评论
打印
Hey there! Welcome to Life Noggin!
大家好！欢迎来到脑洞大开的生命奇想！
You know what would be really cool, if we had a hole that travelled straight through the Earth from pole to pole.
如果有一个洞，可以从一个极点穿过地球到另一个极点，你知道会很酷的。
I mean, you could go from seeing Santa to seeing some penguins in Antarctica in no time at all.
我的意思是，你可以上一秒还看到圣诞老人，下一秒就在南极洲看到企鹅。
But anyway, you might be wondering: how long would a trip like that actually take?但是，你可能想知道：这样的旅行实际会花多长时间?
Well, let's start off with some simplifications:
我们先来做一些简化：
firstly, we're going to assume that the Earth has the same density everywhere, is a perfectly symmetric sphere, and the hole has no air in it.
首先，我们假设地球各个部分密度相同，本身是一个完全对称的球体，而且这个洞里没有空气。
because otherwise, the air resistance will cause you to reach terminal velocity, meaning your speed would eventually plateau.
否则，空气阻力会让你达到终端速度，意味着你的速度最终会趋于平稳。
So with those assumptions out of the way, we're ready to begin!
有了这些假设，我们就可以开始了!
Let's suppose you're standing next to this super dangerous hole and fall in.
假设你站在这个超级危险的洞旁边，不小心掉进去了。
And like you'd normally experience if you fell into any hole, you're going to accelerate down.
如同你平常掉进别的洞那样，你会加速下落。
But how much you accelerate depends on how far you are in the hole.
但是你的加速度取决于你掉了多深。
See, when you are at the top of the hole, the entire Earth is below you,
看，当你在洞的顶端时，整个地球在你下面，
so you'll experience the same gravitational acceleration as you normally would, 9.8 meters per second squared and you'll start to speed up as you fall.
所以你的重力加速度和平时一样，是9.8米每平方秒，下落时你还会加速。
But then, things change. Now, you are inside the hole, so some of the Earth is above you and some of it is below you.
但是，一切都在变化。现在，你在洞里面，一部分地球在你上面，一部分在你下面。
And this means that the gravitational forces are both pulling you up as well as pulling you down.
这就意味着重力既把你往上拉又把你往下拉。
So your acceleration is going to change. Luckily for us, there's a simple trick that we can make use of to figure out how much.
所以加速度会改变。幸运的是，有一个简单的技巧，我们可以用它来算出加速度是多少。
Let's pretend that you are inside a spherical shell with a uniform density.
假设你在一个密度均匀的球壳内。
In here, no matter where you are, the gravitational forces from every part of that shell will cancel out.
在这里的任何地方，这个壳每一部分的引力都会抵消掉。
To actually prove this, you'd need to know a super cool thing called calculus and add up the forces from every single tiny portion of the shell.
为了证明这一点，你需要知道一个非常酷的东西，叫做微积分，然后把球壳上所有的力都加起来。
But to keep this video from getting too math-heavy, just trust me that it works.
但是为了让这个视频不要太数学，你就相信我这个管用就行了。
Now, as you are falling toward the center, the parts further from the center than you are form a spherical shell.
现在，当你向中心下落时，离中心比你远的部分形成一个球形的壳。
And we just said that all of the gravitational forces from that shell will cancel out.
我们刚说过，这个壳里所有的重力都会被抵消掉。
So, this means that we can simply pretend that that part of the Earth isn't there, and, instead, you're standing on the surface of a smaller Earth.
所以，这意味着我们可以简单地假设地球的那部分消失，这样，你就站在一个更小的地球的表面上。
So, as you fall, the Earth basically gets smaller and smaller and your downward acceleration decreases.
因此，当你下落时，地球基本上变得越来越小，你的向下加速度会下降。
And once you reach the center, and you won't experience any acceleration at all.
一旦你到达中心，你就没有加速度了。
But remember: you are still falling down pretty quickly, so you'll zoom right past the center towards the other side.
但请记住：你仍在快速下落，所以你会经过地心，落到剩下的那一半。
And from here, instead of the Earth shrinking, it's getting larger and larger as you fall down, since you are now moving away from the Earth's center.
从这里开始，地球不再变小，随着你的下落，它变得越来越大，因为你现在离地心越来越远。
And with all that Earth above you, the acceleration will flip directions and now will be pointing up.
由于你的上方有地球的一大部分，加速度会翻转方向，现在它的方向是向上的。
But since you are still traveling down, this means your velocity will start to slow, eventually reaching zero when you get to the other side of the hole.
但是由于你仍然在下降，这意味着你的速度将开始变慢，最终到达洞的另一端时达到零。
And if you don't jump out, you'll fall right back in and oscillate back and forth in the hole ... forever.
如果你不跳出来，你就会掉回去，在洞里来回摆动……直到永远。
I don't know about you, but I definitely have better things to do with my time. Like make these amazing videos.
我不知道你的情况，反正我有更好的事情要做。比如制作很棒的视频。
But assuming you only travel through the hole once, using some physics, we'll find that this whole trip will take you around 42 minutes.
但是假设你只穿过这个洞一次，借助一些物理知识，我们会发现整个旅程将花费42分钟。
Not too shabby! So what do you think the coolest way to travel across the world is?
还不是太差！那么，你认为环游世界最酷的方式是什么呢?
Let me know in the comment section below.
请在下面的评论栏中告诉我。
If you are into following everything Life Noggin does, you should definitely check out Life Noggin studio's first-ever documentary, Internet Kids.
如果你想要了解我们这个节目，你一定要去看看脑洞大开的生命奇想工作室的第一部纪录片《互联网儿童》。
It's premiering at buffer festival this year. But you can watch the trailor right now.
这是今年在缓冲节上的首映。但你现在可以看预告片了。
And Dogie, my best human friends and co-creator of Life Noggin, helped make the film, so you know it's going to be good. Check it out now.
道奇，我最好的人类朋友和本节目的共同主创，参与制作了这部电影，所以你知道它会很好。现在去看一下吧。
There's a link in the description if you're on your phone.
如果你在手机上看的，描述区就有一个链接。
As always, I'm Blocko and this has been Life Noggin. Don't forget to keep on thinking!
我是宝高，这里是脑洞大开的生命奇想。思考不要停！
