07:41.690 --> 00:07:45.050
Let's say that I have a wedge.

00:07:45.050 --> 00:07:48.760
A wedge is actually considered
a machine, which it took me a

00:07:48.760 --> 00:07:52.220
little while to get my
mind around that, but

00:07:52.220 --> 00:07:53.940
a wedge is a machine.

00:07:53.940 --> 00:07:55.200
And why is a wedge a machine?

00:07:55.200 --> 00:07:57.670
Because it gives you mechanical
advantage.

00:07:57.670 --> 00:07:59.770
So if I have this wedge here.

00:07:59.770 --> 00:08:05.580
And this is a 30-degree angle,
if this distance up here,

00:08:05.580 --> 00:08:09.260
let's call this distance
D, what is this

00:08:09.260 --> 00:08:11.630
distance going to be?

00:08:11.630 --> 00:08:13.530
Well, it's going to
be D sine of 30.

00:08:13.530 --> 00:08:15.540
And we know that the sine of 30
degrees, hopefully by this

00:08:15.540 --> 00:08:19.520
point, is 1/2, so this
is going to be 1/2D.

00:08:19.520 --> 00:08:21.190
You might want to review the
trigonometry a little bit if

00:08:21.190 --> 00:08:23.800
that doesn't completely
ring a bell for you.

00:08:23.800 --> 00:08:27.020
So if I take an object, if I
take a box-- and let's assume

00:08:27.020 --> 00:08:28.280
it has no friction.

00:08:28.280 --> 00:08:29.970
We're not going to go into
the whole normal

00:08:29.970 --> 00:08:31.240
force and all that.

00:08:31.240 --> 00:08:37.200
If I take a box, and I push it
with some force all the way up

00:08:37.200 --> 00:08:42.200
here, what is the mechanical
advantage of this system?

00:08:42.200 --> 00:08:44.670
Well, when the box is up
here, we know what its

00:08:44.670 --> 00:08:46.220
potential energy is.

00:08:46.220 --> 00:08:49.820
Its potential energy is going
to be the weight of the box.

00:08:49.820 --> 00:08:54.510
So let's say this is
a 10-Newton box.

00:08:54.510 --> 00:08:56.790
The potential energy at this
point is going to be 10

00:08:56.790 --> 00:08:59.750
Newtons times its height.

00:08:59.750 --> 00:09:03.540
So potential energy at this
point has to equal 10 Newtons

00:09:03.540 --> 00:09:07.870
times the height, which is
going to be 5 joules.

00:09:07.870 --> 00:09:11.380
And that's also the amount of
work one has to put into the

00:09:11.380 --> 00:09:14.530
system in order to get it into
this state, in order to get it

00:09:14.530 --> 00:09:16.380
this high in the air.

00:09:16.380 --> 00:09:20.090
So we know that we would have
to put 5 joules of work in

00:09:20.090 --> 00:09:23.260
order to get the box
up to this point.

00:09:23.260 --> 00:09:25.490
So what is the force that
we had to apply?

00:09:25.490 --> 00:09:28.490
Well, it's that force, that
input force, times this

00:09:28.490 --> 00:09:31.310
distance has to equal
5 joules.

00:09:33.850 --> 00:09:36.810
So this input force-- oh, sorry,
this is going to be--

00:09:36.810 --> 00:09:38.610
sorry, this isn't 5 joules.

00:09:38.610 --> 00:09:41.700
It's 10 times 1/2 times
the distance.

00:09:41.700 --> 00:09:43.820
It's 5D joules.

00:09:43.820 --> 00:09:47.480
This isn't some kind of units.

00:09:47.480 --> 00:09:49.720
It's 10 Newtons times the
distance that we're up, and

00:09:49.720 --> 00:09:52.610
that's 1/2D, so it's
5D joules.

00:09:52.610 --> 00:09:53.860
Sorry for confusing you.

00:09:56.510 --> 00:10:00.030
And so the force I'm pushing
here times this distance has

00:10:00.030 --> 00:10:04.220
to also equal to 5D joules.

00:10:04.220 --> 00:10:05.500
I just remembered, I
just used D as a

00:10:05.500 --> 00:10:06.820
variable the whole time.

00:10:06.820 --> 00:10:08.710
Dividing both sides by
D, what do I get?

00:10:08.710 --> 00:10:14.780
The input force had to be
equal to 5 Newtons.

00:10:14.780 --> 00:10:17.370
I'm dividing both sides
by D meters.

00:10:17.370 --> 00:10:21.650
So I inputted 5 Newtons of force
and I was able to lift

00:10:21.650 --> 00:10:24.370
essentially a 10-Newton
object.

00:10:24.370 --> 00:10:26.410
So what is the mechanical
advantage?

00:10:26.410 --> 00:10:29.390
Well, it's the force output,
10 Newtons, divided by the

00:10:29.390 --> 00:10:31.195
force input, 5 Newtons.

00:10:31.195 --> 00:10:34.120
The mechanical advantage is 2.


Mechanical advantage (part 2)

WEBVTT
Kind: captions
Language: en

00:00:00.600 --> 00:00:01.240
Welcome back.

00:00:01.240 --> 00:00:03.200
When I left off, I was hurrying
a little bit.

00:00:03.200 --> 00:00:06.510
But we'd hopefully come to the
conclusion that if I have a

00:00:06.510 --> 00:00:09.780
simple lever, like I have here,
and I know the distances

00:00:09.780 --> 00:00:12.280
from where I'm applying
the force, to the

00:00:12.280 --> 00:00:13.360
fulcrum, to the pivot.

00:00:13.360 --> 00:00:16.379
And I know the distance from the
pivot to where the machine

00:00:16.379 --> 00:00:18.745
is essentially applying the
force, the machine being the

00:00:18.745 --> 00:00:21.710
lever in this situation, I know
the relationship between

00:00:21.710 --> 00:00:23.380
the two forces I'm applying.

00:00:23.380 --> 00:00:26.005
The input force-- so actually I
shouldn't call this a force

00:00:26.005 --> 00:00:28.010
too, I should call this an
input force-- anyway, the

00:00:28.010 --> 00:00:31.010
input force times the distance
from the input force to the

00:00:31.010 --> 00:00:36.980
fulcrum is equal to the output
force times the distance from

00:00:36.980 --> 00:00:39.010
the output force
to the fulcrum.

00:00:39.010 --> 00:00:41.860
And that all fell out of what
we did in the last video.

00:00:41.860 --> 00:00:45.280
The conservation of energy and
that the work in has to equal

00:00:45.280 --> 00:00:45.850
the work out.

00:00:45.850 --> 00:00:48.590
And all work is, is a transfer
of energy, so the transfer of

00:00:48.590 --> 00:00:50.980
energy in has to be the transfer
of energy out,

00:00:50.980 --> 00:00:53.050
assuming we have no friction
and none of the energy is

00:00:53.050 --> 00:00:53.690
lost.

00:00:53.690 --> 00:00:55.520
And how is this useful?

00:00:55.520 --> 00:01:00.050
Well we could do a bunch
of problems with this.

00:01:00.050 --> 00:01:07.930
Let's say that I have
a 100 newton object

00:01:07.930 --> 00:01:10.820
right here, 100 newtons.

00:01:10.820 --> 00:01:15.810
And let's say that I know, no
matter what I do, my maximum

00:01:15.810 --> 00:01:18.060
strength that I could push--
well let me draw this a little

00:01:18.060 --> 00:01:19.740
different-- let's say it's like
this, cause of my goal is

00:01:19.740 --> 00:01:20.870
to lift the 100 newton object.

00:01:20.870 --> 00:01:23.050
So the 100 newton object
is right here.

00:01:23.050 --> 00:01:24.150
That's a 100 newtons.

00:01:24.150 --> 00:01:27.180
And let's say I know that the
maximum downward force that

00:01:27.180 --> 00:01:31.530
I'm capable of applying is
only 10 newtons, right?

00:01:31.530 --> 00:01:34.940
So I want my force to
be multiplied by 10

00:01:34.940 --> 00:01:36.380
to lift this force.

00:01:36.380 --> 00:01:37.510
So let's figure out
what would happen.

00:01:37.510 --> 00:01:39.830
My input force is 10.

00:01:39.830 --> 00:01:42.530
And I want to figure
out the distance.

00:01:42.530 --> 00:01:44.530
So let's say my input
force is 10.

00:01:44.530 --> 00:01:47.220
And let's call this the
input distance.

00:01:47.220 --> 00:01:50.920
And I want the output force
to be 100, right?

00:01:50.920 --> 00:01:54.290
And let's call this the
output distance.

00:01:54.290 --> 00:02:00.540
So if I have a fulcrum here,
this is the input distance and

00:02:00.540 --> 00:02:01.770
this is the output distance.

00:02:01.770 --> 00:02:02.340
Let me switch colors.

00:02:02.340 --> 00:02:03.530
This is getting monotonous.

00:02:03.530 --> 00:02:05.670
This is the output distance,
from here to here.

00:02:05.670 --> 00:02:09.680
And let's figure out what the
ratio has to be, for the ratio

00:02:09.680 --> 00:02:11.970
of the input distance to
the output distance.

00:02:11.970 --> 00:02:14.400
Well, if we just divide both
sides by 10, we get the

00:02:14.400 --> 00:02:15.910
distance input.

00:02:15.910 --> 00:02:18.610
It has to be 10 times the
distance output, right?

00:02:18.610 --> 00:02:20.680
100 divided by 10.

00:02:20.680 --> 00:02:24.030
So if the distance from the
fulcrum to the weight is, I

00:02:24.030 --> 00:02:27.980
don't know, 5 meters, then the
distance from where I'm

00:02:27.980 --> 00:02:30.920
applying the force to
the fulcrum has

00:02:30.920 --> 00:02:31.750
to be 10 times that.

00:02:31.750 --> 00:02:34.060
It has to be 50 meters.

00:02:34.060 --> 00:02:37.390
So no matter what, the ratio of
this length to this length

00:02:37.390 --> 00:02:38.350
has to be 10.

00:02:38.350 --> 00:02:40.090
And now what would happen?

00:02:40.090 --> 00:02:43.210
If I design this machine this
way, I will be able to apply

00:02:43.210 --> 00:02:45.790
10 newtons here, which is my
maximum strength, 10 newtons

00:02:45.790 --> 00:02:49.570
downwards, and I will lift
a 100 newton object.

00:02:49.570 --> 00:02:50.960
And now what's the
trade off though?

00:02:50.960 --> 00:02:52.560
Nothing just pops
out of thin air.

00:02:52.560 --> 00:02:56.245
The trade off is, is that I am
going to have to push down for

00:02:56.245 --> 00:02:59.300
a much longer distance, for
actually 10 times the distance

00:02:59.300 --> 00:03:02.360
as this object is going
to move up.

00:03:02.360 --> 00:03:05.210
And once again I know that
because the work in has to

00:03:05.210 --> 00:03:06.000
equal the work out.

00:03:06.000 --> 00:03:10.200
I can't through some magical
machine-- and if you were able

00:03:10.200 --> 00:03:12.330
to invent one, you shouldn't
watch this video and you

00:03:12.330 --> 00:03:15.840
should go build it and become a
trillionaire-- but a machine

00:03:15.840 --> 00:03:18.020
can never generate work
out of thin air.

00:03:18.020 --> 00:03:19.660
Or it can never generate
energy out of thin air.

00:03:19.660 --> 00:03:21.600
That energy has to come
from some place.

00:03:21.600 --> 00:03:23.970
Most machines actually you lose
energy to friction or

00:03:23.970 --> 00:03:25.660
whatever else.

00:03:25.660 --> 00:03:30.080
But in this situation, if I'm
putting in 10 newtons of force

00:03:30.080 --> 00:03:33.660
times some distance, whatever
that quantity is of work, the

00:03:33.660 --> 00:03:34.900
work cannot change.

00:03:34.900 --> 00:03:35.490
The total work.

00:03:35.490 --> 00:03:38.910
It can go down if there is some
friction in the system.

00:03:38.910 --> 00:03:40.470
So let's do another problem.

00:03:45.160 --> 00:03:47.480
And really they're all kind
of the same formula.

00:03:47.480 --> 00:03:55.670
And then I'll move into a few
other types of simple systems.

00:03:55.670 --> 00:03:59.130
I should use the line tool.

00:03:59.130 --> 00:04:03.060
We'll make this up on the fly.

00:04:03.060 --> 00:04:05.180
And you could always create
problems where you can

00:04:05.180 --> 00:04:07.800
compound it further and et
cetera, et cetera, using some

00:04:07.800 --> 00:04:08.870
of the other concepts
we've learned.

00:04:08.870 --> 00:04:10.600
But I won't worry about
that right now.

00:04:16.680 --> 00:04:24.630
So let's say that I'm going
to push up here.

00:04:24.630 --> 00:04:26.830
Well no let me see what
I want to do.

00:04:26.830 --> 00:04:35.380
I want to push down here with
a force of-- let's say that

00:04:35.380 --> 00:04:44.000
this distance right here is 35
meters, this distance is 5

00:04:44.000 --> 00:04:46.550
meters-- and let's say I'm going
to push down with the

00:04:46.550 --> 00:04:49.730
force of 7 newtons, and what
I want to figure out is how

00:04:49.730 --> 00:04:52.190
heavy of an object
can I lift here.

00:04:52.190 --> 00:04:53.840
How heavy of an object.

00:04:53.840 --> 00:04:55.560
Well, all we have to do is
use the same formula.

00:04:55.560 --> 00:04:58.240
But the moments-- and I know I
used that word once before, so

00:04:58.240 --> 00:05:00.670
you might not know what it is--
but the moments on both

00:05:00.670 --> 00:05:02.980
sides of the fulcrum have
to be the same.

00:05:02.980 --> 00:05:05.460
Or the input moment has to
be the output moment.

00:05:05.460 --> 00:05:06.730
So what's the moment again?

00:05:06.730 --> 00:05:10.560
Well, the moment is just the
force times the distance from

00:05:10.560 --> 00:05:12.680
the force to the fulcrum.

00:05:12.680 --> 00:05:19.360
So the input moment is 7 newtons
times 35 meters.

00:05:19.360 --> 00:05:21.915
And realize that that does not
work, because the distance

00:05:21.915 --> 00:05:24.740
this force is traveling
is not 35 meters.

00:05:24.740 --> 00:05:26.240
The distance this force
is traveling is

00:05:26.240 --> 00:05:28.470
something like, here.

00:05:28.470 --> 00:05:31.320
But this 35 meters is going
to be proportional to the

00:05:31.320 --> 00:05:33.490
distance that this is traveling
when you compare it

00:05:33.490 --> 00:05:34.910
to this other side.

00:05:34.910 --> 00:05:36.950
So this quantity, 7
newtons times 35

00:05:36.950 --> 00:05:38.390
meters, is the moment.

00:05:38.390 --> 00:05:41.990
And that is going to be equal
to the moment on this side,

00:05:41.990 --> 00:05:43.500
the output moment.

00:05:43.500 --> 00:05:47.780
So that is equal to 5 meters
times the force that I'm

00:05:47.780 --> 00:05:51.405
lifting, or the lifting force
of the machine, times let's

00:05:51.405 --> 00:05:53.380
say the force out.

00:05:53.380 --> 00:05:56.230
So we can figure out the force
out by just dividing both

00:05:56.230 --> 00:05:58.280
sides by 5.

00:05:58.280 --> 00:06:03.310
So let's see, 35 divided by 5
is 7, so you get 7 times 7

00:06:03.310 --> 00:06:07.720
equals the force out,
or 49 newtons.

00:06:07.720 --> 00:06:10.280
And you can see that, because
you can see that the length of

00:06:10.280 --> 00:06:13.320
this side of the lever is 7
times the length of this side

00:06:13.320 --> 00:06:14.710
of the lever.

00:06:14.710 --> 00:06:18.830
So when you input a force of
7, you output a force of 7

00:06:18.830 --> 00:06:19.650
times that.

00:06:19.650 --> 00:06:23.820
And of course, in order to move
the block 1 meter up in

00:06:23.820 --> 00:06:24.760
this direction, you're
going to have to

00:06:24.760 --> 00:06:27.210
push down for 7 meters.

00:06:27.210 --> 00:06:31.450
And that's where we know that
the input work is equal to the

00:06:31.450 --> 00:06:32.580
output work.

00:06:32.580 --> 00:06:35.920
Well anyway hopefully I didn't
confuse you and you have a

00:06:35.920 --> 00:06:38.470
reasonable sense of
how levers work.

00:06:38.470 --> 00:06:41.050
In the next couple of videos,
I'll introduce you to other

00:06:41.050 --> 00:06:43.680
machines, simple machines like
a wedge-- I've always had

00:06:43.680 --> 00:06:45.140
trouble calling a wedge
a machine, but it

00:06:45.140 --> 00:06:47.040
is one-- and pulleys.

00:06:47.040 --> 00:06:48.290
I'll see you in the next video.