Name: Intro to springs and Hooke's Law
Uploaded: 2013-04-09T05:56:08.000Z
Duration: 10 min 5 s

祈使句型

現在進行式

Let me draw the ground so that we know what's going on with

讓我來畫地，這樣我們就知道是怎麼回事了。

I'll use a thicker one, just to show it's a spring.

我'會用粗一點的，只是為了顯示它'是個彈簧。

Let's say the spring looks something like this.

比方說，彈簧的樣子是這樣的。

This is my spring, my amazingly drawn spring.

這就是我的春天，我那畫風驚人的春天。

Let's say at this end it's attached to a wall.

比方說，在這一端它'連著一堵牆。

And so this is a spring when I don't have any force acting on

所以這是一個彈簧，當我沒有任何力量作用在。

it, this is just the natural state of the spring.

And we could call this, where it just naturally rests, this

我們可以把它叫做，它只是自然地休息，這個

And let's say that when I were to apply a force of 5 Newtons

into the spring, it looks something like this.

So when I apply a force of 5 Newtons-- I'll draw the wall

所以當我施加5牛頓的力時... 我就會畫出牆來。

當我施加一個5牛頓的力時,我就會發現...

我們每天坐在床上或者沙發上。

If this was the normal resting-- so this is where the

如果這是正常的休息... ...所以這是在哪裡的。

spring was when I applied no force, but when I applied 5

當我沒有施加任何力量時，彈簧是，但當我施加5％的力量時，彈簧是，但當我施加5％的力量時，彈簧是，但當我施加5％的力量時，彈簧是，但當我施加5％的力量時，彈簧是，但當我施加5％的力量時，彈簧是，但當我施加5％的力量時，彈簧是，但當我施加5％的力量時，彈簧是，但當我施加5％的力量時，彈簧是，但當我施加5％的力量時，彈簧是，但當我施加5％的力量時，彈簧是，但當我施加5％的力量時，彈簧是，但當我施加5％的力量時，彈簧是，但當我施加5％的力量時，彈簧是，但當我施加5％的力量時，彈簧是，但當我施加5％的力量時，彈簧是

Newtons in that direction, let's say that this distance

牛頓在這個方向上，比方說這個距離。

And so a typical question that you'll see, and we'll explain

所以一個典型的問題，你'會看到，我們'會解釋。

how to do it, is a spring compresses or elongates when

怎麼做，是彈簧在壓縮或伸長的時候。

you apply a certain force by some distance.

你在一定距離內施加一定的力。

How much will it compress when you apply a different force?

當你施加不同的力時，它將壓縮多少？

So my question is how much will it compress when I apply

所以我的問題是，當我應用 "我 "時，它會壓縮多少？

So your intuition that it'll compress more is correct, but

所以，你的直覺，它會壓縮更多是正確的，但。

它與我壓縮的程度是線性的嗎？

Is it a square of how much I compress it?

Or you could just keep watching the video.

所以，讓我們'說我施加一個10牛頓的力。

And if this was the natural place where the spring would

好吧，事實證明，它是線性的。

Well, it means that the more the force-- it's equally

proportional to how much the spring will compress.

If you applied 5 Newtons in this direction, to the right,

如果你向這個方向施加5牛頓，向右。

you would have gone 10 meters in this direction.

So it goes whether you're elongating the spring or

所以，無論你是在拉長彈簧還是在拉大彈簧。

compressing the spring within some reasonable tolerance.

將彈簧壓縮在合理的公差範圍內。

If you compress something too much or you stretch it too

如果你把東西壓得太緊或者你把它拉得太長的話

much, it doesn't really go back to where it was before.

多，它並沒有真正回到以前的地方。

But within some reasonable tolerance, it's proportional.

但在一些合理的容忍度內，它'是成正比的。

That means that the restoring force of the spring is minus

some number, times the displacement of the spring.

So in this example right here, what was the displacement of

所以，在這個例子中，這裡的位移是什麼？

Well, if we take positive x to the right and negative x to

好吧，如果我們取正x向右，負x向右

the left, the displacement of the spring was what?

The displacement, in this example right here, x is equal

在這個例子中，位移，就在這裡，x等於

And so it says that the restorative force is going to

So the minuses cancel out, so it equals 10K.

所以負數抵消了，所以等於1萬。

What's the restorative force in this example?

Well, you might say, it's 5 Newtons, just because that's

好吧，你可能會說，這是5牛頓，只是因為這是我的。

the only force I've drawn here, and you would be to some

我在這裡畫的唯一的力量，你將是一些

And actually, since we're doing positive and negative,

而實際上，既然我們'做的是正反兩方面。

and this 5 Newton is to the left, so to the negative

而這個5牛頓是在左邊，所以是負數

x-direction, actually, I should call this minus 5

Newtons and I should call this minus 10 Newtons, because

牛頓，我應該叫它減10牛頓，因為...

obviously, these are vectors and we're going to the left.

很明顯，這些都是矢量，我們'向左走。

I picked the convention that to the left means negative.

Well, in this example-- and we assume that K is a positive

好吧，在這個例子中 -- 我們假設K是一個正值的。

In this example, the restorative force is a

在這個例子中，恢復力是一種。

So that's actually the force, the counteracting force, of

所以，這其實就是力量，反作用力，的。

So if this spring is stationary when I apply this

所以，如果當我應用這個彈簧時，這個彈簧是靜止的。

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Intro to springs and Hooke's Law

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