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.