## Newton’s Second Law of Motion

Welcome back. We’re now ready for Newton’s
second law. And Newton’s second law can
simply be stated– and you’ve probably seen this before as
force is equal to mass times acceleration. This is probably, if not the
most famous formula in all of time or all of physics,
it’s up there. It’s probably up there with
E equals mc squared. But that one’s a little
bit more complicated. So what does this tell us? This tells us that the force,
the net force upon an object, is equal to the object’s mass
times its acceleration. So let’s stay in the metric
system because most of what you’ll do in physic class is in
the metric system, and that tends to be because the metric
system makes more sense. So let’s say that I have
a 1 kilogram object. So its mass is 1 kilogram. And it’s being pulled down
at– let’s say its acceleration. It’s being accelerated downward
at 9.8 meters per second squared. These kind of units should be
familiar with you from all the projectile motion problems. So the force applied on that
object in order to get this type of acceleration would be–
you just multiply mass times acceleration. The force would have had to be
9.8 kilogram times the meter. kilogram. times meter over
second square. That’s the force applied
on the object. And you’re saying, sal,
this is very messy. I don’t like writing kilogram
meters per second squared. And you are in luck because
there is a unit and that unit is the Newton. 1 Newton is equal to 1 kilogram meter per second squared. So if I’m pulling down on an
object at 9.8 Newtons, that’s just this, right? This is 1 Newton. If I’m pulling down at 9.8
Newtons on an object that is 1 kilogram, its acceleration is
going to be 9.8 meters per second squared down. And notice I said the word down,
but I didn’t write it anywhere in the formula. And I guess we can imply that
both force and acceleration have direction by writing
this in the formula. That force is a vector and
acceleration is a vector. And so we could have written
9.8 Newtons– I don’t know. You’ll never see this
convention. We could say Newtons down is
equal to 1 kilogram times 9.8 meters per second down. So what can we do with
this formula? Well we can solve problems.
So let’s say that I have an object. So my object weighs–
not weighs. The mass of my object. And I’ll differentiate between
weight and mass in a second. Let’s say the mass of some
object is– I don’t know– 50 kilograms. That’s how much a
normal person might weigh or a light person. Mass weighs 50 kilograms. And
let’s say we’re in an inertial frame of reference. We’re in deep space, so we don’t
have all these other– the force of wind and
the force of gravity acting on us, et cetera. My force, let’s say I apply
it to the right. So we know that force
is a vector. Let’s say I apply a force of–
I don’t know– 100 Newtons. And let’s say I apply
it to the right. So this is the object, 50
kilograms. And I’m applying a force to the right
of 100 Newtons. So what’s going to happen
to this object? Well, let’s use the formula. Force is equal to mass
times acceleration. The force is 100 Newtons. 100 Newtons is equal
to the mass. The mass is 50 kilograms.
50 kilograms times the acceleration. So we can divide both sides by
50 and you get 100 Newtons over 50 kilograms is equal
to the acceleration. And it’s 100 Newtons
to the right. I’ll use this little
arrow here. That’s not a traditional
convention, but that’s how we know it’s to the right. So it’s 100 divided by 50. So it’s 2. We get this weird units here,
Newtons per kilogram is equal to the acceleration
to the right. This is also going to be to
the right because the direction of the force is going
to be the same as the direction of the acceleration. So what is this, 2 Newtons
per kilogram? Well, if you remember– well you
could just guess that the unit of acceleration is meters
per second squared. But let’s show that this
simplifies to that. So we said earlier that– let
me just switch colors. That a Newton is kilogram meter
per second squared. And we’re taking this Newton
over this kilogram over kilogram, right? So that will cancel out with
that and you get meters per second squared. And you wouldn’t have to do this
on a test. Essentially, if you did everything right, you
would know that the unit acceleration is meters
per second squared. So you would have the
acceleration– I’m just switching the two sides–
is equal to 2 meters per second squared. And it’ll be to the right. So that’s useful. We just figured out based on how
hard I push something, how fast it’s going to accelerate
while I push it. And you could use the
same formula to figure out other things. Let’s say I know that an object
is accelerating– let’s say my acceleration is
3 meters per second squared to the right. Let’s say to the left, just
to switch things. And let’s say that I know the
force being applied on it is– I don’t know– 30 Newtons
to the left. And I want to figure
out the mass. Well you use the same thing. You say force, 30 Newtons to
the left is equal to mass times acceleration. Times 3 meters per second
squared to the left. Divide both sides by the 3
meters per second and you get 30 Newtons over 3 meters
per second squared is equal to the mass. 30 divided by 3 is 10. You can figure out that Newtons
is kilogram meters per second squared. So you’re just left with
10 kilograms is equal to the mass. It’s very important that if you
see a problem where the answer’s given in– I don’t
know– kilometers per second squared or you know, instead of
giving it in kilograms it’s giving it in grams or decagrams,
you should convert back to kilograms or meters just
so you make sure you’re using the right units. And that tends to be frankly,
I think, the hardest thing for people. And we’ll do all of that when
we tackle harder problems. I think now is a good time back
to actually differentiate between mass and weight. And you’ve probably thought the
two were interchangeable, but they’re not. Mass is how much of an
object there is. You can almost view it as how
much of the stuff there is or you can almost it view it–
how many atoms there are. But even atoms have mass. So just how much
stuff there is. And another way to view mass is,
how much does the object resist change? And that actually falls
out of F equals ma. Because if our mass is bigger,
it’s going to take a lot more force to make it accelerate
a certain amount. If the mass is smaller it’ll
take less force. So mass can be viewed as how
much stuff there is, of an object there is. Or you can view it as how hard
is it to change what that object is doing. If it’s stationary, how hard
is it to accelerate it? If it’s moving, how hard
is it to maybe stop it? Which would essentially
be decelerating. How hard is it to accelerate
an object? Weight is actually how much
is– what is the force of earth upon an object? So you’re weight would actually
change if you go from one planet to another because
the force of gravity changes. So your weight is 1/6 on the
moon as it is on earth because the pull of gravity is 1/6. But your mass doesn’t change. There’s still the same amount
of Sal on earth as there is on the moon. So your weight really– when you
ask someone in Europe and they say hey, you know, I weigh
50 kilograms. You should say, no, you don’t weigh 50
kilograms. You weigh whatever 50 times 9.8 is. That’s like 400 something–
you weigh 490 Newtons or something. This is mass. And it’s interesting because in
the English system, and all of us Americans, we use
the English system. When we say that we weigh 10
pounds, we’re actually using the correct terminology
because pounds are a unit of force. We’re saying, if I weigh– and
I do weigh about 150 pounds. That means the earth is this
pulling on me with 150 pounds of force. And actually, turns out that
my mass is measured in the unit called a slug, which
we might discuss later. Actually, we’ll do some problems
where we do it in the metric system and the
English system. And I’ll see you in the
next presentation.