Can you solve the banana puzzle?
Vložit
- čas přidán 22. 11. 2020
- Check out the Maths Inspiration shows here: mathsinspiration.com/
24 Nov: Visualizing Math(s)
04 Dec: Christmas Special
You should definitely watch Destin's SmarterEveryDay video:
Why Snatch Blocks are AWESOME (How Pulleys Work) • Why Snatch Blocks are ...
Thanks to Hugh for actually weighing the bananas.
www2.eng.cam.ac.uk/~hemh1/
The puzzle is a creation of Rob Eastaway.
robeastaway.com/
Support me on Patreon and I swear I'll not waste the money on a banana costume. I'll totally use the money to make more, serious maths videos.
/ standupmaths
You also get to watch me eat a banana. While dressed as a banana. / 44219338
CORRECTIONS
- None yet. Let me know if you spot any mistakes.
As always: thanks to Jane Street who support my channel. They're amazing.
www.janestreet.com/
Filming by Matt Parker
Editing by Alex Genn-Bash
Diagrams by Jennie Vallis
Music by Howard Carter
Design by Simon Wright and Adam Robinson
The Banana Who Feels: himself
MATT PARKER: Stand-up Mathematician
Website: standupmaths.com/
US book: www.penguinrandomhouse.com/bo...
UK book: mathsgear.co.uk/products/5b9f...
Nerdy maths toys: mathsgear.co.uk/
Fine. Here it is. Hugh's video.
• Hugh and the Pulleys
And the actual problem sheet from Hugh.
www.dropbox.com/s/f60srd6qny8... - Zábava
I used pounds for the mass unit and pounds for the currency. That way units cancel out and nothing has meaning anymore
Ahahaha, this is the best joke so far :D
AHahaha that's so good. Matt should have made that joke in the vid! :D
Also, if you look closely, there are actually two jokes in there. The first one is "I used pounds for the mass unit". That part is already totally ridiculous for obvious reasons...
@@flyingsquirrel3271 yes, he should have used slugs for the mass unit instead, haha!
@@OtakuNoShitpost Ah yes... but scales measure force not mass, making pounds more appropriate than either Kg or slugs.
I want to open a shop that sells products by price per newton of local gravitational acceleration. And to please the economists the prices will be stated as relative quantities of other products.
@@mytech6779 that was the joke, they called pounds a unit of mass
Honestly the Banana for Scale reference being 15 years old was the wildest thing I've heard in a few days
Yup. Made me feel ridiculously old.
He had us in the first half ngl
The meme peaked in popularity around 2014 according to know your meme. Albeit the meme originated in 2005
I have no idea what it was about
@@I_Echion ironically, know your meme probably also peaked in 2014
So the answer is “the shop scale isn’t calibrated correctly”.
This is exactly my problem with the puzzle. The setup is that you're in a shop weighing bananas, and you're asked how much you would pay for them, so it's natural to assume that whatever the scale is like it displays the correct weight and we're just figuring out how to turn that into cost. So I thought the point of the video would be "why do so many people get fooled into thinking it'd be 0.80?"
If it were presented without that context I'd be able to think about it more clearly, but as is I didn't even consider the setup of the scale until I got the answer so it feels like I was robbed of the puzzle
@@ericpeterson6520 I looked at the setup, and assumed the pulley and anchor were an accounted far part of the weight display. Plenty of grocers’ scales are anchored in some way so they don’t swing about wildly.
@@ericpeterson6520 I'm in a similar boat. It wasn't until Matt mentioned that it's on a pulley that I actually started paying attention to how the scale was set up and immediately had physics flashbacks and went "Oh, .80."
@@ericpeterson6520 yeah the setup screwed me! Although, tbh, I'd have gotten the wrong answer in isolation too XD
I give up. Its such a poor question so both answers are correct. I mean who's to say this is all occurring on Earth anyway?
I was thinking: "The scale says 1.6 so they'll cost 1.60£." without even considering the mechanism as a part of the puzzle. To me the puzzle was "The bananas weigh 1.6 kilos and cost 1£ per kilo. How much do they cost?"
That is exactly the puzzle, but the bananas never weighed 1.6 kilos.
Same. I only really understood the setup once it was shown in real life at 5:18.
If I saw that setup in the supermarket I'd assume that system is made for weighing and thus should be properly calibrated (if the force gauge has a force of 16N/1.6Kg the corresponding number on the face should read 0.8Kg not 1.6Kg) So I would obviously sue the supermarket for 1.6 gazillion funny-moneys
@@ALifeOfWine The scale might be calibrated to take into account the leverage of the pulley, but in general at a shop you have to pay what the scale tells you to pay, regardless of what the actual weight is.
This puzzle is unsolvable without assumptions on the scale, any reasonable person would assume that the scale was made to account for the factor of 2. This is a question of who trusted the teacher to not trick students and make them feel stupid, which I think is counter productive, especially for young students.
Matt sees a banana hat. He thinks to himself "how can I make that a business expense?".
Reminds me of this: czcams.com/video/xg8qDPGeFMU/video.html
@@JivanPal I don’t even have to click on that link to know it’s the Gus Johnson video
Love the “SnatchBlock” interruptions from SmarterEveryDay
SNATCK BLOCK!!
🤣🤣 Best part of the video!! 😁
SMASH BL0K!
Yeah the editor for a great job including those!
💯
Plot twist: The scale is calibrated taking into account the pulley system below. Bananas weigh 1,6kg
You know, like you'd expect in a shop.
If a real shop were to try this they would get sued for false advertising.
@@pickle5666 You mean the way it's presented in the problem?
You can't calibrate this scale for all weights because it always shows double the mass suspended from it
@@KurtisStell Just spread the numbers out twice as far.
"I can't remember the name of james grime's channel right now ;)" had me rollin. For those who don't know, it's "SingingBanana".
As soon as he mentioned James Grime I thought "Oh, is Matt.. err, The Banana that Feels... going to sing?"
yes i do wonder what that guy's banana channel is. Sorry, I mean singing channel. CZcams banana.
I was waiting for the James Grime reference the whole video lol
Same!
I too exist primarily on out-of-date references
YMMV
100th like
I know that feel bro
They are only out of date if you let others dictate your world.
It's peanut butter jelly time!
My first thoughts were: since the scale is used in a store in this specific way in order to weigh fruits, the scale would be calibrated to show the correct value. I should have known better, seeing this is a maths channel after all.
Yeah, or alternatively the store will use this scale to decide how much you pay so they're ripping you off.
I completely agree with you. You can look at it from the banana's point of view, but they don't usually have anything useful to say (barring Matt Parker dressed as a banana). From a storekeeper's point of view, putting up this scale would be a nightmare if not downright illegal. Unless you like dealing with complaining customers, you'd better calibrate the scale to display half the actual weight. Because the setup looks like an off-the-shelf solution, I would assume the calibration is 'correct' out of the box.
It actually annoys me that this is even a math(s) question, because the actual question is: can/should/would you expect a scale in a store to display the correct weight? Of which the answer obviously is: yes!
(spends several minutes looking for the test / cal sticker traceable to NIST to find out if it's calibrated separately or with the pulley setup lol )
This was exactly my thought, if this is how the scale works and is used, the measurement must be aligned to how it works.
@@EnderSword A kilogram is defined by taking the fixed numerical value of the Planck constant h to be 6.62607015×10−34 when expressed in the unit J⋅s, which is equal to kg⋅m2⋅s−1, where the metre and the second are defined in terms of c and ΔνCs
... or whatever your local grocer says a kilogram is.
3:53
This moment is when I found out that the horizontal line at the bottom of the image was meant to represent the ground and not a stick-shaped counterweight.
Me too. That start of this video needed an explanation not 'jokes'
I thought that too, i feel so silly now
Same but on the other hand.. it made the puzzle simpler in the head, but gave the same result.. the force must be the same...
I just realized that from your post. I found the attempted humor too annoying to make it that far.
This actually made me understand the problem intuitively. The situation is the same if instead of the ground there was a counterweight that weighed the same as the banana.
I solved it like that, without actually doing any maths:
Lets say we replace the attachment on the right with another identical set of bananas. The pulley will then act as a balanced scale and stay in place.
We are now weighing two sets of bananas, but from the point of view of the pulley nothing has changed, the rope sees the pull of bananas from the left and the same pull from the right.
Therefore, in both situations the scale will show double the weight.
I was thinking the same. The easiest way to understand what's happening is to replace the job that the attachment to the ground is doing with some bananas doing the same job.
Exactly what I was thinking. And I waited for them to show that, because it's much more intuitive, without needing equations and complicated explanations. So a bit dissapointed.
Although the banana jokes were so much fun, I don't care anymore :D
This is the best and most intuitive explanation given so far.
Yep. Or if you picture yourself holding the other end, you can see you have to pull down on it for the bananas to stay still. So the string is being pulled down on both sides
Except isn't that still doing math? You still have to convert 2 identical weights to determine the weight of 1.
as a wise professor once said: draw the free body diagram
Haha amen to that.
Only once? My professor says that approximately 3.5*10^5 times per hour
God, you gave me Statics flashbacks.
@@laurensverheij921 that is 1750000 diracs
Hugh Hunt was my lecturer and he said it all the time.
You know you should probably make mention that it's a pulley anchored to the ground before giving people time to solve the puzzle. It's not entirely obvious what's going on until that's made clear.
I spent an embarrassingly long time pausing the video and trying to work out how that wacky bar was remaining horizontal before I realised 😅
It doesn't actually matter whether the other end of the rope is anchored or just the perfect weight to balance the bananas - the key point is that the bananas are stationary.
Its pretty obvious to see the pulley is attached to a ceiling and a floor
Draw a stick person it that gap in a way that does not make it awkward...
Like, the ceiling is either real low or the dial is at a really awkward height.
Yeah, I really think more time should have been spent explaining the actual setup at the beginning - at first I thought the whole pulley thing was part of how the scales themselves work, and then I thought the thing at the other end of the pulley was a weight right up until he said "the bananas are the only thing with mass in this situation", at 3:18 in the video, long after the question had been posed and the bit where you're supposed to pause to come up with your answer. That was the first point when I considered £3.20 could even be a possible answer, although I then quickly realised that it probably doesn't really make a difference (to the scales) whether it's a weight or a fixed anchor (because of equal and opposite reactions and all that)
Did not expect Destin in this episode.
SNATCHBLOCK!
So the answer is "call whoever is responsible for regulating scales used in trade"?
So the real question is then "why is the scale not calibrated properly?" I feel like I'm back in school with bad textbook tasks that assume you hate what you're doing and have the quality to reinforce that sentiment.
Ah yes, the banana will be "berry upset." How pleased were you with yourself when you came up with that one, Matt?
Probably super pleased- showing off his obscure botanical knowledge!
Berry pleased.
I was about to complain about this joke because I thought bananas weren't berries. Are you telling me that bananas are berries? That's bananas!
@@DavidTriphon Bananas are berries, as are many other fruits we don't call berries, but ironically, strawberries aren't berries. Language is weird.
2 seconds after I saw that part, I rewinded the video to make sure he really made that joke. Oh, yes, he did.
The bananas would still cost $1.60 so the store could make more money.
You're assuming that people take the reading on the scale to be the weight of the bananas. I surely wouldn't.
Or maybe they're having a sale on bananas to clear out inventory and get more people to buy, thus increasing revenue, but the price is only deducted at checkout...
@@blindleader42 Well given that you're watching this video, you likely aren't like most people, who would simply say "Oh, I guess those bananas are 1.6kg."
@@duwb0 And those people would be correct, since scales in the real world are calibrated to give correct readings.
@@chriss1331 just a quick reminder that this a math/physic puzzle on a math channel and not a documentary about how scales actually work
I mean I just assumed it was some kind of weird scale and that it was calibrated to accurately show the forces involved, not that it was some kind of "Aha! gotcha!".
going into a grocery store i have to asume that their scale setup displays the right amount of mass, so the scale would be calibrated to show the right answer, regardless of the pulley setup
I personally assume the clerk will be Margaret Thatcher but that usually have not been the case in the last few banana buying attempts.
but in a supermarket scenario, why wouldn't the scale be recalibrated for the double force in the same way that it's been clearly calibrated for the acceleration due to gravity??
Exactly, its a poor question.
Just to add, he didn’t specify what planet the grocery store was on, did he? So sloppy ;-)
@@mikedelhoo As the Kg is a unit of mass, the scales would clearly be calibrated for the local gravity.
That's also true on Earth where precision is required. Electronic scales have to be calibrated for the location as the acceleration due to gravity varies according to latitude (plus some other minor factors). At the poles somebody will weigh about 0.4% more than at the equator.
I won a few dollars off my high school physics teacher with this. He kept insisting we were measuring mass, but it's just weight with a (hopefully) reliable spring constant.
@@TheEulerID That 0.4% is negligible at a grocery store.
Why did the banana go to the doctor?
- It wasn't peeling well!
My answer was "if the scale was designed to be used in that way, with a pulley, then obviously it's gonna be recalibrated to show the real weight and compensate for what the pulley is doing, so if it says 1.6kg then it's surely 1.6kg."
But it's a math/physics problem and presented as such.
@@Thunterise you cant handwave a wordproblems context away by going "but its a math problem".
These bananas are for sale. Therefore, in almost every western country, an error of 100% is going to get the store heavily fined. Seeking to avoid that, the scale is properly calibrated, reading half the actual weight.
In that case, not enough information. We have no information on the forces involved, only an arbitrary inaccurate mass. It could be literally any positive real.
My first instinct was that the scale would be calibrated to take any mechanical advantage into account. If it said 1.6kg...that it would actually be 1.6...because the scale would be designed to this purpose.
Another simple way to answer the puzzle, without building the system, is to change the system a little bit, to something equivalent.
Just hang the same amount of bananas on the right side, instead of hooking the string to the ground.
Why the same amount? to keep the bananas on the left side hanging with no movement like in the original system.
This way, the scale keep showing 1.6Kg, and now it's pretty obvious, the bananas on the left side weighs half of it.
That's the intuitive approach I've seen yet.
Yeah, but why is a loose bunch of bananas equivalent to being tied to the ground. Sure they don't move, but that's because the ground is effectively infinite weight. I'd be much happier with a tension diagram
@@ancientswordrage The ground might be infinite weight, but the ground doesn't just fall down and ruin the whole thing!
@@ancientswordrage The ground and the top of the scale are rigidly fixed relative to each other, so the ground can exert any amount of force on the bottom of the string. Since the bananas aren't moving, the force exerted by the ground must be exactly the amount that keeps the bananas in place - too much force and the bananas would accelerate upward; not enough, and they'd accelerate downward.
How much force is just right? The exact amount that would be supplied by having a second, identical, bunch of bananas instead of the ground.
*"How do the bananas feel"* - Matt Parker 2020
Most people: "How do the bananas peel?"
Matt Parker: "How do the bananas feel?"
The watch-face part of the pulley is just poorly calibrated
“Nothing here can curve at all, which, for me, feels very unnatural.” It’s all worth it for this single pun
While dressed as a banana he can't remember James Grimes' CZcams channel. Maybe if you sang it you might remember.
The setup doesn't matter; what matters is that the store should be setting up their scale and bananas in a way that what you see is accurate. If their scale's scale is not tuned, it's their fault if the reading is incorrect.
we're really not trying to apply this math problem to real-life grocery store situations ... it's just a physics problem that aids in understanding how pulleys work.
@@Jesse__H and a shitty one while at it, made worse by the cocainic verviage
@@Jesse__H The context of a grocery store overrided the context of a pulley when I heard the question, as it presumably did for everyone else who answered 1.6. Every gocery store scale I have ever seen was correctly tuned.
Banana who feels forgot about singing banana.... *Sad banana noises*
"Yes! We Have No Bananas"
You could call it... bananadrama
The simplest way to approach this:
Detach the string from the ground,
To the detached string, insert a weight, which would cancel up the rotation of the setup,
You are ending up with two banana weights pulling down on the weight.
Therefore, the scale would show up double the amount, so the bananas weight half of the value showed by the scale.
I don't think it could get any simpler than that.
Except that is assuming it's improperly calibrated. The division by two should be within the scale, if this is how it's designed to be used. This isn't a math puzzle at all, it's a test for how honest you think the shopkeeper is.
I'm just going to make a comment about 'one pound per kilo' as they are both units of weight when said aloud and go away again..
Under the right gravity field a 1 kilogram mass would have 1 pound of weight
lets go weigh again!
Pound as a unit of weight has connection to pound as a unit of currency. 1200 years ago Charlemagne wanted pounds (of money) to be equal to pounds (of weight). This is also why pounds use abbreviation of £ 'L' crossed or 'lb'---both for 'libra' = latin for scale or pound.
@@kwzieleniewski +
Pound per pound
While the problem solving here is technically correct, the problem is that it completely missed the obvious. In a common setting such as supermarket as presented, you would halve any value on the display to account for the ""double pulling"" effect, since you would not expect customers to know of this and to half it in their head. From a purely mathematical standpoint, its 0.8, but for a common, every-day scenario like presented, its 1.6
Indeed, this problem was ruined for me by being presented in the way Matt did here, as being found that way in a grocery store. It seemed tautologically obvious to me that whatever the scale reads is the weight of what it is measuring, and will take into account whatever tare and multiplier the setup has, as it's meant to be used by customers.
When Matt got to the part at 1:28 where he lists the percentages of people who gave each answer, I was terribly confused that £1.60 didn't get the vast majority (and also confused that it even deserved to be called a puzzle). Then it dawned on me that he was probably presenting the problem differently to us than it had been to the group of people who gave those answers.
Due to being presented this way, I didn't even try to figure out the intended pulley puzzle, until after the answer was already spoiled at 1:28 by having the highest percentage.
this mostly tells me that the scale is improperly calibrated for its installation
Great fun. Classic statics problem. The one issue is that if this were an engineered device in an actual store designed to measure the weight of fruit, the physical marks on the scale would be *calibrated* for the system that it set up to measure.
The banana getting annoyed at the work equation is comedy genius
Love that Arrested Development reference! I'm sure dozens of us caught it!
As an engineering student, I got stuck at the part where spring scales don't measure mass.
Yeah it seems to be measuring tension. I read your comment at the perfect time and didn't have to finish the video. Now I won't be late for work.
i got stuck @8:22 when he said not to use NM to mesure work, but Joules was ok. I was like, "but Matt, those are equivilent units"
Scales measure mass indirectly, though, because the acceleration due to gravity on the surface of Earth, the only place where these scales is likely to be used, is essentially constant.
Not directly, but given that it is deployed in a fixed location, calibrating it to use the force of gravity to measure mass is trivial.
Have you ever seen a scale that actually measures mass? They always measure force... They than just translate it to mass assuming earth gravity. If you use an earth scale on the moon, you would actually weigh less on the scales, eventhough you'd of course weigh the same.
To keep things simple, I just imagined replacing the other side with identical bunch of bananas. As far as the lower pulley is concerned this is indistinguishable from the force on both sides perspective. If 2 bunch of bananas weigh 1.6kg, each bunch should weigh 0.8kg.
so you assume the shopkeeper is a scammer? the spring scale's dial should be calibrated to take that into account already.
It would be so much easier to just replace the ground tether with another equally heavy set of bananas, both being equivalent in terms of tension.
Easier than that is to attach both ends to the same bunch of bananas (as demonstrated in this very video). No working out necessary, the value on the scale is the mass of the bananas.
Oooh, look at Mr Vanderbilt, can afford to buy two bunches of bananas to solve a physics experiment.
Yes. If you hide the right side and dont tell uf there are more bananas or attached to the ground, the left set of bananas wont feel the difference.
2:42 Thank you Mr Parker for giving me a greater appreciation for all the small but cool/fun things maths teachers do
Haven't watched to the end. I'd say that the scale reads twice the bananas' mass since we could replace the anchor with an identical set of bananas and the setup would remain the same.
Me thinking:
"Yes, yes, i understand it's a math problem, but are you telling me the store didn't zero their scale? I'm never shopping there again!"
The scale is correctly zeroed, that's why you can assume the pulley and rope to be massless. You would need to calibrate the scale to display only half the weight measured (yes, I know they actually measure the gravitational force)
Such chaotic Destin energy happening throughout this 😂
The practical demonstration made it MUCH clearer.
By the way, the most general version of the work = force×distance formula is that work is the line integral through the force vector field over some curve that the object is moving along. If the path is always in the same direction as the force, the line integral simplifies to a regular integral. And if the force is also constant along the path, the formula further simplifies to the given W = Force×Distance.
Everyone asks how the bananas peel, but no one ever asks how do the bananas feel.
I felt that
I pelt that
Intros are getting better and better.
They age not like fine bananas
It depends on if the pully is accounted for in the calibration of the scale. All kinds of scales have built in mechanical advantage between the load and the strain gauge.
Also depends on how crooked the shopkeeper is.
For some reason I thought that the bananas were counter-balanced by a sheet, so they're obviously half as much. Maybe if there were a couple of lines beneath the horizontal line, I would have realised it was a ground...
Nope.
Noob.
Yep.
Weeb.
Completely incorrect and blasphemous.
Physics is a real bother. I prefer complex bothers.
but Matt! if it's setup in a supermarket, it would need be calibrated to match trade regulations. there would need to be 1.6kg of bananas for it to read 1.6kg. otherwise it's illegal bananas. -watson
Perhaps the puzzle just left out the "scale to be used for estimation purposes only" sign
Yeas if we assume there are no law violation we prove that crimes don't exist.
Your videos are always funny and great, but this one was funnier than usual! Thanks for a good laugh!
As soon as i saw the pulleys i thought of Destin from SmarterEverdyDay, great job
Domesticated engineer implies wild and free engineers
seems to me that if the store scale says the bananas weight 1.6kg, they're gonna charge you for 1.6kg of bananas!
The indoor boomerang is really neat.
Went to a maths inspiration in 2015 and it was honestly such a great show, now currently completing my masters in mathematics
Wait, that's not a maths puzzle.
Well, he never said it was a math puzzle, it's just a puzzle.
It was a maths stand-up tho, so no false advertisement here
@@HomeofLawboy It's still cheating! It's like having a priest in full ornate* asking church visitors on a Sunday what happens after you die and then tells everyone they got it wrong because the answer is: your body will rot and the Earth will spin on.
*I'm entirely unsure if that expression works in English and if I haven't accidentally just made this priest into a magical battle priest warrior healer dude guy tank character in a video game from the early 2000's, making the correct answer kind of obvious instead of easy to overlook like I tried to imply. But I don't see many magic battle priests in churches these days, so my point still stands! I call bananigans!!
@@srikrishna_97 he did say "math puzzle", the very first time he said puzzle
Can we assume that the pulley's weight is compensated for? Because the standard scale would not...
I guess we can. I mean why the dial isn't calibrated to compensate for the setup we'll never know...
@@jcskyknight2222 Yep, we must, but this problem has all the trimmings of the classical setup of a head in the clouds teacher setting up a problem ignoring the pitfalls one encounters in real life.
@@HotelPapa100 Its made me so so mad. Unreasonably mad. I think £0.80 & £1.60 are both equally valid answers while £3.20 requires additional argument to be correct.
@@jcskyknight2222 Absolutely. There is no way anyone could have known the shopkeeper was trying to intentionally scam people. The odds of it working when you specifically are the customer buying bananas are insignificantly small and it should be assumed that the scale is calibrated and only has this setup to increase accuracy by a factor of two, still making the bananas cost 1.5 pound + or - 0.5, since the scale only shows half kilos, but whatever. I'd just offer a pound if they throw in 2 citrons and be done with this transaction.
The time's up thing really got me. 😂
I need more Banana that Feels.
oh. so that's grounding on the right?
i though this is just some kind of funny or not drawn properly weight which counterweighs bananas. and so i thought overall weight is 1.6 kilos and they're in balance therefore bananas have to weigh half of pulling weight
Really it's the same thing either way. Any force that a counterweight would exert on the rope, the ground has to exert on a the rope fixed to it.
Me too
Took me until Hugh's demonstration to understand that the metal platform on the right was supposed to be fixed to the ground. I thought it was balanced by the weight of the bananas the whole time, which didn't make any sense if it was weightless.
I found your closing pun very ap-peel-ing. So glad you managed to slip that one in.
I love the Destin cuts lol
MPMP false alarm :>
*Everyone asks how the bananas peel no one ever asks how do they feel.*
LMAO I cried!!!!
Haha same here
Those destin references are brilliant
I found it useful to think of the pulley as a lever with the load in the middle, hence 2x force multiplication.
This video is a-peeling.
...
I'll see myself out.
If they display it that way in the store, the must have calibrated the scale to show the correct mass, so it should still cost £1.60. Otherwise i would be a misleading scam.
Okay but you can just change the display of the scale to be the relative weight of something hanging on one side of the scale... granted that means the mechanism to turn the needle pointing to the correct value would have to move at half the rate, but that's easy to do with a simple gear system. I would assume anyone practically trying to weigh things would have calibrated the scale to work like this
Thinking of this this as a clock arithmetic problem, the dial could have gone past 2Kgs and then to 1.6Kgs so the actual weight on the pulley would be 3.6Kgs. Thus the weight of the bananas would be 1.8Kgs. More generally, the weight of the bananas is (1.6 + 2n) / 2 = 0.8 + n Kgs, where n=0,1,2...
What do you mean answering £1,60 means "they couldn't figure it out"? I mean, if that is how they measure weights in that store, then surely their prices are for the weights given by the measuring system.
Mass is independent from the measuring system.
The measuring system gives you 16N. The mass of the bananas stays at 0,8kg and the price is 1 pound per kg, not 1 pound per 10N.
(yes I rounded to g=10 m/s²)
@@baumundallesandere The numbers on the face of the scale will reflect the mass of the object in the pan under normal operating conditions. That's what calibration means. So if the scale reads 1.6 kg, and it is calibrated correctly, the bananas will mass 1.6 kg. The setup to this problem wasn't explained all that well. They added misleading context of a grocery store scale when what they actually wanted was precisely what will not happen with a grocery store scale.
But yes, when calibrating for a scale of this design, you would need the markings twice as far apart as for a scale without a pulley.
@@EebstertheGreat Ah right the scale says 1,6kg. Fair point.
Matt: Does a show with bananas
Also Matt: Can't remember Grimes' CZcams channel name
LOL!
That little Destin clip around 2:55 made me giggle, I immediately thought of that video when I saw the banana set up
I'm berry impressed in the casual use of that pun with bananas.
Well, assuming this contraption is used in a grocery shop it must comply with the Weights and Measures Act and be calibrated correctly. Therefore I have to assume the weight displayed (1.6kg) is correct, meaning the bananas cost £1.60. That's real world practical maths. So there.
"Assuming there are no unlawful activities we therefore prove that crimes don't exist and I'm very smart beliebe me"
Can I note that a good part of this is a nice little physics/engineering problem.
Knowledge of the tension forces and the "dynamics" of the banana scale like this are a good little intro to pullys and how they work. :)
Really neat to see it getting around the internet.
Thank you so much for uploading this video. It is helping me to get through the pandemic!
*_Suddenly Destin_*
Actually the banana puzzle was missing one important information: How is the scale callibrated? If I see an apparatus like this, I have to assume that the scale is properly callibrated so that it shows the correct weight within that apparatus. If the callibration is something that I can rely on, then the scale could show basically anything. In this case the scale is not properly callibrated, it is callibrated for a different usage. This makes the whole puzzle a little bit meaningless.
1.6: The scale says 1.6 kg, so it must be 1.6 pounds. Surely the store will have this calibrated proper in order to not confuse customers, right?
.8: Well, ackshually...
The way I would word it is that the banana + pulley + rope system is experiencing three forces 1) gravity of the banana downward, 2) the downward tension at the fixture by the ground on the rope, which is exactly equal to gravity on the banana, and 3) upwards tension on the whole thing, which is what the scale sees. 1) and 2) are balanced by 3), so the upwards tension = downward tension + banana gravity = 2 x banana gravity, so the scale reads double the banana's weight.
Here is alternative way to explain the result: Imagine instead of the string being anchored to the ground it is connected to a counterweight of equal mass to the bananas. Now it is pretty obvious that the total mass pulling down = mass of bananas + counterweight of equal weight = 2 x mass of the bananas. Next you only have to realize that in the equilibrium there is no difference (In forces, tension etc.) between anchoring to the ground or using a counterweight of equal mass. The same thought experiment can be applied to the more complicated setup by replacing the middle anchor with 2 bananas and the right anchor with 1 banana in a nice symmetrical fashion, everything is balanced out and the total force is equal that of 4 bananas.
I didn’t even realize until you started explaining it that the bananas were being weighed over a pulley with the other end fixed. It would have been helpful for that to be explained beforehand. I didn’t realize what the puzzle even was at first.
But why does this puzzle assume the meter to be calibrated improperly?
If the meter includes a pulley in its design, shouldn't that be taken into account in the design of the display?
You can't possibly expect every user to make that calculation on the spot while they're in the supermarket weighing bananas...
because the kinds of math "riddles" British people like are ones that make them feel smarter than everyone else, not ones that actually make sense
@@LieseFury love this answer.
They should clarify that one point is anchored
I didn't realise that was supposed to be the ground until you said so. Changed everything...
The question needs to be repeated during the "time to answer", I was barely paying attention the first time.
That isn't really a math or logic problem, it's a "why would a shop have an incorrect scale?" problem
There's no reason a shop would have an incorrect measurement on their scale- unless they were specifically trying to get people to overpay for less food. In which case, it's still going to cost you 1.60
Dude don't come to a math channel to complain about a puzzle being unrealistic... Obviously it's a made-up problem to teach us how pulleys work
@@PeterLostig-kx2hg I didn't come here to just to complain, nor am I complaining?
I like Matt's content, math is interesting, as are physics, programming, and science just in general. This comment was me pointing out that the problem with people not understanding isn't actually based on how pulleys work or the physics behind it, but rather that people will assume the shop would have calibrated a scale to account for such a mechanism, and if they DIDN'T, they'd still charge you for what the scale says, even if it's wrong.
People who post comments like this or any other variation of "the scale would just be calibrated bla bla" just failed at comprehending the problem. It's obvious what the problem is trying to do. The problem is; if using a scale calibrated for normal use and you add a pulley and attach the wire on one end to ground how does the scale reading change?
People who like this are so tiresome. You are not being clever you just conveyed that you didn't understand the problem.
I don't want to admit how hard I laughed at the "time's up" bit...
I flipped my laptop to get the classic pulley system, and then it was obvious. I was very excited to see it later in the video.
I'm a simple man. I see Matt Parker, I click. Also, did you ever end up finding a solution to the Parker Square?
Stand-up Maths : "can you solve..."
Everyone : *Ted-Ed flashbacks*
Lel
The invention of a scale for bananas is the best thing I've heard this year
I watched this when it came out, and I learned all about pulleys and forces years ago, but I only really understood it today: the mas of the banana is not the only mass involved. The floor/table/anchor has a huge mass, effectively infinite for all small objects. It acts like a wealthy person 'matching donations' of money for a charitable cause - up to a certain point (when the upper donation limit is reached, or when the mass is equal on both sides). In this analogy, mass is money and the inextensible string is the promise to match any donations - a 'donation of mass' if you like.