Welcome back.
I will now introduce you to the concept of momentum.
And the letter for momentum is, in physics, or at least in
mechanics, it's the letter P.
P for momentum.
And I assume that's because the letter M has already been
used for mass, which is I guess an even
more fundamental idea.
So P for momentum.
So what is momentum?
Well, you probably have a general idea of it.
If you see a big guy running really fast, they'll say, he
has a lot of momentum.
And if there's a big guy running really fast and a
small guy running really fast, most people would say, well,
the big guy has more momentum.
Maybe they don't have a quantitative sense of why
they're saying that, but they just feel that
that must be true.
And if we look at the definition of momentum, it'll
make sense.
The definition of momentum is equal to mass times velocity.
So something with, say, a medium mass and a huge
velocity is going to have a big momentum.
Or something with maybe a medium mass, but-- the other
way around.
I forgot what I just said.
So medium mass and big velocity, huge momentum, or
the other way around.
Huge mass, medium velocity would have maybe the same
momentum, but it would still have a big momentum.
Or another way of doing momentum is how little you
would like to be in the way of that object as it passes by.
How unpleasant would it be to be hit by that object?
That's a good way of thinking about momentum.
So momentum is mass times velocity.
So how does it relate to everything we've
been learning so far?
So we know that force is equal to mass times acceleration.
And what's acceleration?
Well acceleration is just change in velocity.
So we also know that force is equal to mass times change in
velocity per unit of time, right?
Per change in time.
T for time.
So force is also equal to-- well, mass
times change in velocity.
Mass, let's assume that mass doesn't change.
So that could also be viewed as the change in mass times
velocity in the unit amount of time.
And this is a little tricky here, I said, you know, the
mass times the change in velocity, that's the same
thing as the change in the mass times the velocity,
assuming the mass doesn't change.
And here we have mass times velocity, which is momentum.
So force can also be viewed as change in
momentum per unit of time.
And I'll introduce you to another
concept called impulse.
And impulse kind of means that you think it means.
An impulse is defined as force times time.
And I just want to introduce this to you just in case you
see it on the exam or whatever, show you it's not a
difficult concept.
So force times change in time, or time, if you assume time
starts at time 0.
But force times change in time is equal to impulse.
I actually don't know-- I should look up what letters
they use for impulse.
But another way of viewing impulse is force
times change in time.
Well that's the same thing as change in momentum over change
in time times change in time.
Right?
Because this is just the same thing as force.
And that's just change in momentum, so
that's impulse as well.
And the unit of impulse is the joule.
And we'll go more into the joule when we do
work in all of that.
And if this confuses you, don't worry about it too much.
The main thing about momentum is that you realize it's mass
times velocity.
And since force is change in momentum per unit of time, if
you don't have any external forces on a system or, on say,
on a set of objects, their combined, or their net
momentum won't change.
And that comes from Newton's Laws.
The only way you can get a combined change in momentum is
if you have some type of net force acting on the system.
So with that in mind, let's do some
momentum problems. Whoops.
Invert colors.
OK.
So let's say we have a car.
Say it's a car.
Let me do some more interesting colors.
A car with a magenta bottom.
And it is, let's see, what does this problem say?
It's 1,000 kilograms. So a little over a ton.
And it's moving at 9 meters per second east. So its
velocity is equal to 9 meters per second east, or to the
right in this example.
And it strikes a stationary 2, 000 kilogram truck.
So here's my truck.
Here's my truck and this is a 2,000 kilogram truck.
And it's stationary, so the velocity is 0.
And when the car hits the truck, let's just say that it
somehow gets stuck in the truck and they just both keep
moving together.
So they get stuck together.
The question is, what is the resulting speed of the
combination truck and car after the collision?
Well, all we have to do is think about what is the
combined momentum before the collision?
Well let's see.
The momentum of the car is going to be the mass times the
car-- mass of the car.
Well the total momentum is going to the mass of the car
times the velocity of the car plus the mass of the truck
times the velocity of the truck.
And this is before they hit each other.
So what's the mass of the car?
That's 1,000.
What's the velocity of the car?
It's 9 meters per second.
So as you can imagine, a unit of momentum would be kilogram
meters per second.
So it's 1,000 times 9 kilogram meters per second, but I won't
write that right now just to keep things simple, or so I
save space.
And then the mass of the truck is 2,000.
And what's its velocity?
Well, it's 0.
It's stationary initially.
So the initial momentum of the system-- this is 2,000 times
0-- is 9,000 plus 0, which equals 9,000 kilogram meters
per second.
That's the momentum before the car hits
the back of the truck.
Now what happens after the car hits the back of the truck?
So let's go to that situation.
So we have the truck.
I'll draw it a little less neatly.
And then you have the car and it's probably a little bit--
well, I won't go into whether it's banged up and whether it
released heat and all of that.
Let's assume that there was nothing-- if this is a simple
problem that we can do.
So if we assume that, there would be
no change in momentum.
Because we're saying that there's no net forces acting
on the system.
And when I say system, I mean the combination of
the car and the truck.
So what we're saying is, is this combination, this new
vehicle called a car truck, its momentum will have to be
the same as the car and the truck's momentum when they
were separate.
So what do we know about this car truck object?
Well we know its new mass.
The car truck object, it will be the
combined mass of the two.
So it's 1,000 kilograms plus 2,000 kilograms. So it's 3,000
kilograms. And now we can use that information to figure out
its velocity.
How?
Well, its momentum-- this 3,000 kilogram object's
momentum-- has to be the same as the momentum of the two
objects before the collision.
So it still has to be 9,000 kilogram meters per second.
So once again, mass times velocity.
So mass is 3,000 times the new velocity.
So we could call that, I don't know, new velocity, v sub n.
That will equal 9,000.
Because momentum is conserved.
That's what you always have to remember.
Momentum doesn't change unless there's a net force acting on
the system.
Because we saw a force is change in momentum per time.
So if you have no force in it, you have
no change in momentum.
So let's just solve.
Divide both sides of this by 3,000 and you get the new
velocity is 3 meters per second.
And that kind of makes sense.
You have a relatively light car moving at 9 meters per
second and a stationary truck.
Then it smacks the truck and they move together.
The combined object-- and it's going to be to the east. And
we'll do more later, but we assume that a positive
velocity is east. If somehow we ended up with a negative,
it would have been west. But it makes sense because we have
a light object and a stationery, heavy object.
And when the light object hits the stationery, heavy object,
the combined objects still keeps moving to the right, but
it moves at a relatively slower speed.
So hopefully that gives you a little bit of intuition for
momentum, and that was not too confusing of a problem.
And in the next couple of videos, I'll do more momentum
problems and then I'll introduce you to momentum
problems in two dimensions.
I will see you soon.