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In this video, I want
to clarify two ideas

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that we talk about
on a regular basis,

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but are really muddled up
in our popular language.

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And these are the ideas
of mass and weight.

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And first, I'll tell
you what they are.

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And then, we'll talk about
how they are muddled up.

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So mass is literally-- there's
a couple of ways to view mass.

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One way to view mass
is-- and this is not

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a technical definition,
but it will give you

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a sense of it-- is how
much the stuff there is.

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So this is similar
to saying matter.

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So if I have more
molecules of a given mass,

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I will have a
total of more mass.

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Or if I have more atoms,
I will have more mass.

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So how much stuff
there is of something.

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And I want to be careful
with this definition right

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here, because there are
other things that aren't what

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we would traditionally
associate with matter,

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once we start going into
more fancy physics, that

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still will exhibit mass.

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So another way to define
mass is, how does something

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react to a specific force?

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And we already learned
from Newton's second law

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that if you have a given
force and you have more mass,

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you'll accelerate less.

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If you have less mass,
you'll accelerate more.

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So how something responds
to a given force.

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Something with lower
mass will accelerate more

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for a given force.

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Something with higher
mass will accelerate less.

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Now weight is the force
of gravity on a mass,

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or on an object.

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So this is the force of
gravity on an object.

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And just to think about
the difference here,

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let's think about, I guess,
myself sitting on Earth.

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So if I'm on Earth, my
mass is 70 kilograms.

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My mass-- let me do
this in a new color--

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so my mass is 70 kilograms.

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There's 70 kilograms of
stuff that constitute Sal.

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But my weight is
not 70 kilograms.

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I mean, you'll often hear people
say, I weighs 70 kilograms.

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And that's all right in
just conversational usage,

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but that is not
technically correct.

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Because weight is the force
that Earth is pulling down--

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or I should say-- the force
of gravity on my mass.

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And so my weight-- let me think
about the weight for a second--

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the weight is going to be equal
to the gravitational field

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at Earth.

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Hopefully you've watched
the video on gravity.

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Or if you haven't,
feel free to watch it.

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But the gravitational
attraction between two objects,

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so the force of gravity
between two objects

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is going to big G, the universal
gravitational constant,

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times the mass of
the first object--

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let me actually-- times the mass
of the second object, divided

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by the distance that separates
the two objects squared.

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And if you're on the Earth, and
if you take all of this stuff

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right over here combined-- so
if you say that this right here

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is the mass of Earth.

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If you say this, right
here, is the distance

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from the center to
the surface of Earth,

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because that's where
I'm sitting right now.

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So distance from center
to surface of Earth.

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Then all of this stuff over here
simplifies to what's sometimes

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called as lower case g.

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And lower case g
is-- and I'm just

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rounding it here-- 9.8
meters per second squared.

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So the force of
gravity for something

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near the surface of
the Earth is going

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to be this quantity right
over here times the mass.

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So my weight on the
surface of the Earth

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is this 9.8 meters
per second squared

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times my mass,
times 70 kilograms.

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And so this is going
to be-- I won't do,

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well, I could get
my calculator out.

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Why don't I just get my
calculator out and do the math?

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I was going to round it to
10 and say it's about 700,

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but let's just
actually calculate it.

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So we have 9.8
times 70 kilograms.

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So we have 686.

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So this gives me 686.

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And then the units are kilogram
meters per second squared.

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And these units, kilogram
meters per second squared,

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are the same thing as a newton.

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So my weight-- and
you'll never hear

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people say this-- but my weight
on the surface of the Earth

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is 686 newtons.

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And notice, I just
said that is my weight

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on the surface of the Earth.

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Because as you could
imagine, weight

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is the force due to gravity
on an object, on a mass.

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So if I go someplace else, if
I go to the moon, for example,

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my weight will change.

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But my mass will not.

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So let's write this.

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This is the weight on Earth.

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If I were to take my
weight on the moon-- and I

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haven't looked this
up before the video.

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And you can verify this
for me if you like.

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But I've been told that
the gravitational force

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on the moon, or the
gravitational attraction

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at the surface of the
moon, is about 1/6 that

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of the surface of the Earth.

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So my weight on the
moon will be roughly 1/6

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of my weight on the Earth.

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Times 686 newtons.

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So that gives me a
little bit over-- what

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is that-- 114 maybe?

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I'll just get the
calculator out.

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My brain operates
a little bit slower

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while I'm recording videos.

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Yeah.

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I got it right.

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114.

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So that gets us 114,
approximately 114 newtons.

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So this is the thing I really
want to emphasize then.

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Weight is a force due
to gravity on an object.

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Your weight changes from
planet to planet you go on.

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Your weight would
actually even change

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if you went to a
very high altitude

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because you're getting
slightly further--

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it would be immeasurably
small-- but you're

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getting slightly further
from the center of the Earth.

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Your weight would change
an imperceptible amount.

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In fact, because the Earth
is not a perfect sphere--

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it's often referred to
as an oblique spheroid--

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your weight is actually slightly
different on different parts

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of the Earth.

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If you went to the poles
verses the equator,

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you would have a slightly
different weight.

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Your mass does not change.

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It doesn't matter
where you go, assuming

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that you don't have some type
of nuclear reaction going

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on inside of you.

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Your mass does not change.

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So your mass does not change
depending on where you are.

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Now, you might be
saying, hey, look,

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I don't deal with kilograms,
and newtons, and all of this.

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I operate in America.

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And in America, we
talk about pounds.

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Is pounds appropriate?

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And yes, pounds is
a unit of weight.

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So if I say that I weigh 160
pounds, this is indeed weight.

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I'm saying that the force of
gravity on me is 160 pounds.

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But then you might say,
well, what is mass then

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if you're talking about
the English system

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or sometimes called
the imperial system?

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And here, I will
introduce you to a concept

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that very few people know.

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It's kind of a good
trivial concept.

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The unit of mass--
so let's just be

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clear here-- the unit of mass
in the imperial system, mass

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is called the slug.

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So if you wanted to
figure out how many

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slugs you are, so your weight--
the force of gravity on you

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is 160 pounds.

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This is going to be
equal to-- if you

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were to calculate all of this
stuff-- the force of gravity

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on the surface of Earth.

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But if you were to do
it in imperial units,

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instead of getting 9.8
meters per second squared,

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you would get 32 feet
per second squared, which

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is also the acceleration
near the surface of the Earth

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due to gravity in
feet and seconds,

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as opposed to
meters and seconds.

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And then, this is times
your mass in slugs.

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So to figure it out,
you divide both sides

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by 32 feet per second squared.

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So let's do that.

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Let's divide both sides by
32 feet per second squared.

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It cancels out.

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And then let me get
my calculator out.

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So I have 160 pounds divided
by 32 feet per second squared.

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And I get exactly 5.

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I should have been able
to do that in my head.

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So I get 5.

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And the units here-- in the
numerator, I have pounds.

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And then I'm dividing by
feet per second squared.

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That's the same
thing as multiplying

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by second squared per feet.

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And these units, 5 pounds
second squareds over feet, this

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is the same thing as a slug.

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So if I weigh 160
pounds, my mass

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is going to be equal to 5 slugs.

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If my mass is 70 kilograms,
my weight is 686 newtons.

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So hopefully that clarifies
things a little bit.