Matt & Hugh: the mystery of two balls in a can

Dr Hugh Hunt is a Reader in Engineering at the University of Cambridge and a Fellow of Trinity College.
www.hughhunt.co.uk/
Watch Hugh and I calculate how fast a motorbike can go on a wall of death.
• Postcards from backsta...
CORRECTIONS:
So far, none yet! Let me know if you spot anything.
[And yes: I know the audio is not great. Sorry. Hugh's mic had a load of interference and then died. Better sound next time!]
Thanks to my fine Patreon supporters for making this possible! Here is a random selection of five of them:
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Polly Hammond
Joshua Freihaut
Doug Jones
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/ standupmaths
Music by Howard Carter
Filming and editing by Trunkman Productions
Design by Simon Wright
MATT PARKER: Stand-up Mathematician
Website: standupmaths.com/
Book: makeanddo4D.com/
Maths toys: mathsgear.co.uk/

[@Qermaq]

Ah, it’s that “two balls one cup” video I’ve heard so much about.

[@skyepyro7104]

3:25 "It's gonna move in a moment." I love how you can see how proud Matt is of that joke, and then watch him quickly die inside as it completely fails to land. Classic Parker humour.

[@stylis666]

hahaha You're so mean! smaller than three

[@MegaFPVFlyer]

I know that feeling all too well. It hurts, man.

[@mooncowtube]

Payback at 8:09

[@DesignedbyWill2084]

Just keep throwing them out until one sticks.

[@verward]

wow. I was trying to procrastinate from studying for my mechanics test tomorrow by watching this video, guess that didn't work out.

[@TheMrCarnification]

Ward Huyskes and I was procrastinating for my test next week

[@MrCmon113]

Procrastinating is involuntary.

[@lislehill3198]

I was trying to procrastinate from my mechanics hw... maybe the class is the problem

[@TheBluMeeny]

"They really R"

[@CarnelianUK]

Scale it up! 3 bowling balls and a bucket!

[@SergeofBIBEK]

I was literally planning to do this.

[@the_original_Bilb_Ono]

I think friction will over come the torque at some point. But I'm not sure.

[@nemesisurvivorleon]

A grain silo and three of those boulders from that famous indiana jones scene

[@abijo5052]

I loved Matt’s face of pure fascination when he started to see how the maths was coming together to show the experiment

[@PhilippeAllardRousse]

Parker Sound

[@paaaaaaaaq]

Next time Parker should have enough mics to salvage the video.

[@TrunkmanProductions]

Hugh's mic died on this one. Sorry about that.

[@unvergebeneid]

The background music in the beginning doesn't help either though, does it? *Edit:* which is then replaced by horrible tin and marker background noises and Matt occasionally shouting into his mic. Nah sorry, knowing these guys, there will be a second episode on the same topic anyway. I'll watch that and keep my ears and sanity.

[@emilchandran546]

Penny Lane yeah take your precious ears off to another video mate. Or get them tested because it wasn't that bad you might have a problem. Sorry you definitely have problems, first world problems, but I was referring specifically to your hearing.

[@unvergebeneid]

Emil Chandran, had a bad day?

[@Ultracity6060]

This trick could be improved by leaving it on a counter somewhere for a curious roommate to find. Also, finding a way to get something like confetti in the can. Or spiders.

[@cillianwilliamson16]

Take it easy satin

[@gimli3370]

or confetti spiders

[@uiomancannot7931]

Or you could put razorblades on it and get away with the perfect murder.

[@SchiwiM]

definitely spiders

[@error.418]

satin is a nice material, +cillian williamson, pretty sure you meant satan

[@SQuark]

2:29 "What's going on there, engineer?" is a catchy question. It should be said after every experiment.

[@thulyblu5486]

Should have named it "2 balls, 1 cup"

[@SeanByramTheOneAndOnly]

Would probably get demonetized, lol.

[@DEADB33F]

Will probably get demonetized anyway the way youtube is going.

[@JeanMichelRuiz]

man this was my first reaction too ! is it serious doctor ?

[@enricoalessio5434]

he did 10:01

[@gorillaau]

They probably thought about it but later canned the idea.

[@skepticmoderate5790]

"One metric ball's weight." A Parker unit.

[@asailijhijr]

A Parker unit (™)

[@MaicahRu]

4:39 One metric ball XD I also like how Hugh seems to miss Matt's sense of humour

[@AlexHoratio]

I'm on half-term break from learning Mechanics M2 and this gave me a proper flashback

[@ZonkoKongo]

Asked a friend if he wanted to work out with me after school. He didn't expect that.

[@gojoubabee]

One of these days you should post a video where you play with a math toy and when it gets to the “working out” part it just shows Matt and Hugh on ellipticals.

[@confucheese]

What’s up with this Parker Audio™

[@SPFLDAngler]

Its called read the fkn description for once in your lives.

[@TheArezmendi]

"I've got balls"

[@MisterAppleEsq]

It took balls to say that.

[@Spu7Nix]

Rip sound

[@SydneyApplebaum]

loving the Matt and Hugh show!

[@D33r_Hunt3r_]

1:38 His ability to draw a perfect rectangle is upsetting to me as an engineering student. HOW!!!

[@JoshuaDavidBrown-Jaded423]

I love your videos Matt. Always making a fun subject even better!

[@tijnhollanders6932]

The r's are going to cancel out. - Oh they are!

[@cheaterman49]

The math on this is simply amazing, I didn't get it all to be honest! Congratulations to both of you for the video and special thanks to Dr Hunt for coming up with this :-)

[@sajrra]

Thank you Matt for making those videos. And also thank you for honouring your patreons by mentioning them in the VideoDescription. Like you mentioned me this time :)

[@abelsz4407]

'All the Rs are gonna go.' 'They really R.' *that look*

[@SchutzmarkeGMBH]

For the purists: Cup of diameter D, Balls of radius R with 2R

[@PDG200]

What’s W and mg

[@UnreasonableSteve]

@@PDG200 W is the minimum weight of the ball on top of the can and the can necessary to prevent the can from tipping. m is the mass of each of the two inner balls and g is acceleration due to gravity

[@Sothiamient]

I am so happy you guys continued using that intro XD

[@jamiethemagpie]

Matt & Hugh Play with a thing and then do some working out is my favourite series on KZbin

[@tomgeorge3726]

Another great video guys, takes me back to Applied Mechanics and Structures in UNI.

[@AndrewKay]

Oh, I love this Matt and Hugh Play With A Thing And Then Hugh Does Some Working Out series.

[@TheKingtijger]

Awesome video, just learned about static equilibrium as a first year physics (and maths) student. :) keep it up

[@MATHSOLVESZONE]

Incredible, fabulous and awesome!!!!!

[@sickboi11111]

A fantastic and rare example of physical intuition!

[@andresfernando3342]

please do more maths using real maths like this is so good

[@trucid2]

Good example of how to draw Parker circles.

[@fizixx]

Will be trying this out!!

[@affablegiraffable]

Even the intro is amazing

[@qazedctgb19]

"Lets have a look at your thing." "I have balls"

[@uncommonsense360]

Literally just took a statics test on stuff like this today, and I thought I would watch this to relax. It backfired.

[@yorktown99]

It's difficult to explain why, but there is a rather delightful sense when Matt says "balls" in his Australian accent.

[@andresfernando3342]

this video is so good

[@PDettarso]

My favourite show

[@idjles]

1:30 They don't waste any time with the physical world and go straight to the maths!

[@MisterAppleEsq]

Boo, impure mathematics! Sorry.

[@frankharr9466]

Engineering and bath together at last! Who knew it could be so glorious!

[@ErikOosterwal]

This "2 balls, 1 cup" video is much better than that other video with two of something and 1 cup.

[@vladimircicmanec6103]

"All the Rs are gonna go" "They really R" "*sigh*" I LOL'd

[@johng7410]

8:11 "All the Rs are going to go." "They really R!" MAAAAAATTTTTTTTTT!

[@PeterCraig]

I was waiting for the “two balls, one cup” pun and was more satisfied with its delivery than I had expected.

[@deltav9784]

i love how complicated they make it XD

[@JonMW]

I thought at first it was due to the balls deforming the can - as two opposing sides are pushed out, those forces perpendicular to the can wall aren't going to be perfectly horizontal but now also include a vertical component, which might be enough to lift the can up. But that isn't really what was happening at all, and it was because I let my assumption colour what I thought I saw when the can was thrown off.

[@ankushmenat]

Never expected free body diagrams on this channel.

[@Demki]

3 balls, 2 guys, 1 cup.

[@ClownGathering]

"the tin will have its own moment" jesus Matt

[@Galileocrafter]

Three balls one cup.

[@janJasenwa]

1:39 My ears are bleeding!

[@haroldellis9721]

Love the opening line.

[@Tokahax]

I'm sitting here spilling just a bit of time before class, but now it's time to go STUDY STATICS!!!! Thanks for a horrible distraction from my studies...

[@HarvardHeinous]

But, but... isn't this exactly what they teach in Statics?!?

[@felpshehe]

Just awsome

[@daemonguy2]

A half more than you need

[@emperorpingusmathchannel5365]

TL;DW the two balls take 2/3 of the width with one of them inscribed below the initial ball. The weight of the ball on top balances the forces until its removed. That's because ball1 is taking 2/3 of the column of space while being supported by ball 2 which is suspended by the table which is greater than the constant curvature inscription support. When ball 3 is removed, ball 1's net force is the force of gravity unlike ball 2 which is the table, so the bottom 2/3 of the can rolls off the ball to meet the upper 2/3.

[@chinmaykulshreshthamawar640]

Interesting video. Just one point that i need to make. The video did not consider the weight of the can acting downwards along the same line as W while calculating moments about point O. So the weight of the can + weight of all will have to be greater than or equal to (2/3)*mg. Thus actual minimum weight required on top of the can will be ((2mg/3) - weight of the can). For a heavy can, this can also be zero. Please do keep making such amazing videos

[@TheStryper777]

2 balls, one cup. Loved it.

[@indjev99]

Btw for anyone wondering what the general formula is: W ≥ 2mg(1-p), where p is the ratio (2/3 in the video). Obviously if the three balls are the same then W = mg ≥ 2mg(1-p) (obviously). Also, try working out what happens with multiple balls in the can. It is really interesting. Then for n balls: W ≥ floor(n/2) * 2mg(1-p) This means that if we have another ball on top W = mg; mg ≥ floor(n/2) * 2mg(1-p) 1 ≥ floor(n/2) * 2(1-p) 1-p ≤ 1 / (2 * floor(n/2)) p ≥ 1 - 1 / (2 * floor(n/2)) So: 2: p ≥ 1/2 3: p ≥ 1/2 (p needs to be strictly greater than 1/2 to have the effect anyway) 4: p ≥ 3/4 5: p ≥ 3/4 6: p ≥ 5/6 7: p ≥ 5/6 8: p ≥ 7/8 9: p ≥ 7/8 10: p ≥ 9/10 And so on. This means that as the number of balls increases, so should their radii.

[@althaz]

That intro gets me every time :). lol.

[@aDifferentJT]

The 60 degrees is just a guess. Honestly Matt, one might even call it a Parker angle.

[@andykillsu]

Jonathan Tanner The 60 degrees is right for the size of the can they used for the math. They just never said until close to the end that the diameter of the cylinder was 3R.

[@aDifferentJT]

TheWioreks they said at the beginning that it looks like 2/3 but that was a guess.

[@twistedsim]

Its an hypothesis that the ball are 2/3 the size of the can,

[@andykillsu]

Jonathan Tanner They assumed that to be true in their derivation. If you don't like that then you will have to figure out how the angle changes with different cup sizes and replace the tan30 with it.

[@aDifferentJT]

Simon Bouchard a hypothesis should be proven, it’s an assumption and should be stated as such.

[@chrismclam9172]

I hit the like button so fast and so unconsciously that when i went to hit the like button at the end of the video it tiook me a second to figure out why it was already lit up. That is the true Parker effect.

[@MagisterMalleus]

Hooray! Another great episode of M&HPWATATDSWO

[@7markhunter]

That's a very interesting statics problem, what's more interesting is the dynamic physics at time equals zero when the system is allowed to accelerate.

[@MakeItWithJim]

Great to see an Engineer out-mathing a mathematician

[@bdnugget]

I'm totally gonna do this next time I play snooker with a friend. Even going to order a canned drink for it instead of beer.

[@DestroManiak]

the squeaky felt tip pen is kind of killing me lol

[@superjugy]

This was the perfect example of parker sound. XD

[@AlexKing-tg9hl]

I know elementary physics but have no idea what any of this math means

[@andykillsu]

#ParkerDiagram

[@wierdalien1]

TheWioreks parkerpost

[@andykillsu]

Alistair Shaw Nope

[@HarvardHeinous]

Matt and Hugh have a moment while playing with their balls.

[@RainingArtillery]

the last time two guys showed me 2 balls in a cup tricks I can't say I enjoyed it as much.

[@ghanshamchandel1854]

that title again is hilarious!

[@nickys11999]

matt its not a third more than you need it a half more than you need.

[@41-Haiku]

Half again is the final third. Context, I guess. *shrug*

[@EGarrett01]

1:38 In case you needed some nails across a chalkboard randomly in your life.

[@colinsmith6480]

well that video took me back to my advanced Applied Mathematics A level, over 30 years ago !

[@6infinity8]

- What do you have today? - I've got balls! 😂

[@mysteryman7877]

Just bring this to Penn & Teller: Fool Us

[@Morchlasse]

What ist with the sound... im given up

[@achu11th]

Lasse Mørch RIP Hugh’s Microphone. It died after a lot of interference.

[@fuglsnef]

A lot of the videos on this channel have terrible audio, it's a shame.

[@wierdalien1]

fuglsnef stop whining.

[@chemicalbrother5743]

It's a Parker Sound.

[@error.418]

He doesn't seem to use a stand-alone microphone. He mixes the audio from the camera.

[@BIWCTensia]

new name: Matt tries to talk over Hugh while Hugh explains what's happening

[@jumperluk6267]

341.592 subs? Damn such a Parkersquare of a channel!

[@QuiznosBear]

Haven't had a chance to watch this video yet. But it immedit reminded me of dice stacking. I'd be curious to see the maths behind that trick.

[@HeavyboxesDIYMaster]

This was really interesting stuff! I'm glad it was 2 balls and not 2 girls.

[@arrowed_sparrow1506]

I love that you're not a smarta$$, you're a smart jacka$$. :) I love this channel.

[@neilisbored2177]

Somehow this has a more suggestive name than "The three body problem".

[@karlkastor]

If I'm honest I didn't get much of that (the audio certainly didn't help). But you can quite easily rationalize this result: (I'm ignoring all the rotational stuff because of course I am) All the force acting on the can is coming from the top ball in the can. Some part of that force goes against the lowest ball. Some of that force pushes against the can and some of that is pushing against the ground. So the force acting on the can can't be more than the gravitational force acting on the ball. So one ball ontop of the can is enough! 2/3 is also enough because the second ball is at a 60° slope.

[@weckar]

Love the balls, but the marker squeak just tears through my skull

[@kingmikethe1st]

The banter between them when he is drawing the diagram really reminds me of Mr. Squiggle.

[@Danicker]

Matt: "yep, yep, okay, uhuh, ah yes, okay..."

[@NLF02]

haha. the sharpee sound again. Its disgusting. But I keep watching. I promise. :D

[@achu11th]

NutzLast i find the squeeking can more annoying, but I can definitely hear the pen way better now (unfortunately).

[@lucianodebenedictis6014]

argh i even get chills for every comment about it!

[@chrisborgars-smith2439]

it makes me nauseous

[@johnbouttell5827]

The Eric and Ernie of Maths

[@allendavis7635]

If there’s one thing my statics professor has drilled into my head, it’s to always draw a coordinate system with your free body diagrams

[@MisterAppleEsq]

It took a moment for me to understand that.

[@danielzandbergen8115]

lol when you said working out i was half expecting a gym workout

[@dhruvshaileshbhaipatel4233]

You really good mathematican

[@IllidanS4]

The title should have been "Two balls, one can."