An introduction to physics in the context of everyday objects.

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來自 University of Virginia 的課程

生活中的物理

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An introduction to physics in the context of everyday objects.

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Bumper Cars

Professor Bloomfield examines the physics concepts of momentum, impulse, angular momentum, angular impulse, and the relationship between potential energy and force using bumper cars.

- Louis A. BloomfieldProfessor of Physics

Does a moving bumper car carry a force? The answer to that question is no.

The moving bumper car carries momentum, but it cannot carry a force.

A force is exerted by one object on another object.

So a single object can't carry a force. But we intuit, that a moving bumper car

carries some physical quantity of motion with it, some capacity to make other

objects, move in the direction of its motion.

That physical quantity of motion does exist.

And the bumper car is in deep carryig it as it moves.

That physical quantity is called momentum and momentum is the conserved qualtiy of

moving. As required by conserved quality momentum

can not be created or destroyed but it can be transfered between objects.

So when I bump these two bumper cars into one another, they transfer some of their

momentum, and you can almost see that. If I, if I make one of them move and hit

the other, one stops; the other goes. They're transferring momentum.

Now Momentum differs from energy another conserved quantity that we've already

encountered in a number of crucial ways, two of them in particular.

First unlike energy, I got to stop these guys before they get out of control.

First unlike energy, momentum can not be stored.

There's no such thing as potential momentum.

Potential energy exists because energy isn't about moving, it's about doing.

So moving objects [SOUND] have kinetic energy but even a stationary object can

have potential energy. Right now the bumper car has

gravitational potential energy. Momentum however is really about moving,

so without motion there's no momentum. A moving object has momentum, a

stationary object does not. Or, to be more technically accurate, a

stationary object has zero momentum. [NOISE] The second way in which momentum

differs from energy is that momentum is a vector quantity; it has a direction.

To show you this, along with the fact that momentum is truly conserved, I need

more room. So, here I am in a bigger venue, a

classroom, and I have a wheeled cart. It's kind of like a skateboard for real

beginners, like me. And, I need the wheeled cart because

friction tends to give away my momentum to the earth.

And I don't need that. I mean, as it is, air resistance, there

are many ways in which my momentum can leak out of me, not because I'm

destroying it but because I'm giving it away.

So the wheel cart makes that effect relatively small.

I can show you momentum going in and out of me.

Back in the lab I use air cushions. To move around the objects without

letting them retain their momentum. Here it's wheels so to start with I have

no momentum. And because momentum's conserved unless

something gives me momentum I'm never going to move.

I need to get me some momentum. And where we're going to get from is the

wall. I'm going to have the wall give me

momentum to the right. Momentum has a direction its a vector

quantity so the wall's going to give me momentum to the right.

Now that will cost the wall the wall will be giving up momentum to the right.

Which is actually meaning that it ends up with momentum to the left.

We'll deal with that a little bit later on.

But imagine right now, when I push on the wall, we'll talk about how the transfer

occurs later, next video. I'm going to have them, the, the wall

push on me, give me momentum to your right, and I'm going to carry it with me.

Are you ready? Here we go.

I have momentum, I can't stop until I give my momentum away.

When I got over to this wall I gave it my rightward momentum and came to a stop.

That's great, now I can do the reverse. But not in this time I don't want the

wall to give me rightward momentum I want the wall to give me leftward momentum.

Here we go I'm going to push on the wall the wall is going to push on me, it's

going to give me a nice dose of leftward momentum and I got it I can't stop, I

can't stop, I can't stop until I give it away again.

So I can do this all day. It's kind of fun.

And a little dangerous but not too bad. Off I go.

I'm carrying it back and forth. And each time I do this, I'm exchanging

momentum with the wall and therefore the whole earth, carrying whatever I end up

with, with me. And eventually giving it back to the wall

and the whole Earth. Let's start that again, but now I want to

have you watch when I encounter the wall on the right.

So, I'm going to obtain rightward momentum.

I'm going to head toward the wall on your right, and when I get there I'm going to

do two transfers of momentum in sequence. Here we go.

First, I'm going to get the momentum to the right, out of the wall.

I got it. I'm carrying it with me.

I give it all to the wall. And then I give more momentum to the

right to the wall, and that costs me. I end up missing momentum to the right,

which is to say, I have momentum to the left.

A negative amount of momentum to the right is momentum to the left.

And so when I encounter that wall on the right I can do it again.

I can do this over and over as long as I don't get injured off I go.

I'm going to give it my rightward momentum and extra rightward momentum.

I gave it more rightward momentum than I had.

And I ended up with a deficit of rightward momentum, less then zero

rightward momentum. Which is to say leftward momentum.

That's what you do when you bounce off something.

So when you bounce, you might want to bounce something other then yourself, off

of a wall. Unless your a small child, having a lot

of fun. and our boucing off walls.

So when I encounter that wall and I give it more rightward momentum then I ever

had. Here it goes I'm going to give it all one

my momentum and extra. I end up with leftward momentum until I

give it away to the wall again. As you can see in order to go from having

momentum to the right To momentum in the left.

I have to make a huge exchange of momentum with something else.

Its not something I can't just simply turn my momentum around.

Rightward momentum and leftward momentum are very different.

And therefore when I'm heading ot your right I can't simply turn around and head

to the left without help. I need some other object like this wall

to exchange momentum with in order to reverse my direction of travel.

And that's one of the reasons why objects that are all by themselves just keep

going in a straight line at a steady pace.

This is Newton's first law of motion again but with a more sophisticated twist

on it. One way of looking at why objects that

are left to themselves keep going at a constant velocity, is they have a certain

momentum. And without help, they can't change their

momentum, and they have to keep going. Well, for me here on this cart, when I'm

out in the middle of the room. I have to carry my momentum with me, I've

got no choice, but in a bumper car arena there are lots of other objects around

with which to exchange momentum and that's part of the fun of bumper cars.

So we'll go back to the lab and start playing with bumper cars.

So here we are back in the lab, I am going to save the exchanges of momentum

between bumper cars for the next video and concentrate for now on the momentum

of a single bumper car. So here we are bumper cars solitaire It's

boring but it's instructive. You can think of momentum as the currency

of motion. And the momentum of our lone bumper car

reflects how much of that currency had to be invested into the bumper car to bring

it from rest to its current motion. It turns out that a bumper car's

momentum, like that of any object, depends on only two things: it's mass,

and it's velocity. Let's start with mass.

Momentum is proportional to mass, and I can show you a simple reason why that

should be true. Let's start with one bumper car that's

moving. It has a certain momentum, in this case

to the right. If I take a second identical bumper car,

and make it move exactly lie the first bumper car, then it has the same

momentum, again, to the right in that case.

Well suppose that these two bumper cars are being driven by people who are

friends [NOISE] and they hold hands. Doing that turns this pair of bumper cars

into one single, larger bumper car. And if we get it moving exactly as it was

before, it's now a single bumper car with twice the momentum of each bumper car

individually. All I've done then, is double the mass of

a bumper car and I'm evidently doubled the momentum of the bumper car as well.

Well this is a typical physicist analyst where you look at the situation, the two

cars by themselves each one has one portion of momentum.

And when you do something that has essentially no effect on the situation,

you just have the people just touch hands, they become a single bumper car

with twice the mass and twice the momentum.

That analysis is, is typical of what physicist would do.

But the bottom line is quite important. The momentum an object has is

proportional to its mass. It turns out that a bumper car's momentum

is also proportional to its velocity. To start with momentum and velocity have

the same direction. But even the amount of the bumper car's

momentum is proportional to the amount of its velocity.

To see that momentum should be proportional to velocity, I'll put away

the double bumper car and bring out two bumper cars that have Velcro bumpers.

These bumper cars don't bounce off one another when they hit, they stick.

And now, I will give a usual portion of rightward momentum, to the first bumper

car, and let it collide with a motionless second identical bumper car.

When that collision occurs, The first bumper car will have to share its

momentum with the second identical bumper car.

What will happen to the velocity of the first bumper car when it's got half the

momentum it started with? Its velocity drops By a factor of two.

It travels only with half its original velocity.

So, so decreasing the momentum of the first bumper car by a factor of two

decreases its velocity by a factor of two.

Showing that it's exactly a factor of two requires a calculation that I won't do,

but it's really that, that's really the case.

Momentum really does drop by a factor of two.

So, overall then momentum, the momentum of a bumper car is proportional to its

velocity. Combining these two observations then,

the momentum of a bumper car is equal to its mass times its velocity.

That realtionship gives us some intresting insight into what happens with

bumper cars. Let me turn these guys off.

The vehicles themselves have reltively little mass, so the riders contribute

significantly to the total mass of a bumper car, and thus to its total

momentum... The bumper cars behavior changes

depending on who's riding in the car. When the only rider in a bumper car is a

little child, the car carries relatively little momentum.

As we'll see in the next video, when I start crashing bumper cars into one

another. The low mass cars can't transfer much

momentum to whatever they hit, and don't effect other cars very much.

In the world of a bumper car arena again, the cars with the little kids in them,

are like bugs zipping around a lawn party.

You barely notice when they hit you. At the other extreme is a bumper car

that's carrying a couple of couch potatoes.

I'm thinking in terms of really big people.

In a car that's filled with really big people has a truely enormous mass.

That car carries considerable momentum, even when it's moving slowly.

And it can transfer large amounts of momentum to whatever it hits.

It's effects on other cars then, are substantial.

It's like, it's like a big hammer in a box of nails or a bowling ball in an

alley full little bowling pins. It knocks everything for a loop.

So, how about velocity issues? You know, what insights can we gather

from the fact that momentum is proportional velocity?

Well, the faster a bumper car is moving, the more momentum it carries.

Carrying a huge momentum is fine. But huge transfers of momentum can be a

problem. In fact, even dangerous.

So, think about dropping a melon off a tall building.

Near the bottom of its fall, the melon has enormous downward momentum.

And that, alone, isn't a problem for the melon.

Hey, says the melon. Wow.

This is kind of cool. The whole world is rushing up at me

really fast. It's not the fall that's the problem;

it's the ground. When the melon reaches the ground, it

transfers its enormous momentum to the ground, and the melon stops having fun.

So the melons fate and all the associated lawsuits the people who run bumper car

arenas limit the speed of bumper cars. So bumper cars supposed to be fun and

exciting, not death defying. So the masses of the car's themselves are

small Everybody who sits in the cars then has a big influence on a car's mass and

therefore the momentum the car carries with it.

The velocity of the car, well the faster it's going the more momentum it's

carrying in the direction of the velocity, but they limit That maximum

amount, so that you're not transferring too huge amounts of momentum when you

collide with things. So now for a question, one that's easiest

to answer if you think in terms of momentum.

Suppose your spaceship is coasting forward through empty space at constant

velocity. You decide to get rid of the trash by

throwing backward out behind the ship. In other words, you give the trash

backward momentum. What affect, if any, does that actually

have on your ship's velocity? That's correct.

By throwing the trash out backward You're giving the trash backward momentum.

You have less backward momentum as a result.

You've given it away and it's a conserved quantity so you have less backward

momentum which is equivalent to more forward momentum because a negative

amount of backward momentum is a positive amount of forward momentum.

So the remaining ship, you included Have more forward momentum, then your ship had

before. It also has less mass, then it had

before. So, with more forward momentum, and less

mass your traveling at a greater forward velocity.

So, your ship is traveling faster. This whole process of throwing stuff out

the back is how a rocket engine works. Now, you threw trash out the back and

you're possibly in trouble with the galactic police.

But if you throw gasses out the back, as you would with a rocket engine.

You're not going to get arrested, and you're going to propel the ship forward

at a greater velocity. The act of throwing gases out the back of

the ship at, at, at great speed ha-, causes them to carry away backward

momentum and leaves the ship with additional forward momentum.

And so it picks up for velocity. That is how rocket engines work, as we'll

see in the episode on rockets. At this point you could picture a bumper

car arena as filled with vehicles, each carrying its own momentum equal to its

mass times its velocity. The stage is set for big things to

happen. But that's going to require collissions

which is the subject of the next video.