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## Newton's laws of motion

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# Newton's second law of motion

## Video transcript

Newton's First Law tells
us that an object at rest will stay at rest, and object
with a constant velocity will keep having that
constant velocity unless it's affected by
some type of net force. Or you actually could say an
object with constant velocity will stay having a
constant velocity unless it's affected
by net force. Because really, this
takes into consideration the situation where
an object is at rest. You could just have
a situation where the constant velocity is zero. So Newton's First
Law, you're going to have your constant velocity. It could be zero. It's going to stay being
that constant velocity unless it's affected,
unless there's some net force that acts on it. So that leads to the
natural question, how does a net force affect
the constant velocity? Or how does it affect of
the state of an object? And that's what Newton's
Second Law gives us. So Newton's Second
Law of Motion. And this one is maybe
the most famous. They're all kind of
famous, actually. I won't pick favorites here. But this one gives us
the famous formula force is equal to mass
times acceleration. And acceleration is
a vector quantity, and force is a vector quantity. And what it tells us--
because we're saying, OK, if you apply
a force it might change that constant velocity. But how does it change
that constant velocity? Well, let's say I have
a brick right here, and it is floating in space. And it's pretty nice for us
that the laws of the universe-- or at least in the classical
sense, before Einstein showed up-- the laws of
the universe actually dealt with pretty simple mathematics. What it tells us is if
you apply a net force, let's say, on this
side of the object-- and we talk about net force,
because if you apply two forces that cancel out and that
have zero net force, then the object won't change
its constant velocity. But if you have a
net force applied to one side of this
object, then you're going to have a net acceleration
going in the same direction. So you're going to have
a net acceleration going in that same direction. And what Newton's
Second Law of Motion tells us is that acceleration
is proportional to the force applied, or the force
applied is proportional to that acceleration. And the constant
of proportionality, or to figure out what you have
to multiply the acceleration by to get the force, or what you
have to divide the force by to get the acceleration,
is called mass. That is an object's mass. And I'll make a
whole video on this. You should not confuse
mass with weight. And I'll make a whole
video on the difference between mass and weight. Mass is a measure of
how much stuff there is. Now, that we'll
see in the future. There are other things
that we don't normally consider stuff that
does start to have mass. But for our classical, or at
least a first year physics course, you could
really just imagine how much stuff there is. Weight, as we'll see
in a future video, is how much that stuff
is being pulled down by the force of gravity. So weight is a force. Mass is telling you how
much stuff there is. And this is really neat that
this formula is so simple, because maybe we could have
lived in a universe where force is equal to mass squared
times acceleration times the square root of acceleration,
which would've made all of our math much
more complicated. But it's nice. It's just this constant
of proportionality right over here. It's just this nice
simple expression. And just to get our feet wet
a little bit with computations involving force, mass,
and acceleration, let's say that I have a force. And the unit of force
is appropriately called the newton. So let's say I have a
force of 10 newtons. And just to be clear, a
newton is the same thing as 10 kilogram meters
per second squared. And that's good that a newton
is the same thing as kilogram meters per second squared,
because that's exactly what you get on this side of the formula. So let's say I have a
force of 10 newtons, and it is acting on a mass. Let's say that the
mass is 2 kilograms. And I want to know
the acceleration. And once again, in this video,
these are vector quantities. If I have a positive
value here, we're going to make the assumption
that it's going to the right. If I had a negative value, then
it would be going to the left. So implicitly I'm
giving you not only the magnitude of the
force, but I'm also giving you the direction. I'm saying it is to the
right, because it is positive. So what would be acceleration? Well we just use f equals ma. You have, on the
left hand side, 10. I could write 10
newtons here, or I could write 10 kilogram
meters per second squared. And that is going to be
equal to the mass, which is 2 kilograms times
the acceleration. And then to solve
for the acceleration, you just divide both
sides by 2 kilograms. So let's divide the
left by 2 kilograms. Let me do it this way. Let's divide the
right by 2 kilograms. That cancels out. The 10 and the 2, 10
divided by 2 is 5. And then you have kilograms
canceling with kilograms. Your left hand side, you get
5 meters per second squared. And then that's equal
to your acceleration. Now just for fun, what happens
if I double that force? Well then I have 20 newtons. Well, I'll actually work it out. Then I have 20 kilogram
meters per second squared is equal to-- I'll
have to color code-- 2 kilograms times
the acceleration. Divide both sides by 2
kilograms, and what do we get? Cancels out. 20 divided by 2 is 10. Kilograms cancel kilograms. And so we have the
acceleration, in this situation, is equal to 10 meters
per second squared is equal to the acceleration. So when we doubled the force--
we went from 10 newtons to 20 newtons-- the
acceleration doubled. We went from 5 meters
per second squared to 10 meters per second squared. So we see that they are
directly proportional, and the mass is that how
proportional they are. And so you could imagine what
happens if we double the mass. If we double the mass in this
situation with 20 newtons, then we won't be dividing
by 2 kilograms anymore. We'll be dividing
by 4 kilograms. And so then we'll have 20
divided by 4, which would be 5 and would be meters
per second squared. So if you make the mass
larger, if you double it, then your acceleration
would be half as much. So the larger the mass
you have, the more force you need to accelerate it. Or for a given force, the less
that it will accelerate it, the harder it is to change
its constant velocity.