An introduction to physics in the context of everyday objects.

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来自 弗吉尼亚大学 的课程

生活中的物理

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An introduction to physics in the context of everyday objects.

从本节课中

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 differently do different balls fall? The simple but remarkable answer to that

question is, that all balls fall at the same rate.

Now remember, we're neglecting air resistance, which is a pretty good

approximation for balls that you just drop in front of you.

But don't try to apply the same story to a sheet of paper because the sheet of

paper is really affected a lot by air resistance.

So, returning then to the balls and this question whether it's a basketball, a

tennis ball, a handball, a golf ball or a baseball, if you drop them together, they

all fall [SOUND] together. So here, we have a tennis ball and a

basketball, we'll see whether they fall together.

Ready, get set, go. [SOUND] Exactly together.

[SOUND] Exactly together. [SOUND] Not only do all balls fall

together, but if you were to begin falling with them, you would keep pace

perfectly. You would all fall together.

Well, we can do that. Now, I'm not going to take you and drop

you with a bunch of balls, but I can allow you to take that trip with this

gadget. So here, I've got a frame with a camera

mounted on it, and Catherine and I are going to let this frame fall down a pair

of strings. So, it'll plummet down to the ground in a

somewhat controlled way, with springs at the bottom so that it, it comes to a safe

a safe stop near the ground. And you'll be looking out that little

window at the world in front of you and the balls that are dropping as you drop

with them.

[SOUND]

Here's you guys. There's Catherine down there.

Hi down there, Catherine. Hi.

You ready to have some balls and the camera drop at you? We're ready.

Alright. [SOUND] Alright, everyone. Here you guys

go. Ready,

get set, [SOUND]. Ready get set, [SOUND].

Ready gets set, [SOUND].

Ready, set, go.

[SOUND]

Go.

[SOUND]

Go. [SOUND] Go.

[SOUND] 3, 2, 1.

[SOUND]

You're probably wondering whether one of those falling balls ever hit the camera

down below where Catherine was standing. The answer is, yes, and it wasn't pretty.

That's one of the reasons why I didn't drop a bowling ball.

Why does that happen? Why does a bowling ball and a baseball fall together and hit

the ground at the same time? After all, the bowling ball weighs much more than

the baseball. So, from a weight point of view, the

bowling ball's pulled downward much more strongly by the earths gravity than the

baseball, and the so the bowling ball should accelerate faster.

It should clearly outpace the baseball and hit the ground first.

What's wrong with that thinking? Well, there's another difference between the

bowling ball and the baseball apart from their difference in weight.

The bowling ball has much more mass than the baseball, which is to say that it's

an awful lot harder to shake a bowling ball, to make it accelerate first away

from me, toward me, away from me, toward me.

much harder [SOUND] than just shaking a baseball, right? This, this guy

excellerates very easily in response to small forces.

So, from the point view of mass, the baseball is the more responsive one, less

mass. So, when it's pulled downward by the

earth's gravity, it should accelerate faster,

it should clearly outpace the bowling ball and the baseball should hit the

ground first. we've got two opposite predictions.

From the weight point of view, the bowling ball should hit first.

From the mass point of view, the baseball should hit first and actually from

observation, we know that both of those predictions are just wrong.

The two balls hit together. So, what have we done wrong? Well, you

can't separate the weight point of view and mass point of view, you have to

combine them. We have to have one point of view which

we take into account both the higher weight of the base, bowling ball and the

greater mass of the bowling ball. And when we put those all together and do

the analysis more carefully, we discover that, yeah, the bowling ball has more

weight. It's pulled downward harder and that

alone would make it go, accelerate faster.

But it also has more mass, so it resists accelerations more, and that alone would

slow its acceleration. The two together, more downward force,

more mass resisting that force. Those two increases, cancel perfectly, so

the bowling balls response, that is its downward acceleration caused by gravity,

the earth's gravity, is exactly the same as the down response of the baseball to

the earth's gravity. The two balls accelerate downward at

exactly the same pace and hit the ground together.

When you're carrying a ball at constant velocity, the ball is moving at constant

velocity, you're most aware of the balls weight because you're having to support

that weight. Without your upward push on the ball, the

ball would fall. And so, you have to push up just enough

to balance the ball's weight. And you know it, I mean, you feel that

you are pushing up. So, you are, you are detecting gravity as

you walk along a constant velocity. When you push a ball back and forth on

the table, you're causing the ball to accelerate first one direction then the

other. You're changing its velocity.

And as a result, you're quite aware of the ball's mass.

It's resistance to acceleration or the measure of its inertia. The table on the

other hand is supporting the weight of the ball, so you are completely oblivious

to that weight, it could be large, it could be small, that's the table's

responsibility. Yours is the accreleration and therefore,

the mass of the ball. Now, this course is about the objects of

everyday experience and the Physics concepts that make them do what they do.

In other words, it's about understanding how things work more than it is about

calculating how they work. That said, however, there are times when

looking at the Quantitative Physics, opening up the hood and staring at the

Mathematics that underlie the concepts is a useful activity and will give us

insight into how the machinery of our universe works.

This is one of those times. So, bear with me as I do a little bit of

Algebra to look at why all balls when draw from rest, fall together.

[SOUND] When a ball is falling, the only force acting on it is its weight.

So, the net force on a falling ball is the ball's weight.

Well, Newton's Second Law of Motion tells us, that the acceleration of any object

is equal to the net force on that object divided by the object's mass.

So, in this specific case of a falling ball, the acceleration of a falling ball

is equal to the net force on the ball, which is the ball's weight.

So, it's the ball's weight divided by the ball's mass.

That's pretty simple. The falling ball's acceleration is equal to the ball's

weight divided by the ball's mass. Well, we can make it simpler, we can make

it simpler because we know something about the ball's weight.

Here, near the surface of the Earth, a ball weighs 9.8 Newtons for every

kilogram of mass it has, that is its weight is proportional to its mass and

the constant of proportionality is 9.8 Newtons per kilogram.

For those of you who prefer to talk about pounds, because Newton is kind of an

esoteric concept, that's about 2.2 pounds force per kilogram of mass.

Alright, so we now know something about the weight, we can substitute in this

version of the weight, that is that constant of proportionality times the

mass of the ball. When we do that, we discover that

Newton's Second Law becomes quite simple. It's the acceleration of a falling ball

is equal to that constant of proportionality times mass divided by

mass, the ball's mass divided by the ball's

mass. That cancels,

the ball's mass disappears from this Newton's Second Law and Newton Second Law

says that the falling ball's acceleration is simply the constant of

proportionality, which is to say, a falling ball's acceleration is 9.8 N/kg

or equivalently 2.2 pounds per kilogram. Done. Well, that's a strange result.

It's, it's kind of cool. What this says is the ball's mass doesn't

matter. The acceleration of this ball is the same

as the acceleration of this ball. The mass was unimportant and this is

consistent with our observation. You drop all these balls, they all go

down together, they all accelerate downward together.

But what remains to be done and it's bizarre, is, that constant

proportionality has wacky units. 9.8 Newtons, that is a unit of force, per

kilogram, that is unit of mass. That doesn't sound like an acceleration.

Recall that the SI unit of acceleration is the meter per second squared.

So, where, is the connection? Well, it turns out that the unit, this unit's

Newton per kilogram is exactly same as this unit, the meter per second square,

they're the same and how does that ever happen?

Well, it turns out that the Newton is defined in an interesting way by Newton's

Second Law. One Newton is the force that causes a one

kilogram mass to accelerate at one meter per second ^2.

That defines the Newton. And as a result, Newton's Second Law

written out in that way says, that one meter per second squared of acceleration

is equal to one Newton of force divided by 1 kilogram of mass.

Get rid of the ones and you have the meter per second squared is equal to the

Newton per kilogram, they're the same unit.

As a result, that little g constant of proportionality is an acceleration, it is

9.8 meters per second squared. And that is the acceleration of any

falling object here near the Earth's surface, as long as air resistance can be

neglected.