How to mathematically calculate a fall through the Earth

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  • เผยแพร่เมื่อ 2 ส.ค. 2016
  • Huge thanks to the Great Courses Plus for sponsoring this video. Click here to check out the free trial: ow.ly/gSm4302OFJw
    Watch the full integration! Worth it even just for the Simple Harmonic Motion which drops out at the end. • Integrating a fall thr...
    Try the ISS challenge! Will you get there before the after the International Space Station orbits half-way around the planet? Even if you don’t try to work it out, you can have a guess at the outcome. • Race the ISS through t...
    Python code that I used is here: www.dropbox.com/s/vbwymdxjz47...
    My values:
    R = 6,371,000 m (radius of the Earth)
    G = 6.674 × 10^-11 m^3 kg^-1 s^-2 (gravitational constant)
    M = 5.972 × 10^24 kg (mass of Earth)
    Yes, people have since pointed out a similar topic was covered in a Minute Physics video. They skip over the "constant stuff" and how the mathematics is derived, but it’s a great look at how the density changes within the Earth and how that impacts the travel time. Well worth checking out as well. • How Long To Fall Throu...
    CORRECTIONS:
    - I accidentally wrote "v" instead "s" on the board in "s = ut + ½at^2". First spotted by Joel Low.
    - Around 9:30 I used a dot for both 1,000's and decimal point. The first should be a comma. Spotted by Mezgrman.
    - I normally play pretty fast and loose with centripetal force vs centrifugal effect; I think arguing about the difference is not useful so I often use them as synonyms. In this case, as Wayne Ernst politely pointed out, I should have said "centripetal force" not "centrifugal force". And they're right.
    Discuss on reddit: / mattparker
    Music by Howard Carter
    Design by Simon Wright
    Apple wrangling by Lucie Green
    MATT PARKER: Stand-up Mathematician
    Website: standupmaths.com/
    Maths book: makeanddo4D.com/
    Nerdy maths toys: mathsgear.co.uk/
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ความคิดเห็น • 2K

  • @NoriMori1992
    @NoriMori1992 7 ปีที่แล้ว +288

    "Your fragile face scraping against the rock surface will cause friction, which is frankly inconvenient for the maths."

    • @jayveeascano4570
      @jayveeascano4570 3 ปีที่แล้ว +1

      Norimori

    • @collin5577
      @collin5577 3 ปีที่แล้ว +1

      @@jayveeascano4570 jayvee Ascaño

    • @vwlz8637
      @vwlz8637 2 ปีที่แล้ว +1

      @@collin5577 collin

    • @yoyoyonono
      @yoyoyonono 2 ปีที่แล้ว +1

      @@vwlz8637 vwlz

    • @trickytreyperfected1482
      @trickytreyperfected1482 2 ปีที่แล้ว +1

      @@yoyoyonono Aaron Thapa Ch. - Games, Music and Stuff

  • @nerdy5999
    @nerdy5999 5 ปีที่แล้ว +131

    Repeatedly falling through the hole, emerging at the other end of the sphere and plummeting once again is technically orbiting (mathematically).

    • @jakesanchard461
      @jakesanchard461 ปีที่แล้ว +1

      if you watched the full video, he actually says this

  • @theCodyReeder
    @theCodyReeder 6 ปีที่แล้ว +677

    “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?

    • @standupmaths
      @standupmaths  6 ปีที่แล้ว +307

      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!

    • @CraftQueenJr
      @CraftQueenJr 6 ปีที่แล้ว +5

      Cody'sLab or you would just get stuck in the center.

    • @jeffreyblack666
      @jeffreyblack666 6 ปีที่แล้ว +19

      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.

    • @NickRoman
      @NickRoman 6 ปีที่แล้ว +25

      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.

    • @jeffreyblack666
      @jeffreyblack666 6 ปีที่แล้ว +25

      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.

  • @philippenachtergal6077
    @philippenachtergal6077 3 ปีที่แล้ว +119

    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.

    • @zecuse
      @zecuse 3 ปีที่แล้ว +6

      Complicated suicide doesn't get too much simpler than that.

    • @saipavand4064
      @saipavand4064 2 ปีที่แล้ว

      69 likes

  • @Yoshimaster96smwc
    @Yoshimaster96smwc 6 ปีที่แล้ว +279

    0:13
    "a apple"

    • @rasseboiii3505
      @rasseboiii3505 6 ปีที่แล้ว +3

      Yoshimaster96smwc Lol

    • @benmcdaniel
      @benmcdaniel 4 ปีที่แล้ว +23

      Parker grammar.

    • @WaterShowsProd
      @WaterShowsProd 4 ปีที่แล้ว +3

      "Certainly it can core a apple."
      -Chef of The Future

    • @zoranbg
      @zoranbg 3 ปีที่แล้ว +11

      Well, he is a Maths teacher, not an English teacher... ;)

    • @henrikholst7490
      @henrikholst7490 3 ปีที่แล้ว +4

      Apple is just an instance of a Earth.

  • @dodsg
    @dodsg 7 ปีที่แล้ว +156

    Walking through Fremantle today and my son grabs my sleeve - "Dad, Dad, that's the guy who does those cool TH-cam videos!" I learned two things today:
    - The world is smaller then you think.
    - My son is a bigger nerd than I realised.

    • @standupmaths
      @standupmaths  7 ปีที่แล้ว +86

      +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.

    • @omikronweapon
      @omikronweapon 3 ปีที่แล้ว +42

      Imagine being the boy that comes home from school and his dad goes "Matt Parker told me to tell you, what's up"

    • @jerelull9629
      @jerelull9629 3 ปีที่แล้ว +12

      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.

    • @jerelull9629
      @jerelull9629 3 ปีที่แล้ว +8

      @@omikronweapon Heck! Imagine being the PARENT.

  • @DegonTheMighty
    @DegonTheMighty 7 ปีที่แล้ว +29

    The re-capping of the sharpie at 4:32 was done so professionally.

  • @FrostMonolith
    @FrostMonolith 7 ปีที่แล้ว +55

    2:07 Until you said "Oh grow up" I never noticed. THANKS MATT.

  • @offtheball87
    @offtheball87 7 ปีที่แล้ว +497

    2:13 how did I not see that? What's happened to me? Did I accidentally remove my mind from the gutter?

    • @alazrabed
      @alazrabed 7 ปีที่แล้ว +23

      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.)

    • @offtheball87
      @offtheball87 7 ปีที่แล้ว +57

      Sandler movies? I want my mind in the gutter, not the sewer :P

    • @alazrabed
      @alazrabed 7 ปีที่แล้ว +1

      I'm afraid the sewers are your last and only hope...

    • @longevitee
      @longevitee 7 ปีที่แล้ว +14

      +Elf Friend He said "Grow up."

    • @justindesilets3526
      @justindesilets3526 7 ปีที่แล้ว +7

      saw it just before he said "grow up". then I said "sorry mom"

  • @NintendoSunnyDee
    @NintendoSunnyDee 6 ปีที่แล้ว +379

    "Oh grow up!"
    What, were you saying it was silly to think we'd just bounce back and forth?
    (Thirty entire seconds pass)
    Wait...

    • @BLSXful
      @BLSXful 3 ปีที่แล้ว +65

      I was in math mode, so I didn't get it. I had go into teen mode

    • @jrbleau
      @jrbleau 3 ปีที่แล้ว +25

      @@BLSXful Which explains why teens are so useless at math... except for the nerds, of course.

    • @TheAleQc
      @TheAleQc 3 ปีที่แล้ว +16

      He should have used a peach for that joke.

    • @NintendoSunnyDee
      @NintendoSunnyDee 3 ปีที่แล้ว +5

      @@jrbleau Tbh, you're right. It took me failing a math class to kick it into high gear.

    • @grogsrevenge
      @grogsrevenge 3 ปีที่แล้ว +3

      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.

  • @eoghan.5003
    @eoghan.5003 4 ปีที่แล้ว +263

    "assuming there is no air resistance"
    me, a highschool student: "air resistance? What air resistance?"

    • @renedekker9806
      @renedekker9806 3 ปีที่แล้ว +12

      me: "what about magma resistance?"

    • @ellesko
      @ellesko 3 ปีที่แล้ว +3

      @@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.

    • @MANU123423
      @MANU123423 3 ปีที่แล้ว +1

      @@ellesko Dam, the point of a cheeky reply is to make it short.. Go tired of reading at the second line!

    • @samuelwikstrom7721
      @samuelwikstrom7721 3 ปีที่แล้ว +3

      @@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.

    • @davidrojas4687
      @davidrojas4687 3 ปีที่แล้ว

      is what you never assume.

  • @connorhale3842
    @connorhale3842 7 ปีที่แล้ว +470

    I knew the answer would be 42.

    • @nowonmetube
      @nowonmetube 5 ปีที่แล้ว +7

      I was about to comment the exact same thing, before looking in the comments section for the same answer.

    • @Puddymom
      @Puddymom 5 ปีที่แล้ว +11

      Life the universe and everything

    • @nowonmetube
      @nowonmetube 5 ปีที่แล้ว +3

      @@alexanderschmidt6787 I like the way of your thinking

    • @ninjapancake2239
      @ninjapancake2239 5 ปีที่แล้ว +7

      I had to like this. I was number 42.

    • @juandelgado8338
      @juandelgado8338 5 ปีที่แล้ว +3

      ninjapancake you are a god

  • @henrikwilson
    @henrikwilson 7 ปีที่แล้ว +51

    Matt, what on EARTH are you doing (@9:28)?!
    You're using a dot as both a decimal and thousands separator!!!

    • @savagenovelist2983
      @savagenovelist2983 4 ปีที่แล้ว +15

      Henrik Wilson He’s offending both sides of the debate at the same time, just to keep everything balanced.

    • @rogervanbommel1086
      @rogervanbommel1086 4 ปีที่แล้ว +1

      Yea, or shall I say what the fall are you doing

  • @Tker1970
    @Tker1970 5 ปีที่แล้ว +19

    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.

  • @anthonybeers
    @anthonybeers 6 ปีที่แล้ว +25

    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.

  • @ishashka
    @ishashka 4 ปีที่แล้ว +16

    I actually had this problem as an exercise demonstrating harmonic oscillation in my high school physics textbook. Good times.

  • @jameshumphreys9715
    @jameshumphreys9715 7 ปีที่แล้ว +41

    this had to involve the apple, the iconic symbol of gravity.

    • @standupmaths
      @standupmaths  7 ปีที่แล้ว +18

      +James Humphreys That did please me.

  • @agent45267
    @agent45267 7 ปีที่แล้ว +317

    Isn't this assuming that the Earth's mass is even distributed? Most of the Earth's mass comes from the very center.

    • @SoulSukkur
      @SoulSukkur 7 ปีที่แล้ว +32

      in the description, he linked to a minutephysics video that takes it into account

    • @bohitargep
      @bohitargep 7 ปีที่แล้ว +20

      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.

    • @user-jr8rz7bx3v
      @user-jr8rz7bx3v 7 ปีที่แล้ว +4

      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.

    • @fossil98
      @fossil98 7 ปีที่แล้ว +9

      +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.

    • @user-jr8rz7bx3v
      @user-jr8rz7bx3v 7 ปีที่แล้ว +1

      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.

  • @spipsdew6157
    @spipsdew6157 3 ปีที่แล้ว +140

    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 😎

    • @IceMetalPunk
      @IceMetalPunk 3 ปีที่แล้ว +46

      You got full credit on a math question on a test without showing any work? That's... concerning.

    • @QPUNeptune
      @QPUNeptune 3 ปีที่แล้ว +10

      @@IceMetalPunk well to be fair, he said it was a free question on a physics final so...

    • @IceMetalPunk
      @IceMetalPunk 3 ปีที่แล้ว +19

      @@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...

    • @QPUNeptune
      @QPUNeptune 3 ปีที่แล้ว +5

      @@IceMetalPunk welp, my fault, i misread that, thanks for pointing that out

    • @MiccaPhone
      @MiccaPhone ปีที่แล้ว

      That doesn't reflect well on the college.

  • @fedexdiver
    @fedexdiver 4 ปีที่แล้ว +24

    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?

    • @damionwhitehead1165
      @damionwhitehead1165 3 ปีที่แล้ว +2

      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.

    • @fedexdiver
      @fedexdiver 3 ปีที่แล้ว +1

      @@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

    • @HunterJE
      @HunterJE ปีที่แล้ว +2

      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.

  • @richardaversa7128
    @richardaversa7128 7 ปีที่แล้ว +17

    "This is not going to be exact... I'm using a food product."

  • @ashmenser7959
    @ashmenser7959 6 ปีที่แล้ว +3

    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

  • @michaelmiranda5757
    @michaelmiranda5757 7 ปีที่แล้ว

    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.

  • @blalolblalol
    @blalolblalol 3 ปีที่แล้ว

    With all due respect yo your more recent videos (which I thoroughly enjoy BTW), this is my favorite video on your channel!

  • @NoxmilesDe
    @NoxmilesDe 7 ปีที่แล้ว +15

    "oh, grow up"
    you got me 😂

  • @MrTnbopp123
    @MrTnbopp123 7 ปีที่แล้ว +3

    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. ;)

  • @skadogg22
    @skadogg22 7 ปีที่แล้ว +1

    Great timing! We just discussed this topic in my Classical Mechanics course.

  • @KingSyilver
    @KingSyilver 3 ปีที่แล้ว +18

    For falling through a hole not on a central axis, you'd end up scraping against the walls I assume

    • @drusillawinters212
      @drusillawinters212 2 ปีที่แล้ว

      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.

  • @Zaurthur
    @Zaurthur 7 ปีที่แล้ว +133

    Why didn't you cut the onion the other way? Then the layers are much more concentric and you can peel them easier.

    • @headrockbeats
      @headrockbeats 7 ปีที่แล้ว +7

      Yeah, I face-palmed when it happened.

    • @rickyoswald
      @rickyoswald 7 ปีที่แล้ว +92

      He wanted to use Parker Spheres.

    • @VeteranVandal
      @VeteranVandal 7 ปีที่แล้ว +80

      It was the Parker Cut.

    • @OrchidAlloy
      @OrchidAlloy 7 ปีที่แล้ว +56

      It was a Parker Square of a demostration.

    • @PetraKann
      @PetraKann 7 ปีที่แล้ว +8

      Cooking habits are almost impossible to break

  • @peppermintmiso4341
    @peppermintmiso4341 3 ปีที่แล้ว +4

    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!

  • @linkedXaverage
    @linkedXaverage 5 ปีที่แล้ว +1

    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

  • @isacami25
    @isacami25 ปีที่แล้ว

    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.

  • @JohnViolidakis
    @JohnViolidakis 7 ปีที่แล้ว +168

    The Answer to Life, the Universe and Everything, plus 10.5 sec!
    Is that a coincidence??

    • @SuperSonicBlur
      @SuperSonicBlur 7 ปีที่แล้ว +21

      John Violidakis and how 42/4 is 10.5...and 4 has 4 letters! it's all connected!

    • @KarachoBolzen
      @KarachoBolzen 7 ปีที่แล้ว +8

      Betcha when the magratheans built earth it was exactly 42m - there were just too many meteorite collisions happening since then :P

    • @anteconfig5391
      @anteconfig5391 7 ปีที่แล้ว +4

      @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.

    • @gabbyholloman9398
      @gabbyholloman9398 6 ปีที่แล้ว

      Exactly what I was thinking!

    • @tqnohe
      @tqnohe 5 ปีที่แล้ว

      John Violidakis
      It is not.

  • @dibbydoda7160
    @dibbydoda7160 7 ปีที่แล้ว +8

    I probably laughed more than I should have at 2:12 !

  • @cstiger4
    @cstiger4 3 ปีที่แล้ว

    Your enthusiasm is totally catching!

  • @qubolo
    @qubolo 7 ปีที่แล้ว

    Spectacular video man :D you are really creative!

  • @bentoth9555
    @bentoth9555 5 ปีที่แล้ว +19

    "Will cause friction which is, frankly, inconvenient for the maths." It's also inconvenient for the face that's scraping along the rock.

  • @octavioferreira2846
    @octavioferreira2846 5 ปีที่แล้ว +4

    I wish there was a love button because this is an absolutely awesome video. I loved it to bits.

  • @NFM1337
    @NFM1337 7 ปีที่แล้ว +1

    This takes me back. Did this during introductory theoretical physics back in the day. :)

  • @DaneBrooke
    @DaneBrooke 6 ปีที่แล้ว

    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.

    • @DaneBrooke
      @DaneBrooke 6 ปีที่แล้ว

      (Just noticed that sqrt(miles/kilometers) almost exactly = 54/42. Hm.)

  • @eskimoprime09
    @eskimoprime09 7 ปีที่แล้ว +9

    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?

    • @bryanreed742
      @bryanreed742 3 ปีที่แล้ว

      No, the peak is a couple thousand miles down. He was wrong at that point.

    • @roland9189
      @roland9189 3 ปีที่แล้ว +1

      @@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.

  • @dunkmania5155
    @dunkmania5155 2 ปีที่แล้ว +3

    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!"

  • @danteregianifreitas6461
    @danteregianifreitas6461 7 ปีที่แล้ว

    wow this vid was amazing! I've enjoyed every piece of maths and physics of it

  • @vanessathenavigator
    @vanessathenavigator 7 ปีที่แล้ว +1

    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.

    • @standupmaths
      @standupmaths  7 ปีที่แล้ว

      +Vanessa W I do that sometimes. But TH-cam is my home.

  • @nicnakpattywhack5784
    @nicnakpattywhack5784 4 ปีที่แล้ว +8

    "a apple"
    "oh, grow up!"

  • @weebitch1708
    @weebitch1708 7 ปีที่แล้ว +27

    How can i "fall" not through the middle of the earth? im always pulled to there? i would have to walk?

    • @weebitch1708
      @weebitch1708 7 ปีที่แล้ว +3

      or like using a sledge

    • @weebitch1708
      @weebitch1708 7 ปีที่แล้ว +2

      without friction

    • @arnoutkroeze4704
      @arnoutkroeze4704 7 ปีที่แล้ว +2

      +haskia jimmi Yes a sledge.

    • @henrikwilson
      @henrikwilson 7 ปีที่แล้ว +1

      +

    • @superdau
      @superdau 7 ปีที่แล้ว +2

      Same way as planets or comets don't have to fall into the sun. Have a little sideways speed and you'll miss the center.

  • @michaelibrahim9275
    @michaelibrahim9275 4 ปีที่แล้ว +1

    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)

  • @N3bu14Gr4y
    @N3bu14Gr4y 5 ปีที่แล้ว

    That was actually a well-put-together demonstration... Taking it apart was another story!

  • @ibonitog
    @ibonitog 7 ปีที่แล้ว +5

    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.

    • @oberdiah9064
      @oberdiah9064 7 ปีที่แล้ว +5

      Completely agree. Would also support him on patreon :P

    • @standupmaths
      @standupmaths  7 ปีที่แล้ว +1

      +Benedikt Geiben Thanks! I'm now convinced I should set up a Patreon. Would be nice to have the stability to keep making videos.

    • @ibonitog
      @ibonitog 7 ปีที่แล้ว

      Great, really looking forward to it!

  • @lilweez2175
    @lilweez2175 7 ปีที่แล้ว +6

    2:07 I like that a lot...................

  • @LoomisPowderdogs
    @LoomisPowderdogs 7 ปีที่แล้ว

    instant sub after the leapyear episode. love being precise

  • @markmorton2519
    @markmorton2519 7 ปีที่แล้ว

    Blew my mind. Thank you!

  • @Lavaloid
    @Lavaloid 7 ปีที่แล้ว +6

    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.

    • @XxJ0nas98xX
      @XxJ0nas98xX 7 ปีที่แล้ว

      I have HD available, so it apparently becomes available fast

    • @standupmaths
      @standupmaths  7 ปีที่แล้ว +2

      +Lavaloid the Human You were so early you had the first comment!

    • @Solitaan
      @Solitaan 7 ปีที่แล้ว

      How slow is your internet? Mine is 0.65 mbps, max.

  • @rchandraonline
    @rchandraonline 7 ปีที่แล้ว +9

    Another Parker Square: drawing on the inside of an apple with a Sharpie.

  • @bryansutphen1884
    @bryansutphen1884 4 ปีที่แล้ว

    This is FANTASTIC!!

  • @joefisher3950
    @joefisher3950 5 ปีที่แล้ว

    Thats actually really cool!

  • @rednax3788
    @rednax3788 7 ปีที่แล้ว +169

    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

    • @michaels4340
      @michaels4340 7 ปีที่แล้ว +14

      Very cool! Of course, here in America that happened back in April :p
      I wish I'd known!

    • @cupass6179
      @cupass6179 7 ปีที่แล้ว +1

      Gawsome technically that's the time and date

    • @gamingwithgabe6156
      @gamingwithgabe6156 5 ปีที่แล้ว

      @@michaels4340 in Britain they use the weird format: dd/mm/yy, so they have a completely different date for it

    • @goddamnmaddog2024
      @goddamnmaddog2024 5 ปีที่แล้ว +4

      ​@@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

    • @michaels4340
      @michaels4340 5 ปีที่แล้ว

      @@gamingwithgabe6156 Yes, I'm aware!

  • @steenbruggen9445
    @steenbruggen9445 7 ปีที่แล้ว +52

    "Oh grow up!"

  • @AndrewBennettScience
    @AndrewBennettScience 6 ปีที่แล้ว +1

    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).

  • @eawesomest
    @eawesomest 6 ปีที่แล้ว

    One of the best videos ever

  • @jondoolio
    @jondoolio 7 ปีที่แล้ว +251

    You know when you've grown up is when you realize the dirty joke after he says "grow up"

    • @santoriomaker69
      @santoriomaker69 6 ปีที่แล้ว +11

      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

    • @Hextator
      @Hextator 6 ปีที่แล้ว +5

      Scared me when I heard him say that because he caught me at the height of my shame

    • @draevonmay7704
      @draevonmay7704 5 ปีที่แล้ว +13

      I’ve gotta be honest. I’ve got a mildly perverted mind. My only thought at though moment was “Jesus, we understand oscillations, get to the point.”

    • @throkir1
      @throkir1 5 ปีที่แล้ว +6

      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

    • @kindpotato
      @kindpotato 5 ปีที่แล้ว +6

      I guess I'm not grown up because before he even put the apple together I was anticipating it.

  • @camerongray7767
    @camerongray7767 5 ปีที่แล้ว +2

    Not even kidding my eyes started watering when he cut the onion 😮

  • @volbla
    @volbla 7 ปีที่แล้ว +1

    This prompted me to _finally_ look up the shell theorem. I've been wondering how to prove that literally for years, but i've never found it before because... well, maybe i just didn't look hard enough.

  • @skibalovesya
    @skibalovesya 6 ปีที่แล้ว

    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).

  • @JROwensPhotos
    @JROwensPhotos 7 ปีที่แล้ว +61

    8:00 Lost me at 'density of the Earth doesn't change', especially after all that earlier mention of the core.

    • @jlittlenz
      @jlittlenz 7 ปีที่แล้ว +16

      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.

    • @WJS774
      @WJS774 3 ปีที่แล้ว +1

      @@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.

    • @alidurrani4645
      @alidurrani4645 3 ปีที่แล้ว

      @@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

    • @alidurrani4645
      @alidurrani4645 3 ปีที่แล้ว

      where r is the instantaneous position reference to the center of the earth

    • @WJS774
      @WJS774 3 ปีที่แล้ว

      @@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.

  • @sirpikapika1129
    @sirpikapika1129 2 ปีที่แล้ว +3

    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?

    • @Sheph100
      @Sheph100 2 ปีที่แล้ว +1

      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.

  • @deemotion
    @deemotion 6 ปีที่แล้ว

    It's awesome ! I'll to cry ....Thank so much

  • @meggylee8078
    @meggylee8078 2 ปีที่แล้ว

    This answers a question that was on my 1st year mechanics exam!

  • @JeffBourke
    @JeffBourke 3 ปีที่แล้ว +4

    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.

  • @eskimoprime09
    @eskimoprime09 7 ปีที่แล้ว +15

    So, it would take me 42 mins to fall to me neighbors house? What would that even be like?

    • @andyli1890
      @andyli1890 7 ปีที่แล้ว +6

      Mitchell if your neighbour lives on the other side of the world, I don't think he is your neighbour

    • @S7evieRay
      @S7evieRay 7 ปีที่แล้ว +3

      If there was no friction and a direct path then yes

    • @jasondahlen9555
      @jasondahlen9555 7 ปีที่แล้ว +5

      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.

    • @sage5296
      @sage5296 7 ปีที่แล้ว +2

      Mitchell think frictionless skateboard over a flat area. The force is not quite perpendicular

    • @octavioferreira2846
      @octavioferreira2846 5 ปีที่แล้ว +3

      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.

  • @thomashughes4859
    @thomashughes4859 4 ปีที่แล้ว

    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!

  • @toniburon3162
    @toniburon3162 7 ปีที่แล้ว

    Your videos are amazing! Couldn't laugh more!!

  • @livintolearn7053
    @livintolearn7053 7 ปีที่แล้ว +2

    "is someone cutting onions in here?"
    hahahaha

  • @nicktalati4211
    @nicktalati4211 7 ปีที่แล้ว +28

    This was great but I still don't understand how you put a hole in that apple so fast.

  • @ericsbuds
    @ericsbuds 3 ปีที่แล้ว

    yes! i am a little mad i only came across this 4 years late. i have thought about this many times over the years. thanks Matt!

  • @centurysword
    @centurysword 5 ปีที่แล้ว

    thank you matt, i am working on a physics problem about this right now

  • @alexanderreusens7633
    @alexanderreusens7633 6 ปีที่แล้ว +7

    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!

  • @miles2419
    @miles2419 7 ปีที่แล้ว +14

    "It's very hard to draw on an onion."
    Ah, yes. The kind of quality information I came here to learn.

  • @brycepemble7547
    @brycepemble7547 3 ปีที่แล้ว

    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.

  • @chrislivepiano9306
    @chrislivepiano9306 7 ปีที่แล้ว +1

    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!!

  • @cibrinyark339
    @cibrinyark339 7 ปีที่แล้ว +11

    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?

    • @Kahitar
      @Kahitar 7 ปีที่แล้ว +11

      I think you would not be falling at all. You could actually just walk through that hole ;D

    • @shootingblueyes
      @shootingblueyes 7 ปีที่แล้ว +3

      All of these measurements are assuming that you're falling directly through the center of the tube with no friction.

    • @georgefowler6120
      @georgefowler6120 7 ปีที่แล้ว +3

      It would also require some sort of friction-less rail system, yes. I thought of this too.

    • @freshrockpapa-e7799
      @freshrockpapa-e7799 7 ปีที่แล้ว +1

      Not the gravity of the center, but the coriolis effect.

    • @steelman1506
      @steelman1506 6 ปีที่แล้ว +2

      Caleb Brinyark If the walls are lined with Teflon and you were covered in butter you'll be fine sliding along the side

  • @adammullarkey4996
    @adammullarkey4996 4 ปีที่แล้ว +5

    "Journey to the centre of the onion," the far less exciting sequel.

  • @otakutom17
    @otakutom17 7 ปีที่แล้ว +2

    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!"

  • @davidm.johnston8994
    @davidm.johnston8994 7 ปีที่แล้ว

    Great video!

  • @Mixa_Lv
    @Mixa_Lv 7 ปีที่แล้ว +3

    If the hole was filled with air, how would the air pressure be in different sections of it? Is it the strongest or weakest in the middle since that's the zero gravity point?

    • @Rackergen
      @Rackergen 7 ปีที่แล้ว +9

      Strongest, because you have a giant planet / air column pushing on you.

    • @unvergebeneid
      @unvergebeneid 7 ปีที่แล้ว +4

      At the center of the Earth, gravity is lowest and pressure is highest.

    • @youngbloodbear9662
      @youngbloodbear9662 7 ปีที่แล้ว

      +Penny Lane gravity is highest, pressure is highest, gravitational acceleration is lowest, for a singularity, and second lowest to anything with volume, considering the edges of the universe

    • @unvergebeneid
      @unvergebeneid 7 ปีที่แล้ว

      Tim T. Well true, one should distinguish gravitational field strength and its gradient. The latter is zero, the former at its maximum.

  • @adarshtiwari6374
    @adarshtiwari6374 7 ปีที่แล้ว +4

    by making that hole, would nt it decrease the mass of earth

    • @brokenwave6125
      @brokenwave6125 4 ปีที่แล้ว

      Not unless the mined material was being lauched off the planet...

  • @abstractapproach634
    @abstractapproach634 7 ปีที่แล้ว

    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

  • @iAMGorman
    @iAMGorman 7 ปีที่แล้ว

    I always wondered how long the fall was in 'Total Recall'! And now I know!

  • @philadams9254
    @philadams9254 7 ปีที่แล้ว +6

    The answer to everything is 42!

  • @deeelmore4560
    @deeelmore4560 6 ปีที่แล้ว +4

    "The reason I'm using [the onion]... it's made of concentric spheres."
    Yeah, onions have layers. Like ogres.

  • @frankburgum4478
    @frankburgum4478 3 ปีที่แล้ว

    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 ...

  • @kunjupulla
    @kunjupulla 4 ปีที่แล้ว +4

    00:13 Matt: "a apple"
    Me thinking: "Were my kindergarten books wrong?!"

  • @jpaugh64
    @jpaugh64 7 ปีที่แล้ว +6

    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

    • @asneakychicken322
      @asneakychicken322 6 ปีที่แล้ว

      jpaugh64 only if the Earth orbited at the surface level of the Sun

    • @FlyingDominion
      @FlyingDominion 6 ปีที่แล้ว

      The time would change based on the sun's density.

    • @corneliuscorcoran9900
      @corneliuscorcoran9900 5 ปีที่แล้ว

      I really hope it doesn't...just sayin'

  • @kimgosseye8588
    @kimgosseye8588 4 ปีที่แล้ว

    this one is GREAT!

  • @CaioMGA
    @CaioMGA 7 ปีที่แล้ว

    this videos are so entertaining

  • @JoeyPsych
    @JoeyPsych 7 ปีที่แล้ว +9

    I didn't even think about it untill he said: oh grow up.

  • @TheDeffend
    @TheDeffend 7 ปีที่แล้ว +34

    So basically what you're saying at 4:04 is that onions are like ogres?

    • @shorterneilisbored7078
      @shorterneilisbored7078 7 ปีที่แล้ว +1

      someBODY once told me the world was a gummy so I took a bite out of a tree.

    • @KVBA
      @KVBA 5 ปีที่แล้ว +3

      ONIONS. HAVE. LAYERS.

    • @alistairferguson6590
      @alistairferguson6590 4 ปีที่แล้ว

      Shrek is love. Shrek is life.

    • @newcantinacrispychickentac7754
      @newcantinacrispychickentac7754 4 ปีที่แล้ว

      @@shorterneilisbored7078 it tasted kind of funny so spit it at a bunny that started cursing at me

  • @kimba381
    @kimba381 8 หลายเดือนก่อน

    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!

  • @gnothisauton2116
    @gnothisauton2116 6 หลายเดือนก่อน

    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.

  • @simonhallin8909
    @simonhallin8909 4 ปีที่แล้ว +4

    Matt: "Assuming there's no air resistance"
    Me: High-School Physics all over again