"Your fragile face scraping against the rock surface will cause friction, which is frankly inconvenient for the maths."
@jayveeascano45703 жыл бұрын
Norimori
@collin55773 жыл бұрын
@@jayveeascano4570 jayvee Ascaño
@vwlz86373 жыл бұрын
@@collin5577 collin
@yoyoyonono3 жыл бұрын
@@vwlz8637 vwlz
@trickytreyperfected14823 жыл бұрын
@@yoyoyonono Aaron Thapa Ch. - Games, Music and Stuff
@theCodyReeder6 жыл бұрын
“Earths density does not change” well that just triggered all the geologists. The center of the earth is much more dense than the exterior. In fact the core is a mars scized chunk of iron! Now if you were to just fall through the iron bit the time to fall through would less than the 42 minutes. This means that going through the core would take LESS TIME! Right? Or am I missing something?
@standupmaths6 жыл бұрын
My instinct is that the assumption that the density of the Earth is a constant changes the answer less than other assumptions but that is just a guess. If a geologist can give me an agreed density profile of the Earth I'll re-do the calculations!
@CraftQueenJr6 жыл бұрын
Cody'sLab or you would just get stuck in the center.
@jeffreyblack6666 жыл бұрын
CraftQueen, only if you include air resistance. Otherwise that greater mass will accelerate you downwards faster so you are going at a higher speed when you go past the middle and the greater decceleration will be unable to stop you.
@NickRoman6 жыл бұрын
But, since the Earth is symetrical, wouldn't the differences cancel out so that the overall density is all that matters, since we're talking about going through the entire Earth through the center? In which case, if you're not going through the center, then you would have to recalculate that.
@jeffreyblack6666 жыл бұрын
Nope. As an extreme example, consider all the mass located at a single point at the centre. In that case the acceleration due to gravity will be the standard GM/r^2. That applies all the way until you reach the centre, with the rate of acceleration increasing the closer you get. Conversely, with uniform density you have M=4/3*pi*rho*r^3. Thus a=4/3*pi*rho*r^3/r^3=4/3*pi*rho*r. This means acceleration would be greatest at the surface. Or a more extreme counterexample, the entire mass is a spherical shell at the surface. Then in passing through this shell you accelerate at roughly 9.8 m/s^2 then don't accelerate at all until you come out the other side. So for these 2 extremes, one has the smallest acceleration on the surface and greatest at the centre, the other has the greatest on the surface and least under it.
@nerdy59996 жыл бұрын
Repeatedly falling through the hole, emerging at the other end of the sphere and plummeting once again is technically orbiting (mathematically).
@jakesanchard4612 жыл бұрын
if you watched the full video, he actually says this
@dodsg8 жыл бұрын
Walking through Fremantle today and my son grabs my sleeve - "Dad, Dad, that's the guy who does those cool KZbin videos!" I learned two things today: - The world is smaller then you think. - My son is a bigger nerd than I realised.
@standupmaths8 жыл бұрын
+Turn it off! Yes, that was me! I'm from Perth originally; was out for a day with my siblings. Be sure to say hello next time! Say hi to your son for me.
@omikronweapon4 жыл бұрын
Imagine being the boy that comes home from school and his dad goes "Matt Parker told me to tell you, what's up"
@jerelull96294 жыл бұрын
LOL! There's much hope for at least one kid; Nurture that nerd-ness, please. (and it might help to teach him some cool fighting/defensive style, bullies being what they are ... ignorant and belligerent, in my experience.) I was the 3rd-grader who discovered how NEAT slide rules were and other nerdy things.
@jerelull96294 жыл бұрын
@@omikronweapon Heck! Imagine being the PARENT.
@DegonTheMighty8 жыл бұрын
The re-capping of the sharpie at 4:32 was done so professionally.
@philippenachtergal60774 жыл бұрын
18:20 Imagine that, you fell all the way through the earth and came out alive on the other side only to get obliterated by a tennis ball going at 28,000km/h that you yourself threw. That's karma for daring to drill through our beloved earth I tell you.
@zecuse3 жыл бұрын
Complicated suicide doesn't get too much simpler than that.
@saipavand40643 жыл бұрын
69 likes
@FrostMonolith8 жыл бұрын
2:07 Until you said "Oh grow up" I never noticed. THANKS MATT.
@eoghan.50034 жыл бұрын
"assuming there is no air resistance" me, a highschool student: "air resistance? What air resistance?"
@renedekker98064 жыл бұрын
me: "what about magma resistance?"
@ellesko4 жыл бұрын
@@renedekker9806 Just gave you a thumbs up on that remark. Although imho there's no need to take that into consideration. Because by definition the hole goes all the way through the earth. Ergo you won't touch any magma. What is actually not mentioned in the set-up definition is the heat. I assume you'd evaporate long before you reach the earth's core. But still you won't have to fear that because you'd be already dead before the temperature becomes really uncomfortable. I'm just not sure if you die from your blood vessels bursting or from cardiac arrest, both due to the acceleration... On a more serious note: What about the earth's rotation? Would that affect the fall in a way that you'd hit the wall of the hole? I think not, but I'm not sure about that. I suppose it's the same as when jumping straight upwards and landing on the exact same spot although the earth has been spinning underneath you.
@MANU1234234 жыл бұрын
@@ellesko Dam, the point of a cheeky reply is to make it short.. Go tired of reading at the second line!
@samuelwikstrom77213 жыл бұрын
@@ellesko actually, since gravity isn't a real force, you don't feel acceleration until you encounter resistance. So, if you fall, and there is no air to resist you, you would feel weightless until you hit the ground.
@davidrojas46873 жыл бұрын
is what you never assume.
@Yoshimaster96smwc7 жыл бұрын
0:13 "a apple"
@rasseboiii35056 жыл бұрын
Yoshimaster96smwc Lol
@benmcdaniel5 жыл бұрын
Parker grammar.
@WaterShowsProd4 жыл бұрын
"Certainly it can core a apple." -Chef of The Future
@zoranbg4 жыл бұрын
Well, he is a Maths teacher, not an English teacher... ;)
@henrikholst74904 жыл бұрын
Apple is just an instance of a Earth.
@Tker19706 жыл бұрын
When Matt pointed out 17K MPH as the max velocity, I thought "That's the velocity of the Space Shuttle in orbit" (when we had one) The he explained the rest. VERY COOL STUFF.
@NintendoSunnyDee6 жыл бұрын
"Oh grow up!" What, were you saying it was silly to think we'd just bounce back and forth? (Thirty entire seconds pass) Wait...
@BLSXful4 жыл бұрын
I was in math mode, so I didn't get it. I had go into teen mode
@jrbleau4 жыл бұрын
@@BLSXful Which explains why teens are so useless at math... except for the nerds, of course.
@TheAleQc4 жыл бұрын
He should have used a peach for that joke.
@NintendoSunnyDee4 жыл бұрын
@@jrbleau Tbh, you're right. It took me failing a math class to kick it into high gear.
@grogsrevenge4 жыл бұрын
Actually, I didn't spot that one as I was too busy pointing out the fact that you're exerting a pull on the earth as well, which, hmm... on second thought, does it matter? Would you end up stationary at the centre of the earth, or would both of you wobble around your barycentre? Hm, on third thought I think I answered that one myself (it's the latter, so they cancel out. Right?) Anyway, my point is, maths is no joking matter.
@offtheball878 жыл бұрын
2:13 how did I not see that? What's happened to me? Did I accidentally remove my mind from the gutter?
@alazrabed8 жыл бұрын
I wouldn't want to alarm you, but it's often even worst than we like to think at first glance. You might be succumbing hopelessly into disgusting seemliness, where only grief and sorrow awaits you. Quick, go refresh your mind with delightful Sandler's comedies before it's too late. (In fact just watch them all in one go, can't be too safe.)
@offtheball878 жыл бұрын
Sandler movies? I want my mind in the gutter, not the sewer :P
@alazrabed8 жыл бұрын
I'm afraid the sewers are your last and only hope...
@longevitee8 жыл бұрын
+Elf Friend He said "Grow up."
@justindesilets35268 жыл бұрын
saw it just before he said "grow up". then I said "sorry mom"
@ishashka5 жыл бұрын
I actually had this problem as an exercise demonstrating harmonic oscillation in my high school physics textbook. Good times.
@ashmenser79597 жыл бұрын
I have been watching these math channels for years and they are so amazing. I started watching these videos when i was a freshman in high school taking algebra 1, now i am in 12 grade AP Calculus and AP Physics. The math has gone from complete gibberish to things I understand. Its so cool. So to all of the math channels, thanks for being a part of my life and thanks for being one of the few intelligent corners left on youtube. ❤️ love you guys
@anthonybeers7 жыл бұрын
It is actually more fun with air resistence. You will have damping that willl give you some decaying oscillation that will likely end you sitting susupended in the middle of the earth.
@connorhale38428 жыл бұрын
I knew the answer would be 42.
@nowonmetube5 жыл бұрын
I was about to comment the exact same thing, before looking in the comments section for the same answer.
@Puddymom5 жыл бұрын
Life the universe and everything
@nowonmetube5 жыл бұрын
@@alexanderschmidt6787 I like the way of your thinking
@ninjapancake22395 жыл бұрын
I had to like this. I was number 42.
@hypergalois5 жыл бұрын
ninjapancake you are a god
@henrikwilson8 жыл бұрын
Matt, what on EARTH are you doing (@9:28)?! You're using a dot as both a decimal and thousands separator!!!
@savagenovelist29834 жыл бұрын
Henrik Wilson He’s offending both sides of the debate at the same time, just to keep everything balanced.
@rogervanbommel10864 жыл бұрын
Yea, or shall I say what the fall are you doing
@fedexdiver4 жыл бұрын
Wait... in the 'London to New York' part of the video, wouldn't you need a non linear path/tunnel? Gravity would not pull you straight from London to NY but instead would pull you along the side of the tunnel towards the lopsided mass side... So how did we manage to get the same answer for time? Did we take a parabolic route sling-shot-ing around the core of earth similar to a gravity assist in space?
@damionwhitehead11653 жыл бұрын
This is the one part of the video I really didn't understand very well. He said it's take the same amount of time no matter where you drilled to. What if I drilled a hole to my neighbors yard? I doubt it'd take me 42min to walk through that tunnel.
@fedexdiver3 жыл бұрын
@@damionwhitehead1165 I think this is assuming you drill a hole to at least the center of the earth... still a little iffy in my opinion
@HunterJE2 жыл бұрын
It does seem dubious, a hole that doesn't pass through the center of the planet isn't going in a downwards direction and you'd just fall in to the slanted wall of the tunnel.
@spipsdew61574 жыл бұрын
This question came up as a free response question on my physics final and I had no idea how to do the math but I remembered this video, wrote 42 minutes and got full credit 😎
@IceMetalPunk4 жыл бұрын
You got full credit on a math question on a test without showing any work? That's... concerning.
@QPUNeptune4 жыл бұрын
@@IceMetalPunk well to be fair, he said it was a free question on a physics final so...
@IceMetalPunk4 жыл бұрын
@@QPUNeptune He said it was a "free response" question, as opposed to a multiple choice, true/false, or fill in the blank question. One where you write freeform to answer it. That doesn't mean the question is free...
@QPUNeptune4 жыл бұрын
@@IceMetalPunk welp, my fault, i misread that, thanks for pointing that out
@MiccaPhone2 жыл бұрын
That doesn't reflect well on the college.
@MrTnbopp1238 жыл бұрын
I love how he says "oh, grow up!" before it even occurred to me what was going on. Thanks for putting your ideas into my mind Matt. ;)
@peppermintmiso43413 жыл бұрын
This has been one of the videos that gave me the most laughs! Well done for a math lecture! From apples to onions to whiteboard and chalkboard too!
@dunkmania51553 жыл бұрын
At 10:50, my first thought was "Gee, if only we had a planet with an earth-like chemical makeup and a diameter of at least 299792.458 * 60 * 42.18 Kilometers!"
@jameshumphreys97158 жыл бұрын
this had to involve the apple, the iconic symbol of gravity.
@standupmaths8 жыл бұрын
+James Humphreys That did please me.
@DeJay73 ай бұрын
@@standupmaths I misread "That" as "They" "They did please me.", especially after the "Oh grow up" incident would have been diabolical.
@linkedXaverage6 жыл бұрын
As though 42 minutes wasn't a good enough connection, "There is an art to flying, or rather a knack. The knack lies in learning how to throw yourself at the ground and miss. ... Clearly, it is this second part, the missing, that presents the difficulties." The hitchhikers guide to the galaxy is the best trilogy ever and if you don't think so I'll fight you
@vanessathenavigator8 жыл бұрын
I have been a fan for years and was pleasantly surprised today when I came across you on a tv science show talking about rainbows! What a delight. You are awesome.
@standupmaths8 жыл бұрын
+Vanessa W I do that sometimes. But KZbin is my home.
@eskimoprime098 жыл бұрын
3:13 that seems a bit counterintuitive. I've always thought of it as if I'm in a basement, I'm closer to the center of the earth, so that gravity has more of a pull on me. But I guess his logic makes sense, because if you continue this until you reach the center, you are "essentially" weightless. But if you go higher than the surface, your weight will also decrease, so the surface is where you weigh the most?
@bryanreed7423 жыл бұрын
No, the peak is a couple thousand miles down. He was wrong at that point.
@roland91893 жыл бұрын
@@bryanreed742 No, at least if the density is the same everywhere (which it isn't). When you go up above the surface, the mass that pulls you down stays the same but your distance increases -> less Force. When you go below the surface, the mass that pulls you down gets cancelled by mass that is above you and pulls you up. You are also MUCH closer to the mass pulling you up - the Molecules in the concrete above you "count" a lot more than the Molecules down in Australia (or Sweden, if you happen to live on the Southern Hemisphere). In the end, while the distance to that centerpoint decreases, the Mass of that thing is also decreasing. The Distance gets squared, but Mass is dependent on Volume, and that gets cubed, so the Force in total decreases as well.
@agent452678 жыл бұрын
Isn't this assuming that the Earth's mass is even distributed? Most of the Earth's mass comes from the very center.
@SoulSukkur8 жыл бұрын
in the description, he linked to a minutephysics video that takes it into account
@bohitargep8 жыл бұрын
If the more dense part is at the center this would still work as its still symetric. But if the denser bit is on a side it wouldn't work.
@7186B8 жыл бұрын
Yes and no. Technically you're right, but everything is statistically scattered extremely even from the centre, that you don't need to do that. You really only need the complete mass and the distance.
@fossil988 жыл бұрын
+71866B Actually because the mass is non evenly distributed it takes less time to fall through the earth. The centre is more dense. Its kind of similar to how better solutions to the Brachistochrone problem arent a straight line. Matt is assuming wrong in this case and is overestimating the time.
@7186B8 жыл бұрын
Just imagine that you have a small 50kg ball. The centre of mass is exactly in the middle of that ball. If you now put that into a hollow light ball that has a bigger space, the centre of mass is still in the middle. That's why you don't need those 2 mass seperatively if the centre of mass is exactly in the middle. This is 100% with the earth. All elements on the earth have different distances to the centre and has different mass, but all those have the same centre, that's why you don't need to seperate things.
@octavioferreira28466 жыл бұрын
I wish there was a love button because this is an absolutely awesome video. I loved it to bits.
@thomashughes48595 жыл бұрын
I don't know if in the 1,619 comments this was addressed, but if you take a simple pendulum of a certain length, and you take a hula hoop of a diameter equal to that of the length of the simple pendulum (ignoring the lack of isochronism, of course), your Periods would be identical! I noticed that during this excellent discussion. Great work on the video!!! Thanks a million!
@skadogg228 жыл бұрын
Great timing! We just discussed this topic in my Classical Mechanics course.
@richardaversa71288 жыл бұрын
"This is not going to be exact... I'm using a food product."
@JohnViolidakis8 жыл бұрын
The Answer to Life, the Universe and Everything, plus 10.5 sec! Is that a coincidence??
@SuperSonicBlur8 жыл бұрын
John Violidakis and how 42/4 is 10.5...and 4 has 4 letters! it's all connected!
@KarachoBolzen8 жыл бұрын
Betcha when the magratheans built earth it was exactly 42m - there were just too many meteorite collisions happening since then :P
@anteconfig53917 жыл бұрын
@Eli Soo, your telling me that it's a coincidence that coincidences look like coincidences because otherwise they wouldn't be a coincidence? Wouldn't that be a coincidence? p.s. I was trying to make sense so I kept re-reading my comment before I posted. This made me forget the meaning of coincidence and now I feel like I just made up the word so I'm just gonna post this before I go even more crazy.
@gabbyholloman93987 жыл бұрын
Exactly what I was thinking!
@tqnohe6 жыл бұрын
John Violidakis It is not.
@NoxmilesDe8 жыл бұрын
"oh, grow up" you got me 😂
@DaneBrooke7 жыл бұрын
Right. Love your stuff! Glad the Great Courses is helping out. Must say its now been about 45 years, and its always interesting what you recall after a long span of time. There were 8 of us in that particular class during university days, and we each arrived at an identical result, which was memorable in itself. Fifty four minutes. That is the number we got. Offhand I can't say where our assumptions, methods or reference values may have deviated from yours, but a 30% variance can't be dismissed as mere experimental error. I believe that if I search diligently enough I will turn up the old notebook with those calculations, so perhaps an additional comment later.
@DaneBrooke7 жыл бұрын
(Just noticed that sqrt(miles/kilometers) almost exactly = 54/42. Hm.)
@isacami252 жыл бұрын
this was so entretaining. i saw years ago minutephysics video about the same subject. but the math perspective on this one is a great bonus.
@nicnakpattywhack57844 жыл бұрын
"a apple" "oh, grow up!"
@Zaurthur8 жыл бұрын
Why didn't you cut the onion the other way? Then the layers are much more concentric and you can peel them easier.
@headrockbeats8 жыл бұрын
Yeah, I face-palmed when it happened.
@rickyoswald8 жыл бұрын
He wanted to use Parker Spheres.
@VeteranVandal8 жыл бұрын
It was the Parker Cut.
@OrchidAlloy8 жыл бұрын
It was a Parker Square of a demostration.
@PetraKann8 жыл бұрын
Cooking habits are almost impossible to break
@rednax37888 жыл бұрын
JUST SO EVERYBODY KNOWS, BECAUSE APPARENTLY I'M THE ONLY ONE: Today is international Power of 2 Day!!! At 1:02, the date and time will read 2^0:2^1 2^2/2^3/2^4
@michaels43408 жыл бұрын
Very cool! Of course, here in America that happened back in April :p I wish I'd known!
@cupass61797 жыл бұрын
Gawsome technically that's the time and date
@gamingwithgabe61566 жыл бұрын
@@michaels4340 in Britain they use the weird format: dd/mm/yy, so they have a completely different date for it
@goddamnmaddog20246 жыл бұрын
@@gamingwithgabe6156 dd/mm/yy is the only logical solution. XD yy-mm-dd or mm-dd-yy is just people on drugs and a big ego justifing their ideas and believes without thinking a split second about the advantages of other ideas. like using empiric measuring system.. XD degree fahrenheit, lol.. when ever it sounds plausible to use a measuring scale that got fit to the coldest day in danzig and the body temperature of a sick inventor, then you are in the states (he had high temperature that day, lol) address and date go from fine detail to coarse detail aswell: First Name Last Name Street City State Country
@michaels43406 жыл бұрын
@@gamingwithgabe6156 Yes, I'm aware!
@michaelibrahim92754 жыл бұрын
You can also substitute the density, rho, for the mass of the earth over the volume of the earth (we already assumed constant density) to get ρ=3M/4πr^2, and then the 4/3s cancel and you get sqrt(π^2 r^2/GM)
@chrislivepiano93068 жыл бұрын
well, you take 42 minutes (and a bunch of seconds) to fall from one spot to any other spot on earth (the math going on is absolutely amazing btw.) and you take this time for any planet no matter which size but with the same density as earth, may this is the thing that they wanted to point out, when they said “forty-two is the answer of all questions“ in the movie “the Hichhiker's guide to the galaxy“!! I'm absolutely amazed!! mind's blown!!
@bentoth95556 жыл бұрын
"Will cause friction which is, frankly, inconvenient for the maths." It's also inconvenient for the face that's scraping along the rock.
@JROwensPhotos8 жыл бұрын
8:00 Lost me at 'density of the Earth doesn't change', especially after all that earlier mention of the core.
@jlittlenz8 жыл бұрын
This is a glaring inaccuracy that should be mentioned in the video! The earth's density increases with depth, and in particular the core (being mostly iron) is much more dense than the rest, being rock. Gravity increases (at first) as you go down into the earth from the surface! (Mostly because you get closer to the core.) However, the end result is still the same, which I imagine standupmaths would say is really cool.
@WJS7744 жыл бұрын
@@jlittlenz While it's still symmetric and you'll still reach the other side with a net velocity of zero, you'll arrive there sooner due to the different acceleration profile so I'd say the end result isn't still the same.
@alidurrani46454 жыл бұрын
@@WJS774correct me if i am wrong, the amount by which the acceleration is happening due to increasing density while moving towards the center is same as the amount of deceleration due to decreasing density once u move past the center, since the force is decreasing. like if density is "g" then f is proportional to g but since g is not a constant and is changing we can say f is proportional to g - dg/dr +dg/dr which cancels out if the density of the starting and the ending point is same. the question i want to ask is why should the time decrease
@alidurrani46454 жыл бұрын
where r is the instantaneous position reference to the center of the earth
@WJS7744 жыл бұрын
@@alidurrani4645 Imagine the extreme case where the mass of the earth is in fact a point mass. In that case, gravity _increases_ the closer you get to the centre. The greater acceleration means greater velocity and greater velocity means less time. Obviously the earth is not in fact a point mass, so the gravity does not increase _all_ the way to the centre, but it _does_ increase until you reach the core.
@jondoolio7 жыл бұрын
You know when you've grown up is when you realize the dirty joke after he says "grow up"
@santoriomaker697 жыл бұрын
Hahaha, that's what I like about these kinds of jokes. When it works for both people who have grown up, and those who haven't grown up
@Hextator7 жыл бұрын
Scared me when I heard him say that because he caught me at the height of my shame
@throkir15 жыл бұрын
In fact, there are no grown ups, just people with different complex minds, some are more childish and some are used to think they are grown up, that's all :D
@kindpotato5 жыл бұрын
I guess I'm not grown up because before he even put the apple together I was anticipating it.
@WildStar20024 жыл бұрын
@@Hextator Me too!
@brycepemble75474 жыл бұрын
I love it! I have watched many of your videos. I really liked "How to mathematically calculate a fall through the Earth". The only issue I have, is that "Rho" would be changing significantly as you fell. Because of chemical fractionation, when the Earth was molten, all the denser materials became concentrated in the Inner and Outer Core. Call it "Metal Hurlant", if you will: Iron, Nickel and other "Heavy Metals". The Mantle is much less dense due to all of the silicates, and the crust is the rarest of all. And it is not just a trivial difference either... The Core is estimated to be a factor of 3 to 4 times denser than the outer layers. It seems like this would lead to a significantly different result.
@NFM13378 жыл бұрын
This takes me back. Did this during introductory theoretical physics back in the day. :)
@dibbydoda71608 жыл бұрын
I probably laughed more than I should have at 2:12 !
@KingSyilver3 жыл бұрын
For falling through a hole not on a central axis, you'd end up scraping against the walls I assume
@drusillawinters2122 жыл бұрын
He is incorrect because the majority of the mass would be on one side. Therefore the force would not up in the same direction as the direction that you are falling.
@JeffBourke4 жыл бұрын
4:04 You made a mistake here. You could have cut the onion accross the "equator" if you will and you would have got more concentric circles.
@michaelmiranda57578 жыл бұрын
Matt parker! thanks for the videos! always looking forward to them when i get home, after a long day of work, only to turn into mush what ever chunks of brain i have left. I appreciate it.
@blalolblalol4 жыл бұрын
With all due respect yo your more recent videos (which I thoroughly enjoy BTW), this is my favorite video on your channel!
@miles24198 жыл бұрын
"It's very hard to draw on an onion." Ah, yes. The kind of quality information I came here to learn.
@ibonitog8 жыл бұрын
Hey Matt, I just finished this, as always fantastic, video and the saw the sponsoring at the end. Which I think is great to keep your channel up and running. But then I was wondering whether there was another way to support you? Since I'm from Germany, I was only able to buy a digital copy of your "festival" and couldn't show up in person - btw, love it! Something like flattr or patreon or at least a PayPal account to donate something. I love your channel and your videos and I understand that you're doing this in your spare time, so give us a chance to support you even more! Lovely greetings from Aachen, Germany.
@oberdiah90648 жыл бұрын
Completely agree. Would also support him on patreon :P
@standupmaths8 жыл бұрын
+Benedikt Geiben Thanks! I'm now convinced I should set up a Patreon. Would be nice to have the stability to keep making videos.
@ibonitog8 жыл бұрын
Great, really looking forward to it!
@sirpikapika11293 жыл бұрын
I'm not sure if I missed it during the explanation, but wouldn't it be more of a circular horizontal slice than just the sphere around the center that determines your gravitational pull force? Like, some of the spheres "above" you as you fall have a portion of the sphere below you as well, so instead of an onion wouldn't it be like a line perpendicular to the falling direction? Because (In your scenario in which the earth is all the same density, which it isn't actually) it doesn't matter that it's a part of the outer sphere(s), it's still pulling on you with the same mass as before and that pull would have a vertical and horizontal portion of its pull vector, but the horizontal portions would get counteracted by the same portion from the opposite direction, so just the vertical part would remain Do the numbers work out to the same results with this line of reasoning?
@Sheph1003 жыл бұрын
Falling through the center of the earth is a special case where the horizontal components, using your terms (I might call them the y and z axes), effectively cancel each other out at all points, leaving only the vertical component to affect your acceleration. The two parts of the onion is just a useful visual to simplify the problem into two parts (the sphere below you and the "shell" above you). The shell of the onion can be further split (see the cut he made) into two parts which have equal and opposite effects on you in ALL directions.
@junxianwu18744 жыл бұрын
Had an interesting thought, since the time taken for an object to fall through a planet/body is independent of the size of said body, say we have a planet with uniform density that is more than 7.59 x10^11 metres in diameter, does this mean that the falling object will exceed the speed of light? 7.59x10^11m/2530.5s = 299940723.2 m/s > c
@junxianwu18744 жыл бұрын
Assuming of course that said planet's density is equal to that of the Earth.
@abstractapproach6348 жыл бұрын
9:45 just thinking he should mention it doesn't matter if your going through the center or not, then saw video was'nt even half over, good on ya Matt
@kunjupulla5 жыл бұрын
00:13 Matt: "a apple" Me thinking: "Were my kindergarten books wrong?!"
@Lavaloid8 жыл бұрын
that feeling when you're so early that HD is not available yet but it doesn't matter anyway because your internet is really slow, yeah, it's painful.
@XxJ0nas98xX8 жыл бұрын
I have HD available, so it apparently becomes available fast
@standupmaths8 жыл бұрын
+Lavaloid the Human You were so early you had the first comment!
@Solitaan8 жыл бұрын
How slow is your internet? Mine is 0.65 mbps, max.
@deeelmore45607 жыл бұрын
"The reason I'm using [the onion]... it's made of concentric spheres." Yeah, onions have layers. Like ogres.
@JohannPetrak4 жыл бұрын
24:06 How can you possibly "fall" in a straight line that does not go through the center ("London to New York")? That would have to be an ellipsis (for a periodic fall) and in order to avoid the center and make it an ellipsis you would need some non-zero tangetial initial velocity.
@gz3zbz4 жыл бұрын
This.
@WJS7744 жыл бұрын
I think the idea is if you are constrained to that line in some manner, you would fall across it the same way in the same time. Like if you had a train on a track going in a straight line from London to New York then if you ignore friction you would 'fall' there in the same time, assuming a constant density for the Earth (which isn't actually true).
@sicktj4 жыл бұрын
I wondered the same thing. You would be pulled towards the more massive side
@spacewarpphotography16678 жыл бұрын
At 18:52, he claims that a satellite orbiting at the surface of the earth would go halfway around in the same time and at the same speed as a person falling through the earth. That claim doesn't hold up however, when you consider that the length fallen by the person (2r) is not the same as the distance around the planet (pi * r). The ball somehow moves at the same speed for the same time but travels further?
@DrRChandra8 жыл бұрын
Another Parker Square: drawing on the inside of an apple with a Sharpie.
@simonhallin89094 жыл бұрын
Matt: "Assuming there's no air resistance" Me: High-School Physics all over again
@nicktalati42118 жыл бұрын
This was great but I still don't understand how you put a hole in that apple so fast.
@skibalovesya7 жыл бұрын
So glad this exists. There's an episode of Batman Beyond where a villain misusing technology that allows him to phase through matter winds up falling through the Earth. The episode ends with Bruce saying he'd stop falling at the core, but when I asked the physics teacher at my school he explained exactly this (though in super condensed form).
@mrgodfrey15988 жыл бұрын
Great connection between the hole in the Earth problem and simple harmonic oscillators. One correction at around 12:24. Your first equation of motion should read s=ut+1/2at^2. The other two are fine though.
@alexanderreusens76337 жыл бұрын
11:50 What is bugging me the most is that in reality, the density of the sphere below you is not constant, it's a function of x!
@steenbruggen94457 жыл бұрын
"Oh grow up!"
@camerongray77675 жыл бұрын
Not even kidding my eyes started watering when he cut the onion 😮
@cstiger44 жыл бұрын
Your enthusiasm is totally catching!
@computergeek82994 жыл бұрын
The video begins: Stick man falling through onions and apples... The video ends: SO, we just integrated multiple derived equations of motion to derive harmonic oscillators that describe the gravitational influence on objects falling in and around a sphere...
@JoeyPsych8 жыл бұрын
I didn't even think about it untill he said: oh grow up.
@lilweez21758 жыл бұрын
2:07 I like that a lot...................
@adammullarkey49965 жыл бұрын
"Journey to the centre of the onion," the far less exciting sequel.
@trulyUnAssuming8 жыл бұрын
Actually that bit at 20:40 made me actually understand it for the first time. Of course it has to be the same time. Because if you throw a ball sidewise and drop a ball at the same time, they will fall the same distance and land on the ground at the same time. And your Satellite is basically just a ball that starts with sideways movement and falls straight down just like if you fall through earth - just that it also gets pulled to the side aswell.
@TinyFoxTom6 жыл бұрын
That was actually a well-put-together demonstration... Taking it apart was another story!
@TheDeffend7 жыл бұрын
So basically what you're saying at 4:04 is that onions are like ogres?
@shorterneilisbored70787 жыл бұрын
someBODY once told me the world was a gummy so I took a bite out of a tree.
@KVBA6 жыл бұрын
ONIONS. HAVE. LAYERS.
@alistairferguson65905 жыл бұрын
Shrek is love. Shrek is life.
@newcantinacrispychickentac77544 жыл бұрын
@@shorterneilisbored7078 it tasted kind of funny so spit it at a bunny that started cursing at me
@jpaugh647 жыл бұрын
24:06 So, if the Earth fell through the sun, surviving intact, it would reach the opposite side of its normal orbit in the same amount of time? whoa
@asneakychicken3227 жыл бұрын
jpaugh64 only if the Earth orbited at the surface level of the Sun
@FlyingDominion7 жыл бұрын
The time would change based on the sun's density.
@corneliuscorcoran99006 жыл бұрын
I really hope it doesn't...just sayin'
@livintolearn70537 жыл бұрын
"is someone cutting onions in here?" hahahaha
@frankburgum44784 жыл бұрын
In October 1965, at the age of 17, I had an interview at King's College London, to enter their BSc Special Physics course the following year. The interviewer asked me this exact question. I DID manage to work out that it was simple harmonic motion, but no way to calculate the actual period in the heat of the interview. He had to tell me the match to the sea-level satellite period. But I still got the place on the course ...
@otakutom177 жыл бұрын
My train of thought as Matt is demonstrating the ideal motion through the planet given a perfect system: "I need to gif this." Matt: "Oh, grow up!"
@eskimoprime098 жыл бұрын
So, it would take me 42 mins to fall to me neighbors house? What would that even be like?
@andyli18908 жыл бұрын
Mitchell if your neighbour lives on the other side of the world, I don't think he is your neighbour
@S7evieRay7 жыл бұрын
If there was no friction and a direct path then yes
@jasondahlen95557 жыл бұрын
Well, technically, you couldn't. Gravity would pull you to the center of the earth; you can't fall perpendicular to gravitational forces. However you could theoretically set up an oscillation between the two points *using* gravity, which would make that time correct. To answer your question, it would be a nearly 45 minute slide along a frictionless sidewalk.
@sage52967 жыл бұрын
Mitchell think frictionless skateboard over a flat area. The force is not quite perpendicular
@octavioferreira28466 жыл бұрын
This was used as an example of theoretical forms of transportation. If we could build a train over a completely frictionless track in a completely straight vacuum tunnel between any 2 points on the earth's surface (exact same distance to the earth's center of mass), the train would take those 42ish minutes to do the trip using gravity alone. If the two points happen to be a few meters apart, the distance is very short but the acceleration would also be minuscule.
@PerfectChaos78 жыл бұрын
So I have two big problems with this video. The first is when you mentioned the situation in which one falls through a tunnel that doesn't go through the center of the Earth. If one were to jump into such a hole/tunnel, gravity will still pull them directly towards the center of mass of the Earth, so they wouldn't fall perfectly centered through the hole, and would eventually hit the wall of the tunnel, making it impossible to fall through such a hole/tunnel without an external force to keep them centered within that hole. I guess if you can create a device that fights against your off-centered acceleration towards the wall of the tunnel in order to keep you centered, making it only affect that and nothing else, then you'd fall through the off-centered tunnel in the same amount of time, but if it's a system where only gravitational force is applied, then it's only possible to fall through the center of mass. The other problem has to deal with time dilation when gravity changes, which affects how you would calculate the time it takes to cross the planet depending on which point-of-view you're calculating from, but that's on a whole new level of complication, so I don't fault you for not taking that into account.
@adarshtiwari63748 жыл бұрын
by making that hole, would nt it decrease the mass of earth
@brokenwave61254 жыл бұрын
Not unless the mined material was being lauched off the planet...
@davidb28857 жыл бұрын
So as you all are definitely used to the best KZbin content on earth by Matt, you might forget to like the videos... Do it!
@miles24198 жыл бұрын
How do you choose what variables to consider/calculate, such as gravity, (although that one's sort of a given,) and which not to, such as molten rock, possible additional gravitational forces? (So like, if you have Mt. Everest one one side of you, and on the other side, uhh,, not Mt. Everest ? Like, a significantly greater amount of land/mass/density on one side of you. Would that affect you?) Would the size/circumference of the hole affect the fall? Would you be able to breath? If the hole wasn't perfectly cylindrical, and had various bumps and craters or indentations, would that affect the fall? Would breathing affect your fall in the slightest? How would the pressure /not/ kill you? I mean, I'm assuming that's one factor we're avoiding, but still, is that at all possible (I'm only at 2:26, by the way, so it's likely that a portion of this comment's questions will be answered, at least? idkk.) Uhhh I had more questions but I forgot them, which is probably a good thing since it limits my rambling. 🙃🙃🙃🙃 #rip
@cibrinyark3398 жыл бұрын
Would, when falling from London to new York, the gravity of the center of the earth be great enough to pull you along the wall of the tunnel causing friction?
@Kahitar8 жыл бұрын
I think you would not be falling at all. You could actually just walk through that hole ;D
@shootingblueyes8 жыл бұрын
All of these measurements are assuming that you're falling directly through the center of the tube with no friction.
@georgefowler61208 жыл бұрын
It would also require some sort of friction-less rail system, yes. I thought of this too.
@freshrockpapa-e77997 жыл бұрын
Not the gravity of the center, but the coriolis effect.
@steelman15067 жыл бұрын
Caleb Brinyark If the walls are lined with Teflon and you were covered in butter you'll be fine sliding along the side
@philadams92548 жыл бұрын
The answer to everything is 42!
@tompov2278 жыл бұрын
2:13 was specifically at me :(
@lolstandunited4 жыл бұрын
Thomas P i was waiting for something like this and what like no he can’t be that professional
@gnothisauton2116 Жыл бұрын
We finally have the question to the ultimate answer of life, the universe and everything. 42 = how long to orbit or fall through a planet? Simply stunning.
@JeffBourke4 жыл бұрын
is the middle guts constant? Isn't the density a funtion of radius? Iron core, rock, magma, water etc?
@Confuseddave4 жыл бұрын
I feel like you glossed over the point that the gravity above you is cancelled out by the gravity of the shell outside your altitude below you. Is that something to do with the way the inverse square law for gravity falling off over distance cancels out the volume of a hollowed sphere?
@johnfells69854 жыл бұрын
That's also my assumption.
@Ashcombeguy8 жыл бұрын
but the density of the earth does change. I'm pretty sure that the molten / solid iron core (we're not sure what state it's in under such great temprature and pressure) has a higher density than that of the mantle.
@MrNitua8 жыл бұрын
Ok, but we're already talking about a ridiculous situation, so we can probably assume uniform density
@josephpaine67968 жыл бұрын
Not like any other youtubers have done this ........
@needlessToo8 жыл бұрын
As far I know they didn't calculate time it takes and speed.
@mommailuvu8 жыл бұрын
How many people have you seen play the same game?
@Egonkiller8 жыл бұрын
I wonder how many of these actually used integration ;)
@Theraot8 жыл бұрын
Nobody owns the facts
@AmeshaSpentaArmaiti8 жыл бұрын
how many textbooks covering the exact same material exist? how many of them are published by the same companies? how many of them are written by the same people? not getting to some bit of information first on youtube is not a reason not to do a video.
@kimba381 Жыл бұрын
And the period of a simple pendulum of length R as well! Pendulum, orbit and drop all the same! when I discovered this in high school I was amazed!
@comradepeter873 жыл бұрын
You know what's even more amazing? It will ALWAYS take the SAME amount of time no matter from where the hole starts, and wherever it ends (assuming ideal conditions). It could literally be 2m away from the start point, as long as that end point is also on the circumference of the Earth. EDIT: Nevermind got too excited. He did say it later on.
@old-bitprogaming48577 жыл бұрын
2:00 how to bαng tutorial
@notanimposter8 жыл бұрын
I'm disappointed. That's not even remotely a coincidence. The ball's motion along the "y" axis is the same. It just also happens to be moving along the x axis as well.
@standupmaths8 жыл бұрын
+notanimposter Yep, that's the video in a nutshell.
@AndrewBennettScience7 жыл бұрын
Your first kinematics equation is written as v = ut +1/2at^2 . That v should be the displacement (s) rather than the final velocity (v).
@kahlzun3 жыл бұрын
the orbit at 0 and the time taken to fall through are linked despite what you say! Orbits are basically just falling (with style) except you miss the planet in the process. From the side your corenaut and the orbit will be identical.
@LoomisPowderdogs8 жыл бұрын
instant sub after the leapyear episode. love being precise