Introduction to Momentum What momentum is. A simple problem involving momentum.
Introduction to Momentum
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- 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 what 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.
- 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.
- 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 be 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.
- 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.
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