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  • Hey there and welcome to Life Noggin!

  • You know what would be really cool -- if we had a hole that travelled straight through

  • the Earth from pole to pole.

  • I mean, you could go from seeing Santa to seeing some penguins in Antarctica in no time

  • at all -- well, assuming you'd survive that is.

  • But anyway, you might be wondering: how long would a trip like that actually take?

  • Well, let's start off with some simplifications: 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 -- because otherwise, the air resistance will cause you to reach terminal

  • velocity, meaning your speed would eventually plateau.

  • So with those assumptions out of the way, we're ready to begin!

  • Let's suppose you're standing next to this super dangerous hole and fall in, so

  • your initial speed is zero meters per second.

  • And like you'd normally experience if you fell into any hole, you're going to accelerate

  • down.

  • But how much you accelerate depends on how far you are in the hole.

  • See, when you are at the top of the hole, the entire Earth is below you, 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.

  • 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.

  • And this means that the gravitational forces are both pulling you up as well as pulling

  • you down.

  • 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.

  • Let's pretend that you are inside a spherical shell with a uniform density.

  • In here, no matter where you are, the gravitational forces from every part of that shell will

  • cancel out.

  • 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.

  • But to keep this video from getting too math-heavy, just trust me that this works.

  • Now, as you are falling toward the center, the parts further from the center than you

  • are form a spherical shell.

  • And we just said that all of the gravitational forces from that shell will cancel out.

  • 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.

  • So, as you fall, the Earth basically gets smaller and smaller and your downward acceleration

  • decreases.

  • And once you reach the center, and you won't experience any acceleration at all.

  • But remember: you are still falling down pretty quickly, so you'll zoom right past the center

  • towards the other side.

  • 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.

  • And with all that Earth above you, the acceleration will flip directions and will now be pointing

  • up.

  • 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.

  • And if you don't jump out, you'll fall right back in and oscillate back and forth

  • in the hole ... forever.

  • I don't know about you, but I definitely have better things to do with my time.

  • 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.

  • Not too shabby!

  • How would you want to travel across the world?

  • Leave me a comment to let me know.

  • On a separate note: Have any of you been to Vidcon?

  • What did you think of that incredible experience?

  • Life Noggin Studios just produced an AMAZING documentary about the convention, and you

  • need to check it out!

  • There's a link in the description if you're on mobile.

  • Make sure you come back every Monday for a brand new video.

  • As always, I'm Blocko and this has been Life Noggin.

  • Don't forget to keep on thinking!

Hey there and welcome to Life Noggin!

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どのくらいの時間が地球を通って落ちるのにかかるのでしょうか? (How Long Would It Take To Fall Through The Earth?)

  • 67 4
    angela770911 に公開 2021 年 01 月 14 日
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