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## Newton's law of gravitation

Current time:0:00Total duration:10:41

# Mass and weight clarification

## Video transcript

In this video, I want
to clarify two ideas that we talk about
on a regular basis, but are really muddled up
in our popular language. And these are the ideas
of mass and weight. And first, I'll tell
you what they are. And then, we'll talk about
how they are muddled up. So mass is literally-- there's
a couple of ways to view mass. One way to view mass
is-- and this is not a technical definition,
but it will give you a sense of it-- is how
much the stuff there is. So this is similar
to saying matter. So if I have more
molecules of a given mass, I will have a
total of more mass. Or if I have more atoms,
I will have more mass. So how much stuff
there is of something. And I want to be careful
with this definition right here, because there are
other things that aren't what we would traditionally
associate with matter, once we start going into
more fancy physics, that still will exhibit mass. So another way to define
mass is, how does something react to a specific force? And we already learned
from Newton's second law that if you have a given
force and you have more mass, you'll accelerate less. If you have less mass,
you'll accelerate more. So how something responds
to a given force. Something with lower
mass will accelerate more for a given force. Something with higher
mass will accelerate less. Now weight is the force
of gravity on a mass, or on an object. So this is the force of
gravity on an object. And just to think about
the difference here, let's think about, I guess,
myself sitting on Earth. So if I'm on Earth, my
mass is 70 kilograms. My mass-- let me do
this in a new color-- so my mass is 70 kilograms. There's 70 kilograms of
stuff that constitute Sal. But my weight is
not 70 kilograms. I mean, you'll often hear people
say, I weighs 70 kilograms. And that's all right in
just conversational usage, but that is not
technically correct. Because weight is the force
that Earth is pulling down-- or I should say-- the force
of gravity on my mass. And so my weight-- let me think
about the weight for a second-- the weight is going to be equal
to the gravitational field at Earth. Hopefully you've watched
the video on gravity. Or if you haven't,
feel free to watch it. But the gravitational
attraction between two objects, so the force of gravity
between two objects is going to big G, the universal
gravitational constant, times the mass of
the first object-- let me actually-- times the mass
of the second object, divided by the distance that separates
the two objects squared. And if you're on the Earth, and
if you take all of this stuff right over here combined-- so
if you say that this right here is the mass of Earth. If you say this, right
here, is the distance from the center to
the surface of Earth, because that's where
I'm sitting right now. So distance from center
to surface of Earth. Then all of this stuff over here
simplifies to what's sometimes called as lower case g. And lower case g
is-- and I'm just rounding it here-- 9.8
meters per second squared. So the force of
gravity for something near the surface of
the Earth is going to be this quantity right
over here times the mass. So my weight on the
surface of the Earth is this 9.8 meters
per second squared times my mass,
times 70 kilograms. And so this is going
to be-- I won't do, well, I could get
my calculator out. Why don't I just get my
calculator out and do the math? I was going to round it to
10 and say it's about 700, but let's just
actually calculate it. So we have 9.8
times 70 kilograms. So we have 686. So this gives me 686. And then the units are kilogram
meters per second squared. And these units, kilogram
meters per second squared, are the same thing as a newton. So my weight-- and
you'll never hear people say this-- but my weight
on the surface of the Earth is 686 newtons. And notice, I just
said that is my weight on the surface of the Earth. Because as you could
imagine, weight is the force due to gravity
on an object, on a mass. So if I go someplace else, if
I go to the moon, for example, my weight will change. But my mass will not. So let's write this. This is the weight on Earth. If I were to take my
weight on the moon-- and I haven't looked this
up before the video. And you can verify this
for me if you like. But I've been told that
the gravitational force on the moon, or the
gravitational attraction at the surface of the
moon, is about 1/6 that of the surface of the Earth. So my weight on the
moon will be roughly 1/6 of my weight on the Earth. Times 686 newtons. So that gives me a
little bit over-- what is that-- 114 maybe? I'll just get the
calculator out. My brain operates
a little bit slower while I'm recording videos. Yeah. I got it right. 114. So that gets us 114,
approximately 114 newtons. So this is the thing I really
want to emphasize then. Weight is a force due
to gravity on an object. Your weight changes from
planet to planet you go on. Your weight would
actually even change if you went to a
very high altitude because you're getting
slightly further-- it would be immeasurably
small-- but you're getting slightly further
from the center of the Earth. Your weight would change
an imperceptible amount. In fact, because the Earth
is not a perfect sphere-- it's often referred to
as an oblique spheroid-- your weight is actually slightly
different on different parts of the Earth. If you went to the poles
verses the equator, you would have a slightly
different weight. Your mass does not change. It doesn't matter
where you go, assuming that you don't have some type
of nuclear reaction going on inside of you. Your mass does not change. So your mass does not change
depending on where you are. Now, you might be
saying, hey, look, I don't deal with kilograms,
and newtons, and all of this. I operate in America. And in America, we
talk about pounds. Is pounds appropriate? And yes, pounds is
a unit of weight. So if I say that I weigh 160
pounds, this is indeed weight. I'm saying that the force of
gravity on me is 160 pounds. But then you might say,
well, what is mass then if you're talking about
the English system or sometimes called
the imperial system? And here, I will
introduce you to a concept that very few people know. It's kind of a good
trivial concept. The unit of mass--
so let's just be clear here-- the unit of mass
in the imperial system, mass is called the slug. So if you wanted to
figure out how many slugs you are, so your weight--
the force of gravity on you is 160 pounds. This is going to be
equal to-- if you were to calculate all of this
stuff-- the force of gravity on the surface of Earth. But if you were to do
it in imperial units, instead of getting 9.8
meters per second squared, you would get 32 feet
per second squared, which is also the acceleration
near the surface of the Earth due to gravity in
feet and seconds, as opposed to
meters and seconds. And then, this is times
your mass in slugs. So to figure it out,
you divide both sides by 32 feet per second squared. So let's do that. Let's divide both sides by
32 feet per second squared. It cancels out. And then let me get
my calculator out. So I have 160 pounds divided
by 32 feet per second squared. And I get exactly 5. I should have been able
to do that in my head. So I get 5. And the units here-- in the
numerator, I have pounds. And then I'm dividing by
feet per second squared. That's the same
thing as multiplying by second squared per feet. And these units, 5 pounds
second squareds over feet, this is the same thing as a slug. So if I weigh 160
pounds, my mass is going to be equal to 5 slugs. If my mass is 70 kilograms,
my weight is 686 newtons. So hopefully that clarifies
things a little bit.