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.

從本節課中

Falling Balls

Professor Bloomfield examines the physics concepts of gravity, weight, constant acceleration, and projectile motion working with falling balls.

- Louis A. BloomfieldProfessor of Physics

How would a ball fall on the moon? The answer to this question is simple.

The ball would fall much more slowly than on Earth.

Every aspect of the ball's fall would be slower.

It would pick up speed in the downward direction more slowly.

It would cover distance toward the ground more slowly, and it would take longer to

hit. [SOUND] To understand why that's the

case, however, we need to revisit the issue of gravity and take a look again at

the relationship between weight and mass. Up until now, I've talked about falling

near the Earth's surface. And I've told you that every kilogram of

mass, near the Earth's surface, requires a weight of about 9.8 Newtons.

And if you drop an object near the Earth's surface, it accelerates downward

at about 9.8 meters per second squared. You'll notice that I keep saying, near

the Earth's surface, and that's because those two statements are dependent on the

Earth's gravity here, the local strength of gravity.

Now, as we'll see in the episode on rockets, does local strength of gravity

is local? It varies from place to place.

And the details, we'll save for that episode.

But, for the moment, it's important to know that the strength of gravity, that

is how much weight is produced for each kilogram of mass, depends on two things.

It depends on the mass of the object producing that gravitational force, and

it depends on your distance from that object.

In the present case, here near the Earth's surface, the object that's

producing the gravity is the Earth. And so, we care about the, the mass of

the Earth and the distance that's involved.

That is the distance between the object in question,

namely the Earth and us, is about the distance between us and the

center of the Earth. Quite a distance away.

So, the Earth is very massive and in fact, quite distant from us. And

together, that leads to a strength of gravity that gives every kilogram of mass

a weight of 9.8 Newtons, and causes falling objects to accelerate downward at

about 9.8 meters per second squared. If we go somewhere else, that relation,

those relationships may change. For example, if we go to the Moon where

the strength of gravity locally on the surface of the Moon, is about 1/6th that

on the Earth. Well, every kilogram of mass will acquire

a weight of only about 1.6 Newtons. And if you drop a ball or any other object

there near the surface of the Moon, it will accelerate downward at about 1.6

meters per second squared. You might think this is all very

hypothetical and unimportant to everyday life. But actually, where you are in the

Earth surface matters. When I say that a kilogram of mass weighs

about 9.8 Newtons, here in the Earth's surface,

it's really in about. But, there are places you can go on Earth

that have stronger, local gravity, and places you can go that have weaker local

gravity. Every time you go upward, for example,

into the mountains or into a plane and get farther from the center of the Earth,

the strength of gravity, the Earth's gravity weaken slightly, and you weigh a

little less. You don't actually have to go up or down,

you can move to different locations on Earth.

The Earth, it turns out, is not perfectly spherical. Because it's spinning, it is

in effect flung outward, around its equator.

It's, it's got, the diameter of the Earth is larger around the equator than it is

across, across the poles. So, you can get closer to the center of

the Earth by going to the North or South Pole.

And you can go, get farther from the center of the Earth by going to the

equator and that will affect your weight by about half a percent.

So, you will actually weight, about half a percent more on one of the poles, than

you do on the equator. Half a percent is not trivial,

and so, that 9.8 meters per second squared acceleration of a falling ball.

Don't, don't trust the next digit all that much.

You have to, to be careful about it. So, the relationships between mass and

weight depend on where you are, and the acceleration of a falling ball also

depends on where you are. If you visit the grocery store, you'll

find items being sold by weight, and items being sold by mass, and some items

that are sold by both. This chocolate bar, for example, is

labelled according to both weight and mass.

It says here, net weight 3.5 ounces. That's a weight listing.

The ounce is a unit of force which is equal to 1/16th of a pound force.

So, that's the weight of this chocolate bar as, as promised by, by the

manufacturer. And a second label here says this

chocolate bar has a mass of 100 grams. A gram is a unit of mass equal to

1/1000th of a kilogram. So, we have this bar labelled according

to its weight and according to its mass. The same is true of this bag of cookies.

We have a weight listing. It says net weight 16 ounces or 1 pound,

those are both units of those are both force amounts, so we have a weight. and

we also have 453 grams. That means that this bag of cookies has a

mass of 453 grams. And again, a gram is a unit of mass.

So, these two items are labeled and sold by both weight and by mass.

Which brings us to a question. If I take these items to the Moon, are

they still labeled correctly? And if they're not labeled correctly, what has

gone wrong with the labeling? Their labels still accurately specify their

masses. But those labels are way off when it

comes to weight. Mass, after all, is the measure of an

object's inertia. It has nothing to do with gravity.

So, the mass of say, this chocolate bar is the same on the Moon as it is on

Earth, as it is in deep space. It's, it simply reflects how difficult it

is to make this chocolate bar accelerate. So, the mass is 100 grams here, it's a

mass, mass of 100 grams on the Moon, mass of 100 grams anywhere you like.

On the other hand, weight depends on the local strength of gravity.

So, this bag of cookies [SOUND] weighs 1 pound here on Earth, where the strength

of gravity is a certain amount. But if we go to the Moon where the

strength of gravity is only 1/6th that on Earth, this bag of cookies is no longer

one pound. It's about 1/6th of a pound.

And so, it's no longer accurately labeled.

Long and short of it is, if you're going to be selling items on an intergalactic

basis, you do best to label them according to mass because they'll always

be properly and accurately labeled, regardless of where they're shipped to.

If you label them according to weight, you're likely to run into trouble with

the authorities for selling under, or possibly over weight items.

The bottom line is that a ball's weight and its acceleration due to gravity both

depend on the local strength of that gravity.

In most cases, however, we don't notice that dependence. And that's because the

Earth's gravity is so nearly the same anywhere we can go That the variations in

weight and accelleration of gravity are very subtle.

Whether you're playing baseball at sea level or in the mountains, or on the

North Pole or on the Equator, the game is essentially the same.

It's very hard to notice any changes in the ball's weight or its acceleration due

to gravity as it falls. But if you go and play baseball on the

Moon where the local strength of gravity is only about 1/6th that on Earth, the

game is going to change significantly. The ball will weigh only 1/6th its Earth

weight. And as it falls, its acceleration due to

gravity will be only about 1/6th its value here on Earth.

The game would be a very different game.