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## Physics library

### Unit 6: Lesson 1

Momentum and Impulse- Apply: conservation of momentum
- Introduction to momentum
- Impulse and momentum dodgeball example
- What are momentum and impulse?
- What is conservation of momentum?
- Bouncing fruit collision example
- Momentum: Ice skater throws a ball
- 2-dimensional momentum problem
- 2-dimensional momentum problem (part 2)
- What are two dimensional collisions?
- Force vs. time graphs

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# Introduction to momentum

Momentum (P) is equal to mass (M) times velocity (v). But there are other ways to think about momentum! Force (F) is equal to the change in momentum (ΔP) over the change in time (Δt). And the change in momentum (ΔP) is also equal to the impulse (J). Impulse has the same units as momentum (kg*m/s or N*s). Created by Sal Khan.

## Video transcript

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.