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• You step into an elevator.

你進了電梯。

• It starts going down, fast.

電梯開始快速下降。

• What would happen if you jumped right when it started going down?

此時，如果你突然往上跳的話會發生什麼事？

會撞到天花板嗎？唉唷！

• Do you stay suspended in the air while the elevator plummets down?

還是會懸在空中呢？

• Uh, let's examine the elevator problem one step at a time.

我們一步一步來剖析這個問題。

• First, consider a scale.

首先，想像一個體重計。

• You know, the kind of scale you weigh yourself on.

就是一般用來量體重的體重計。

• When you step on a scale to weigh yourself, there are two forces involved.

你站上體重計量體重時牽涉到兩種力 。

• One, gravity pulls you down.

其一，是地心引力。

• Two, the scale pushes you up.

其二，是體重計的垂直抗力。

• What? You didn't know a scale could push?

什麼？ 你不知道體重計有垂直抗力？

• Of course it can! If it didn't push up on you, you would go crashing through the floor.

當然有！如果沒有它，體重計早被踩壞了。

• This upward push is called the normal force and yes, it is normally there.

這種垂直抗力叫做正向力。

• Since you're just standing there on the scale, you're not moving.

因為你站在體重計上，靜止不動。

• Therefore, you're not accelerating.

所以，你沒有加速度。

• Newton's second law of motionnet force equals mass times accelerationtells us that if the acceleration equals zero, the net force must equal zero.

根據牛頓第二運動定律，施加於物體的淨外力等於此物體的質量與加速度的乘積。意思就是，如果加速度等於零，淨外力也必等於零。

• Which means that the force of gravity pulling you down must be equal to the force of the scale pushing you up.

也就是說，地心引力必然等於體重計施加在你腳上的正向力。

• Now let's suppose you're standing on that scale in an elevator.

現在， 試想你站在電梯裡的體重計上。

• At first, the elevator is standing still, so you and the scale are standing still.

一開始，電梯靜止不動，所以你和體重計也一樣靜止不動 。

• The two forces on you are equal and opposite.

在你身上的兩股作用力相等且相反。

• You can read how hard the scale is pushing by looking at it. We call that your weight.

看體重計就知道體重計對你施加的正向力有多大，而這就是所謂的體重。

• Then, the elevator starts falling down.

接著電梯開始下降。

• You and the scale are in the elevator, so you are falling down too, faster and faster.

你和體重計也跟著電梯一起下降，速度越來越快

• That means you are accelerating downward.

這代表你正在向下加速。

• Now there is a net force in the same direction as the accelerationdown.

此時， 淨外力和加速度的方向相同：向下。

• Since gravity hasn't changed, that must mean the scale isn't pushing up as hard.

既然地心引力從未改變，便代表體重計的垂直抗力不夠大。

• So the scale is reading a smaller number.

因此讓體重計上顯示的數值較小。

• The faster the elevator accelerates, the less the scale pushes up.

由此可知，電梯下降速度越快，體重計的正向力越小。

• What if you jumped? Would you stop falling?

如果你向上跳呢？ 你會停止下降嗎？

還是會撞到天花板呢？

• Well, what's pulling the elevator down? Gravity.

想想為何電梯會下降？ 因為地心引力。

• Is gravity pulling on you? Of course.

那地心引力是否也對你作用？ 當然。

• So your relative position in the elevator will stay the same.

所以你在電梯的相對位置是不會改變的。

• The ceiling will only hit you if you can jump up to the ceiling.

除非你本來就能跳到天花板的高度，否則你並不會撞到天花板。

• Now consider: what would happen if the elevator accelerated upward and, even more frightening, if someone snuck in and cut the cable holding the elevator, what would happen then?

最後，想像一下電梯正在上升，而恐怖的是這時有人突然闖進電梯井道並剪斷鋼索。這樣的話會發生什麼事？

試著想想看吧。

You step into an elevator.

B1 中級 中文 TED-Ed 電梯 體重 地心引力 加速度 天花板

# 【TED-Ed】如果在電梯裡體重會更輕嗎？ Would you weigh less in an elevator? - Carol Hedden

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VoiceTube 發佈於 2021 年 12 月 05 日