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.