@@fardinahsan2069 Nah, you should understand that the USA choose to be hard to understand by others and that others shouldn't be blamed for that Imperial system does nothing but sets up for huge failures like : www.simscale.com/blog/2017/12/nasa-mars-climate-orbiter-metric/ (Yeah, en.wikipedia.org/wiki/English_Engineering_Units is actually an USA thing) Everyone is already basically speaking English for your sake, just use Internationnal units to be understandable, please
@@shadourow-bathory6965 1. This is a puzzle video, not making and deploying satellites, the US already uses metric in most scientific fields. 2. The units are irrelevant when solving the puzzle. 3. Its a damn puzzle, its not a commentary on which system is better.
@@fardinahsan2069 You are right. You don't need to know miles/inches/meters or you don't need to use numbers to solve this problem. Also numbers are just symbols like letters. A good mathematician knows that. How to solve then? Assume 4000miles = 2a and 1inch=2x and height of center=b So our Pythagoras theorem will be a^2+2ax+x^2=a^2+b^2 That gives: b^2=x^2+2ax We know 2a=4000miles, square root 2a= 20miles so b(height of center) is higher than 20miles. You can see it has expanded but can't touch.
99% of people fail to realize that metal can be compressed and there would be no change in all for the pedestrian. The rail ist just a little more stressed. The 1% of people are civil engineers ;)
I AM a civil engineer and I would say it is not "a little" more stressed. The stress induced by idiotic hyperstatic designs could be catastrophic. Avoid using hyperstatic designs unless you really know the consequences. A strain of 1/253440000, multiplied with young's modulus of steel at 210 GPa, results in 828.6 Pascals. If the section area equals 5 cm^2 then it's 0.4 Newtons of elastic force to fix its ends. Well this isn't much but realistic world is another story. The heat expansion rate of steel is around 1.2e-5 per celcius which is 3041.28 TIMES the strain in this question, on 1 celcius of temperature change! That's why those railroad tracks buckle. Without special designs and calculation those nuts won't hold such a drastic elastic force, and rails went free. The special designs known as seamless railroad tracks did it in such a way that elastic forces(horizontal) are loaded onto the fittings(nuts), and prevented buckling.
Well, to be technical, since the given conditions state that the rail expands in summer, then the person at the center of the bridge, and indeed any other person who knows of the given conditions, can confidently say the rail has expanded, whether touching it or not.
The use of the word "and" states they need to be able to touch as well as say yes or no. They can certainly say it has expanded with confidence as the rail is now missing (900+ feet in the air, but they can not touch it if standing on the bridge.. so the use of "and" is the determining facto to the no answer.
even if we assume that it is a triangle the person will be able to touch the center of the bridge bcoz whole bridge move upwards so he will also on the displaced center..........................so still he can touch the center
4000 miles, that's like Florida - Alaska New York - Berlin Tokyo - Hawaii Chicago - Houston :: 4 times If you consider curvature, it is barely noticeable.
No no, I want to see where on Earth you would build a bridge long enough to span virtually the entire flight distance from Anchorage, Alaska to Miami, Florida.
I failed because I erroneously assumed the handrail would be made of a material that required attachments to the bridge along its length to prevent sagging due to gravity. My bad
I think one or more people misplaced a decimal point while transmitting the problem. The bridge probably started at 40 miles, but ended up at 4000 miles.
The length of this bridge is not suppose to surprise you. This is a bridge from the LAND OF MATHEMATICAL RIDDLES. I leave there, believe me - It is a really BIG land!! (I put a copy in the public comments)
It's actually not an accurate answer, because handrail wil not have perfect angle at the center, it will curve, but for an aproximate measurement it's ok. Solved it. Good puzzle. Thx.
Another example of why I should never be given responsibility over anything big haha! Thanks for including the train track example at the end, I love it that you made the problem we're asked to consider make sense with a real life scenario. Hope you're having a lovely day Mr Logically Yours! 😊
This is assuming the pedestrian who is walking across a 4000 mile bridge isn't already a giant at least 1000 feet tall. Otherwise it really wouldn't be practical to have that long of a pedestrian bridge.
My City is in Germany, which is on Earth, there is Gravity here, Handrails are usually not that thick, i think thre might even be a NORM to it. A Handrail out of Metal, i think some kind of Steel would not be able to buckle up 900+ feet. It probably curves multiple times. It might very well be possible to touch the Center AND tell that it expanded. Wanna see that Metal that can hold its own weight over 2000 Miles without curving at all. You cant just take Metal and its property to expand under heat and silently exclude every other property.
Now please do a sequel that takes the curvature of the earth into account. Intuitively, it seems like the answer would be very different (the height change would be very small). Here's my thought process: For simplicity, assume that the earth is a perfect sphere and the bridge follows a great circle of the earth (not likely in reality, but let's say the bridge designers wanted to minimize its length). The bridge length of 4000 miles is an interesting hypothetical choice -- almost makes you think the puzzle designers intended the curvature to be considered -- because that's roughly the radius of the earth, which means the bridge subtends an angle of roughly 1 radian. So, if the handrail's ends are not held fixed (i.e., the whole thing is allowed to rise uniformly), adding one inch to its length means the radius of the handrail's arc increases by the same amount: it rises by one inch. So the question then becomes: how much different is it to hold the endpoints of the handrail fixed? Presumably it bulges into some sort of non-circular arc (elliptical, parabolic, catenary, whatever). At this point I'm beyond the limits of my ability to analyze this. I don't know which type of arc it would be, and I don't know how to calculate the arc height of any of them, but intuitively, the deviation from a true circle would be so small that it seems the height change would be close to negligible.
yeah, i would have failed this one about 4 ways. Curve of earth, compression of metal, assuming multidimensional expansions, what happens in winter with contraction, dL/L doesnt discriminate
The answer is YES because the handrail won't have expanded. This is because summer has only just arrived and so it has not been hot enough for long enough to cause any deformation.
Ok buuuut, if the bridge is 4,000miles long, and the earths circumference is 24,900 miles, that bridge would cover about 16% of the earths circumference. That means it would go through 57.6 degrees out of the 360 degrees if you look at a globe. Are we assuming that this bridge is always parallel to the ground, therefore curving with the surface of the planet, or is it straight and either end are out in space? Because if it curves along the with the surface of the planet, the handrail cannot be straight, it’s already curving but appears straight to the naked eye. Lmao I think I’m over thinking it, but this could drastically change the effect on the handrail.
@@applejuicefool69 If the bridge was flat and runs through a tunnel then the centre of the tunnel is going to be about 472 miles (760 km) underground (about 1/9 the way to the centre of the earth). At that depth there is a heck of a lot of heat - the temperature will be in excess of 1,900 K (1,600+ °C); good luck cooling it.
Triangles? Wrong. On earth, a 4000 mile bridge is curved around the shape of the earth, and an arc with 1 inch more length has 1/pi more radius. Could the pedestrian detect the handrail height changing by less than a third of an inch?
Not so sure...if one end of the bridge touches the earth the centre would be about 472 miles above the earth which is almost twice the height of the International Space Station which orbits at around 250 miles above the surface of the earth; obviously there would need to be a space station crossing installed on the bridge to ensure the safety of pedestrians walking on the bridge...
At 4,000 with the earth having a radius of nearly 4,000 miles, assuming the centre of the bridge touches the earth, the ends of the bridge will be about 472 miles above the earth. If the end of the bridge is on the earth, the centre of the bridge will be about 472 miles above the earth and it is unlikely than anyone would be walking on the centre to be able to attempt to hold any handrail. Alternatively, if the bridge follows the curvature of the earth, pythagoras no longer holds.
Mohammad, there are two problems with your solution: 1. The handrail would not form a triangle with a bend in the middle. If we assume ideal conditions, it would form a catenary arch. This doesn't change the answer much, though, since the height would still be ~9750 inches. 2. More critically, 4000 miles is nearly 1/6th of the Earth's circumference. Thus neither the bridge nor the pre-expansion rail would be a straight line; they'd both be curved. Hell, at that scale you can't even treat gravity as a uniform force; the direction of 'down' changes by 57.8 degrees between the ends of the bridge. Calculating what the curved base does to the problem is beyond me, but it would reduce the height of the midpoint by a *lot.* For instance: * Assume the Earth was smaller, such that its circumference was only 4000.01 miles. * This means the bridge starts at one support, goes all the way around the world, then reaches its other support only 50 feet short of where it started. * Now assume the handrail expands by 1 inch. * The handrail is close enough to a complete circle that we can approximate it as one. * The circumference of a circle is 2 pi times its radius. * Thus to increase the circumference of the railing by 1 inch, we need to increase its radius by 1/2pi inches. * However, the handrail-circle is fixed on one side, where the start and end of the bridge are, so the other side will have to rise by twice that. * Thus the handrail only lifts by 1/pi =~0.31 inches. That's large enough to be easily measurable if you know how high the railing is supposed to be, but too small to be immediately obvious. So, now we've got both an upper and lower bound on an approximation: if the bridge is straight, the height is ~9750 inches; if its a complete circle, ~0.31 inches. My guess would be that for the real scenario, where the bridge is ~1/6th of a circle, the railing would be high enough to be obvious, but not so high that a pedestrian can't touch it.
More realistic: 1km total length, 1cm expansion => well over 2 meters height. Crazy. Reminds me on: Rope around the earth, make it 1 meter longer -> its well above the ground (leave it 2 u to calc ;-) )
Why will the railing buckle up and not bend? 1 inch expansion in 4000 mile long railing and it buckles upward???. That thing would weigh millions of tonnes and it goes up? Lol. Nice logic
I can't believe this. Let's say the handrail is 1m above the surface. Besides the bending effect of his own weight... 4000 miles would mean with an earth circumference of +- 24,900 miles, the extra circumference of the handrail is +- 2*Pi*(4000/24900) = +-1m. So if the handrail is ONLY 1 inch extra, the handrail would very close to the ground. And of course, touchable. 🤷♂️
If the handrail expands it gets the curve and take an shape of parabola but not a triangular point ,practical example transmission lines expands in summer and takes an parobolic shape
This obviously simplified to determine the maximum change possible. More concerning is that the given answer is completely incorrect and no one seems to notice.
The bridge is so long that the handrail wouldn't be heated for every single mile. 4000 miles is like the length of the USA. It could be winter in NY and hot in the mid west.
you should not be using pythagoras theoroem for this, as the bridge has to curve by approx 9792563 feet, because the earth is not flat. (approx because you didnt tell us the height of the bridge )
IMO, Practically speaking the buckling won't be in triangle shape, it will be an arc where the bridge is like the chord of the arc. In case I am wrong can someone clarify why ?
You're right, but that doesn't change the answer; it would form a catenary arch with a height of 'merely' ~9750 inches. However, what does change the answer is that 4000 miles is nearly 1/6th of the Earth's circumference. Thus neither the bridge nor the pre-expansion rail would be a straight line; they'd both be curved. Hell, at that scale you can't even treat gravity as a uniform force; the direction of 'down' changes by 57.8 degrees between the ends of the bridge.
@@macdjord wow, thanks for providing a new perspective. This makes more sense and is as practical as it can get. And above all instead of just simply trying to solve a given problem its really important that we first reflect on the problem thoroughly. For the sake of puzzle the solution provided by Ammar is fine but from an engineering perspective its just impractical.
The answer is No. The curvature of the rails will not be significant. Edit: The rail will never form a triangle, that is not how expanding metal works.
Amazing and really unexpected answer! Until I checked the result in the calculator, I did not believe. Honestly, I thought to myself that the railing would be raised with a very tiny fraction of an inch. Simply amazing. Welcome back Ammar !! (edited: I checked the angle between the new railing and its original line: Well, only 0.00508979315 degrees !!)
I also calculated on calculator, got the same results. But still can't believe that an increase of half an inch in hypotenuse can increase height by 11257 inches. I couldn't figure it out yet but, there must be something missing.
I get the idea of the puzzle. But, it just says hold the center, not reach up and hold. So, barring any limiting criteria, there is no reason that with equipment a person couldn't make their way to the center of the hand rail and hold it. You could argue that if the summer heat buclked the rail that much it would make it to hot to feel the rail.
Hi Amaar, your videos are amazing! Probably late to comment, however, you made the assumption that the dent will be caused at the center, I think the dent will be caused near the extreme ends..
If it is possible to have a bridge 4,000 miles long (which is roughly the distance from San Diego, CA to Lima, Peru), then it seems equally likely that there might be a person who is tall enough to reach 938 feet in the air. So the answer to the riddle should be "yes, but the person must be a giant."
Here's what I did: (2000 mi+0.5 in)^2= (2000 mi)^2+x^2 (x is the height, the 938-foot value) but I imagined that happening to the entire bridge! In the version I accidentally tried, I would say yes to both.😢
OK Ammar, once again the concept is good but when applied to a bridge and you want to think logically then logically the handrail will sag and then when could tighten, to add to that it would have supports which would also expand which would effect your original trigonometry equation.
Obsolete? Today? You mean the imperial system was the norm in the past? It was the USA that invented the imperial system (like the Fahrenheit system and some others of that sort). Hence, they are the only country that uses them (because, let's face it, it is not a really good one, is it?). And some ex-colonies use it too in some contexts (cuz colonization).
@@neliaferreira9983 Ok, but can you give me some fact that imperial system is better than metrical system? Who pass at the metrical system never change mind
@@marcoferranti7132 Why do you ask me for an example that the imperial system is better than the metric? I am not of that opinion myself. I was just saying that your use of "obsolete" and "today" is incorrect because that implies that the imperial system has been the norm before, which it was not (except in a couple of countries out of the 200 hundred countries in the world). The US invented that system, so yes, of course they are the only ones that use it "today" (it is not "obsolete" because they still use it), but noone else in the world as ever agreed that it is a good system and hence no-one else uses it. Maybe you meant to say: "Imperial units are SCIENTIFICALLY IMPRACTICAL. Only the USA and others two countries use them EVER. Please use metric units." With which of course i agree. And millions of other people.
I imagined there was a road in the middle of the bridge, and that you were standing directly in the middle and thus at least 1 lane away from each of the handrails so you wouldn't be able to touch them. So I guess I was correct, even if not for the same reason given. No one would make a 4000-mile walking only bridge.
Pre-2016 I'd agree with you, but nowadays we just need to preface it with 'Trump is planning a bridge between his US golf course and his golf course in Scotland...'. Suddenly it sounds legit, still daft, but legit haha! 😁
That's why he said, "imagine that". These puzzles are to check and improve our problem solving skills. Most of the people start counting mistakes in puzzle when they are not able to solve it.
@@kuls43 Lol, when the problem is so out of sync with reality you'd have to take into consideration the curviture of the planet, it's not really unfair of the OP to point out the measurement being used may be an error. In other news, I just ordered my 4000 mile long handrail and Amazon predicts it will arrive on Tuesday...Wednesday...Thursday...Friday...Saturday...Sunday.... 😁
4,000 miles is just less than a quarter of the earth's circumference. I'm too lazy to figure out the puzzle with this information included... Can you, Ammar, or anyone do it for me?!? - Thank you!!! :) :) :) P.S. miles, inches, feet, blah, blah, blah! Use The Metric System!!! 1,000km bridge and 1cm expansion, for example.
given that the bridge is 16% of the way around the world, the answer would need to be calculated on an arc, not a straight line. And the handrail might be attached at more than the two ends.
agreed, and specifically a parabola that is nearly a perfect circle. and when comparing 2 circles 1 inch apart at a radius of 3958.8 and 3958.80001578, the length along a 4000 mile section increases by 1 inch. so thats the answer, 1 inch longer equals 1 inch taller in the center.
Nonsense. The handrail starts as an arc covering more than 57 degrees of bend. When it expands, it will not just kink in the middle, the whole arc will lift up by less than 1 part in 126720000 above its previous curvature position, which at the midpoint is only 0.025 inch.
That's a long ass bridge. That's basically the flight distance from Anchorage, Alaska to Miami, Florida. Ignoring the bridge for a moment, no handrail would be that long without being broken up into sections since it would need supports as it would sag otherwise.
The question isn’t whether a person can reach the hand rail. The actual question is whether once they touch the handrail can they tell if it expanded. So… the real answer.. and also my big brain answer is; if the rail is warm to the touch the rail must also have expanded.
4000 mile bridge with a handrail for pedestrians? Who is walking across a 4,000 mile bridge? For that matter, given most countries are less than 4000 miles from side to side, this is a humongous bridge and a humongous city. Russia has a length of 5600 miles, for instance. This is an impossible bridge to exist, and so it's not surprising the answer is impossible as well.
The length of this bridge is not suppose to surprise anyone. This is a bridge from the LAND OF MATHEMATICAL RIDDLES. I leave there, believe me - It is a really BIG land!! This bridge connect the city of IMAGINATION to the village of CURIOSITY. I cross this bridge every day in 5 minutes.
this is so wrong. 0ne inch over 4000 miles would not be noticed, and if anything it would go down ,not up the weight of the handrail alone would cause it to sag
Lmao I guessed the answer would be no since the effect of one inch on all 4 miles would be insignificant smh... My dumb ass thought that all of the handrail just expanded by one inch
WRONG. i was too lazy to solve it correctly. so obviously let down when you solved it the way i did. not only should you be calculating arc length, but 4000 miles is not a straight line either. my intuition leads me to believe not only that increasing by 1 inch wouldnt change much, but also that a 4000 mile handrail is way too short for a 4000 mile bridge if it is 3 feet off the ground. lets check. a 3 foot tall rail is 4000.00057 miles (3.03 feet longer) long on a 4000 mile bridge. if the rail were to grow by 1 inch, it would get 1 inch taller in the center. i think you are part of that 90% that fail this. well, and to be fair, so am i since i assumed using triangles woul be a close approximation too.
It could be straight, in which case it would be tangential to the earth where one end would be on the earth, the centre 462 miles above the earth and the other 1,659 miles above the earth (watch out for low flying ISS at 250 miles above the earth). At those heights the effect of the atmosphere and clouds on the weather will affect how hot the handrail gets...
In what way? Imperial clumps smaller units together into larger units in a very sensible way. If you have a field 22 yds (a chain) wide and 220 yards (a furrow long, or furlong) long a team of oxen could plough that in one day. A useful unit is the amount of land a team of oxen could plough: it's called an acre - something easy for a farmer to visualise.
@@neliaferreira9983 Just explaining that metric is easier when dealing with abstract things. The imperial system was built on physical objects and so quite easy to visualise for the non-educated, non-abstract thinkers of its day. 1 ft (12 inches) is the length of my foot - my foot *is* 0.3048 m long! The distance between my finger tips and elbow *is* near enough 0.4572m, or 18", or as it was known for hundreds of years: 1 cubit. Stick out my arm to the side and the distance from the fingertips to my nose *is* near enough 0.9144m (or 3 ft, 36 inches), or as it was known for hundreds of years: 1 yard. Stick out both my arms and the distance between the finger tips *is* near enough 1.8288m, or as it was known for hundreds of years, 1 fathom. The imperial system was based on measurements people carried about with them wherever they went. For example, ask someone back them how long a cricket pitch was and they could visualise it as the team of 11 men standing along its length with their arms stretched out just touching at the fingertips with the players are either end just touching the wicket (ie 22 yards, 11 fathoms). The metric system was based on a fraction of the distance between the north pole and somewhere along a line of longitude (ignoring the undulations caused by hills and valleys, using an average earth radius for it). Curiously, that was then used to measure the speed of light and was then redefined to be the distance light travels in a fraction of a second...rather a circular definition?
@@cigmorfil4101 Well, yes, ok, but when it comes to science and mathematics, why use imperial at all? Also, imperial doesn't deal with abstract. It's the opposite: it deals with concrete. Imperial uses everyday household items or circumstances to measure reality. Which is why it is not good for science.
My _city_ has a longest bridge of 4,000 miles??? The *entire* length of the contiguous USA isn't even 4,000 miles... wtf kind of hypothetical 'city' are we talking about here?
The oversight with this logic problem is that the example it uses. There are far too many pesky details that ruin this as a problem that can be solved in the way shown. ... The Earth's circumference is only 24, 901 miles (laterally at the equator; only 24,860 miles vertically)-- that bridge 4000 miles long would curve to match the curvature of the Earth, not be a straight line. (Perhaps it is a tunnel bridge that goes under the water and comes back up? The imagery suggests a suspension bridge though.) We can determine the straight line distance from fixed points A and B at the end of the 4000 mile bridge, based on the Earth's circumference. We can determine the radius of a smaller circle, where the same fixed distance between A and B when going around the circumference is 4000 miles plus 1 inch. We can then calculate the high point of the arches away from the straight line from A to B, to see how high the handrail raises. ... But that isn't the real issue. ... What is making the handrail go up into the air? Assuming the handrail is periodically attached to the bridge by vertical posts, the extra length would attempt to sag but then be pushed laterally by the posts holding it up. We would see a rail that might curve outward past the edge of the bridge, inward toward the pedestrian walkways of the bridge, or even both in a chaotic zig-zagging pattern. Now we are looking at some complex physics problems. What will the handrail do, based on the bridge's construction? Let's assume that the support posts holding up the handrail are rigid, and are a full 10 feet apart. This means that each section between the posts bows either inward or outward as it expands in the summer heat and seeks to sag due to gravity. There are 5280 feet in a mile, so we are looking at 528 gaps per mile post to post along the 4000 mile long bridge. That's 2,112,000 gaps -- with the extra inch of length divided equally among all of them. There is a 1/2,112,000th of an inch bow inward or outward, between each post as the pedestrian walks along. Safe to say, a pedestrian walking on this bridge would NOT notice an expansion difference of only 1 inch. They will not see it, and they will not feel it. ... The reality of course is that bridges are typically much smaller than 4000 miles, meaning A to B across the bridge is closer to a flat line. Also, a 4000 mile long metal handrail will expand in length much more than just 1 inch -- the exact degree it will expand depends on the metal used in its construction, which is again information we have not been given. The extreme values used in the puzzle made it impossible to solve logically. We had to make many faulty assumptions to arrive at the demonstrated answer, which is in fact not a real answer to the puzzle.
What this amazing metal is we don't know but that is irrelevant as we're given the required information regarding how it expands between the cold of winter and heat of summer: it expands 1 inch (0.0254 m) over a distance of 4,000 miles (6,437,376 m) over the temperature difference, whatever that is. What is more relevant is that if the bridge is flat, it will of necessity be tangential to the earth - if one end is on the earth the other will be about 1,659 miles (2,669,900 m) above the surface of the earth (the centre some 472 miles (759,610 m)). The ISS orbits at about 250 miles (402,336 m) above the surface of the earth.
@@oktopg well sorry sir no offense. I am not saying that Sir Pythagoras & Rushi Baudhayan didn't recognized this. Sir Goguo was first who invented this. And I believe that one who invented first; should get title for that!
@@ignore5147 while in the first place it is arguable whether one shouldn't consider this theorem being 'discovered' rather than 'invented', anyway no one can tell who really got to it first. It's highly likely that it got discovered independently by several people in the course of history. Maybe it should be called 'unknown humans' theorem' then 😂
Well my version has the person holding the rail in the cool of the morning when he is arrested by a cop who gets called away to the other end of the bridge and he doesnt have room in his Cushman to put this criminal (he was drunk and spitting off the bridge, infraction of municipal code of that area), so the cop handcuffed him to the rail ere he drove off. He waited all day, and at the end of the hottest part of the day he saw the cop far down below pulling back up. He spit on the cop as he held the rail. The cop shot him. The End.
@@rogerscottcathey That sounds like a problem fit for a SAW film...wake up to find yourself handcuffed in the middle of the 4000 mile bridge. Obviously there will be an electrical current going through the metal handrail. Which direction do you walk to find the key in time? How long will it take you? How many times will you be electrocuted because you let the metal of the handcuff touch the electrified rail? 😲
![Summer Walker - Heart Of A Woman [Official Lyric Video]](http://i.ytimg.com/vi/SFddctbZzw8/mqdefault.jpg)
[Cries in metric]
You should cry for being bad at math if metric or imperial units are worth crying over
@@fardinahsan2069 Nah, you should understand that the USA choose to be hard to understand by others and that others shouldn't be blamed for that
Imperial system does nothing but sets up for huge failures like :
www.simscale.com/blog/2017/12/nasa-mars-climate-orbiter-metric/
(Yeah, en.wikipedia.org/wiki/English_Engineering_Units is actually an USA thing)
Everyone is already basically speaking English for your sake, just use Internationnal units to be understandable, please
@@shadourow-bathory6965 1. This is a puzzle video, not making and deploying satellites, the US already uses metric in most scientific fields.
2. The units are irrelevant when solving the puzzle.
3. Its a damn puzzle, its not a commentary on which system is better.
@@fardinahsan2069 You are right. You don't need to know miles/inches/meters or you don't need to use numbers to solve this problem. Also numbers are just symbols like letters. A good mathematician knows that.
How to solve then?
Assume 4000miles = 2a and 1inch=2x and height of center=b
So our Pythagoras theorem will be a^2+2ax+x^2=a^2+b^2
That gives: b^2=x^2+2ax
We know 2a=4000miles, square root 2a= 20miles so b(height of center) is higher than 20miles.
You can see it has expanded but can't touch.
99% of people fail to realize that metal can be compressed and there would be no change in all for the pedestrian. The rail ist just a little more stressed. The 1% of people are civil engineers ;)
And the rest of us want to know where they got this metal that can have an unsupported span of 4000 miles!
civil engineers leave room for the metal to expand
@@GerarddeVries And uncivil engineers just let it buckle!
The deck will expand too, plus, the ends cannot be "fixed".
I AM a civil engineer and I would say it is not "a little" more stressed. The stress induced by idiotic hyperstatic designs could be catastrophic. Avoid using hyperstatic designs unless you really know the consequences.
A strain of 1/253440000, multiplied with young's modulus of steel at 210 GPa, results in 828.6 Pascals. If the section area equals 5 cm^2 then it's 0.4 Newtons of elastic force to fix its ends.
Well this isn't much but realistic world is another story. The heat expansion rate of steel is around 1.2e-5 per celcius which is 3041.28 TIMES the strain in this question, on 1 celcius of temperature change! That's why those railroad tracks buckle. Without special designs and calculation those nuts won't hold such a drastic elastic force, and rails went free.
The special designs known as seamless railroad tracks did it in such a way that elastic forces(horizontal) are loaded onto the fittings(nuts), and prevented buckling.
Well, to be technical, since the given conditions state that the rail expands in summer, then the person at the center of the bridge, and indeed any other person who knows of the given conditions, can confidently say the rail has expanded, whether touching it or not.
The puzzle doesn't say that the person holding the handrail has to be standing on the bridge.
The use of the word "and" states they need to be able to touch as well as say yes or no. They can certainly say it has expanded with confidence as the rail is now missing (900+ feet in the air, but they can not touch it if standing on the bridge.. so the use of "and" is the determining facto to the no answer.
90% people fail to realise that the handrails will expand to form a curve and not a perfect right angled triangle
Oh! That's damn true. Even I don't realise.
even if we assume that it is a triangle the person will be able to touch the center of the bridge bcoz whole bridge move upwards so he will also on the displaced center..........................so still he can touch the center
Bro I don't understand how handrials get expanded can u explain?
@@darshantl18 metal objects expand & shrink with rise & fall of temperature respectively
@@rainman2543 yeah bro I know for examples like railway track and Effile tower etc but I don't understand this concept with the bridge
But shouldnt you consider the curvature of the earth?
Nah it's flat! JK
PS. Fun fact: Actor, Neil Armstrong agreed to fake the moon landing but insisted it be filmed on location. NASA agreed. 😉
Lol
The handrail was built so that before the expansion it was equal height from the bridge all across its span.
It must be considered. This case, the handrail just lifts up a few inches. And the pedestrian can actually touch it and feel the difference.
4000 miles, that's like
Florida - Alaska
New York - Berlin
Tokyo - Hawaii
Chicago - Houston :: 4 times
If you consider curvature, it is barely noticeable.
I want to see the foundry where they produced a 4000 mile long rail and the logistics that brought that to the construction site...
And the city that's 4000 miles long.
It was brought in pieces and welded onsite.
No no, I want to see where on Earth you would build a bridge long enough to span virtually the entire flight distance from Anchorage, Alaska to Miami, Florida.
High speed rail is constructed with a piece of continuously welded rail. They deal with thermal expansion by pre-stressing the rails.
I failed because I erroneously assumed the handrail would be made of a material that required attachments to the bridge along its length to prevent sagging due to gravity. My bad
At least you 'failed' because you imagined it in a smart way; I failed just because I'm thick! 😁
The reason it's hard to imagine or believe is that the bridge has 4000 miles, which itself is beyond imagination
Interesting, but a ridiculous length to deal with. Even the distance from Berlin to New York City is less than 4000 miles.
I think one or more people misplaced a decimal point while transmitting the problem. The bridge probably started at 40 miles, but ended up at 4000 miles.
The length of this bridge is not suppose to surprise you.
This is a bridge from the LAND OF MATHEMATICAL RIDDLES.
I leave there, believe me - It is a really BIG land!! (I put a copy in the public comments)
@@stevethecatcouch6532 Yes, this riddle does work for a 40 mile bridge, since the center of the handrail would still be almost 94 ft above the bridge.
It's actually not an accurate answer, because handrail wil not have perfect angle at the center, it will curve, but for an aproximate measurement it's ok. Solved it. Good puzzle. Thx.
The pedestrian can touch to the centre, at night 😜😅
சிறப்பு
Yaaru pa nee. Enga irundhu da vandha 😂
But your logic is a bit creative bro 😝
@@aakaasha6123 😀
Another example of why I should never be given responsibility over anything big haha! Thanks for including the train track example at the end, I love it that you made the problem we're asked to consider make sense with a real life scenario. Hope you're having a lovely day Mr Logically Yours! 😊
This is assuming the pedestrian who is walking across a 4000 mile bridge isn't already a giant at least 1000 feet tall. Otherwise it really wouldn't be practical to have that long of a pedestrian bridge.
My City is in Germany, which is on Earth, there is Gravity here, Handrails are usually not that thick, i think thre might even be a NORM to it.
A Handrail out of Metal, i think some kind of Steel would not be able to buckle up 900+ feet. It probably curves multiple times.
It might very well be possible to touch the Center AND tell that it expanded.
Wanna see that Metal that can hold its own weight over 2000 Miles without curving at all.
You cant just take Metal and its property to expand under heat and silently exclude every other property.
Now please do a sequel that takes the curvature of the earth into account. Intuitively, it seems like the answer would be very different (the height change would be very small). Here's my thought process: For simplicity, assume that the earth is a perfect sphere and the bridge follows a great circle of the earth (not likely in reality, but let's say the bridge designers wanted to minimize its length). The bridge length of 4000 miles is an interesting hypothetical choice -- almost makes you think the puzzle designers intended the curvature to be considered -- because that's roughly the radius of the earth, which means the bridge subtends an angle of roughly 1 radian. So, if the handrail's ends are not held fixed (i.e., the whole thing is allowed to rise uniformly), adding one inch to its length means the radius of the handrail's arc increases by the same amount: it rises by one inch. So the question then becomes: how much different is it to hold the endpoints of the handrail fixed? Presumably it bulges into some sort of non-circular arc (elliptical, parabolic, catenary, whatever). At this point I'm beyond the limits of my ability to analyze this. I don't know which type of arc it would be, and I don't know how to calculate the arc height of any of them, but intuitively, the deviation from a true circle would be so small that it seems the height change would be close to negligible.
yeah, i would have failed this one about 4 ways. Curve of earth, compression of metal, assuming multidimensional expansions, what happens in winter with contraction, dL/L doesnt discriminate
The answer is YES because the handrail won't have expanded.
This is because summer has only just arrived and so it has not been hot enough for long enough to cause any deformation.
Ok buuuut, if the bridge is 4,000miles long, and the earths circumference is 24,900 miles, that bridge would cover about 16% of the earths circumference. That means it would go through 57.6 degrees out of the 360 degrees if you look at a globe. Are we assuming that this bridge is always parallel to the ground, therefore curving with the surface of the planet, or is it straight and either end are out in space? Because if it curves along the with the surface of the planet, the handrail cannot be straight, it’s already curving but appears straight to the naked eye. Lmao I think I’m over thinking it, but this could drastically change the effect on the handrail.
No, you are absolutely right.
Maybe they dug a tunnel for it.
@@applejuicefool69
If it's in a tunnel it won't experience the temperature changes required for the problem.
@@cigmorfil4101 maybe they vented the tunnel.
@@applejuicefool69
If the bridge was flat and runs through a tunnel then the centre of the tunnel is going to be about 472 miles (760 km) underground (about 1/9 the way to the centre of the earth). At that depth there is a heck of a lot of heat - the temperature will be in excess of 1,900 K (1,600+ °C); good luck cooling it.
Triangles? Wrong. On earth, a 4000 mile bridge is curved around the shape of the earth, and an arc with 1 inch more length has 1/pi more radius. Could the pedestrian detect the handrail height changing by less than a third of an inch?
This is assuming that the handrail is fixed at each end and that the bridge itself didn't expand also.
These are implied by the fourth condition in the riddle "when the handrail expands in summer, it buckles upward at its central point."
If a person were to hold the handrail, they would certainly be able to tell that it has expanded. They would be hanging from it.
Not so sure...if one end of the bridge touches the earth the centre would be about 472 miles above the earth which is almost twice the height of the International Space Station which orbits at around 250 miles above the surface of the earth; obviously there would need to be a space station crossing installed on the bridge to ensure the safety of pedestrians walking on the bridge...
How the hell is one inch taller making such a fuzz? It is not even inch per mile but just one puny inch in total.
At 4,000 with the earth having a radius of nearly 4,000 miles, assuming the centre of the bridge touches the earth, the ends of the bridge will be about 472 miles above the earth.
If the end of the bridge is on the earth, the centre of the bridge will be about 472 miles above the earth and it is unlikely than anyone would be walking on the centre to be able to attempt to hold any handrail.
Alternatively, if the bridge follows the curvature of the earth, pythagoras no longer holds.
Mohammad, there are two problems with your solution:
1. The handrail would not form a triangle with a bend in the middle. If we assume ideal conditions, it would form a catenary arch. This doesn't change the answer much, though, since the height would still be ~9750 inches.
2. More critically, 4000 miles is nearly 1/6th of the Earth's circumference. Thus neither the bridge nor the pre-expansion rail would be a straight line; they'd both be curved. Hell, at that scale you can't even treat gravity as a uniform force; the direction of 'down' changes by 57.8 degrees between the ends of the bridge.
Calculating what the curved base does to the problem is beyond me, but it would reduce the height of the midpoint by a *lot.* For instance:
* Assume the Earth was smaller, such that its circumference was only 4000.01 miles.
* This means the bridge starts at one support, goes all the way around the world, then reaches its other support only 50 feet short of where it started.
* Now assume the handrail expands by 1 inch.
* The handrail is close enough to a complete circle that we can approximate it as one.
* The circumference of a circle is 2 pi times its radius.
* Thus to increase the circumference of the railing by 1 inch, we need to increase its radius by 1/2pi inches.
* However, the handrail-circle is fixed on one side, where the start and end of the bridge are, so the other side will have to rise by twice that.
* Thus the handrail only lifts by 1/pi =~0.31 inches. That's large enough to be easily measurable if you know how high the railing is supposed to be, but too small to be immediately obvious.
So, now we've got both an upper and lower bound on an approximation: if the bridge is straight, the height is ~9750 inches; if its a complete circle, ~0.31 inches. My guess would be that for the real scenario, where the bridge is ~1/6th of a circle, the railing would be high enough to be obvious, but not so high that a pedestrian can't touch it.
More realistic: 1km total length, 1cm expansion => well over 2 meters height. Crazy.
Reminds me on: Rope around the earth, make it 1 meter longer -> its well above the ground (leave it 2 u to calc ;-) )
It'd be about 6 1/4 inches off the ground all the way round
Why will the railing buckle up and not bend? 1 inch expansion in 4000 mile long railing and it buckles upward???. That thing would weigh millions of tonnes and it goes up? Lol. Nice logic
Awesome video!!
The best channel for riddles. Keep up the good work!
I can't believe this. Let's say the handrail is 1m above the surface. Besides the bending effect of his own weight...
4000 miles would mean with an earth circumference of +- 24,900 miles, the extra circumference of the handrail is +- 2*Pi*(4000/24900) = +-1m. So if the handrail is ONLY 1 inch extra, the handrail would very close to the ground. And of course, touchable. 🤷♂️
Every inch matters 😝
If the handrail expands it gets the curve and take an shape of parabola but not a triangular point ,practical example transmission lines expands in summer and takes an parobolic shape
Yes...this is what i thought while solving this problem...we get entirely different answer with considering curve
This obviously simplified to determine the maximum change possible. More concerning is that the given answer is completely incorrect and no one seems to notice.
Absolutely
Bro can u explain this puzzle I don't even understand
This is the first ever 90% fail question that I actually failed and I feel so ashamed.
Really?🤔🙄🧐🤨🤨🤨
The bridge is so long that the handrail wouldn't be heated for every single mile. 4000 miles is like the length of the USA. It could be winter in NY and hot in the mid west.
you should not be using pythagoras theoroem for this, as the bridge has to curve by approx 9792563 feet, because the earth is not flat. (approx because you didnt tell us the height of the bridge )
IMO, Practically speaking the buckling won't be in triangle shape, it will be an arc where the bridge is like the chord of the arc. In case I am wrong can someone clarify why ?
The buckling will be smooth. This guy is out of his league on this question.
You're right, but that doesn't change the answer; it would form a catenary arch with a height of 'merely' ~9750 inches.
However, what does change the answer is that 4000 miles is nearly 1/6th of the Earth's circumference. Thus neither the bridge nor the pre-expansion rail would be a straight line; they'd both be curved. Hell, at that scale you can't even treat gravity as a uniform force; the direction of 'down' changes by 57.8 degrees between the ends of the bridge.
@@macdjord wow, thanks for providing a new perspective. This makes more sense and is as practical as it can get. And above all instead of just simply trying to solve a given problem its really important that we first reflect on the problem thoroughly. For the sake of puzzle the solution provided by Ammar is fine but from an engineering perspective its just impractical.
@@macdjord show the math that gives you 9750 inches
@@davidjones-vx9ju Answer's the same as the last time you asked.
The answer is No. The curvature of the rails will not be significant.
Edit: The rail will never form a triangle, that is not how expanding metal works.
Pretty sure the steel rail of 4,000mile length would just absorb the 1inch increase in inner tension and not buckle.
The bigger puzzle is how many days did it take that pedestrian to walk to the centre of a 4000 mile long bridge?
Amazing and really unexpected answer!
Until I checked the result in the calculator, I did not believe.
Honestly, I thought to myself that the railing would be raised with a very tiny fraction of an inch.
Simply amazing.
Welcome back Ammar !!
(edited:
I checked the angle between the new railing and its original line:
Well, only 0.00508979315 degrees !!)
I also calculated on calculator, got the same results. But still can't believe that an increase of half an inch in hypotenuse can increase height by 11257 inches.
I couldn't figure it out yet but, there must be something missing.
@@amitneema5341
Check it again...😀
I get the idea of the puzzle.
But, it just says hold the center, not reach up and hold. So, barring any limiting criteria, there is no reason that with equipment a person couldn't make their way to the center of the hand rail and hold it.
You could argue that if the summer heat buclked the rail that much it would make it to hot to feel the rail.
Only US people use feet/inch now, while other parts of the world using m/km.
You need to be crazy to walk 4000 miles on a bridge as a pedestrian
The question is wrong here because the handrail will move down if it is actually expand
Sorry, having trouble getting past the idea of a bridge that's literally long enough to travel from New York to Berlin.
Hi Amaar, your videos are amazing!
Probably late to comment, however, you made the assumption that the dent will be caused at the center, I think the dent will be caused near the extreme ends..
If it is possible to have a bridge 4,000 miles long (which is roughly the distance from San Diego, CA to Lima, Peru), then it seems equally likely that there might be a person who is tall enough to reach 938 feet in the air. So the answer to the riddle should be "yes, but the person must be a giant."
You accidentally added 000 at the end of the inches and made these calculations HUGE and wrong!
Here's what I did: (2000 mi+0.5 in)^2= (2000 mi)^2+x^2 (x is the height, the 938-foot value) but I imagined that happening to the entire bridge! In the version I accidentally tried, I would say yes to both.😢
OK Ammar, once again the concept is good but when applied to a bridge and you want to think logically then logically the handrail will sag and then when could tighten, to add to that it would have supports which would also expand which would effect your original trigonometry equation.
Imperial units are obsolete. Only the USA and others two countries use them today. Please use metric units.
Obsolete? Today? You mean the imperial system was the norm in the past?
It was the USA that invented the imperial system (like the Fahrenheit system and some others of that sort). Hence, they are the only country that uses them (because, let's face it, it is not a really good one, is it?). And some ex-colonies use it too in some contexts (cuz colonization).
@@neliaferreira9983 Ok, but can you give me some fact that imperial system is better than metrical system? Who pass at the metrical system never change mind
@@marcoferranti7132 Why do you ask me for an example that the imperial system is better than the metric? I am not of that opinion myself.
I was just saying that your use of "obsolete" and "today" is incorrect because that implies that the imperial system has been the norm before, which it was not (except in a couple of countries out of the 200 hundred countries in the world). The US invented that system, so yes, of course they are the only ones that use it "today" (it is not "obsolete" because they still use it), but noone else in the world as ever agreed that it is a good system and hence no-one else uses it.
Maybe you meant to say:
"Imperial units are SCIENTIFICALLY IMPRACTICAL. Only the USA and others two countries use them EVER. Please use metric units."
With which of course i agree. And millions of other people.
I imagined there was a road in the middle of the bridge, and that you were standing directly in the middle and thus at least 1 lane away from each of the handrails so you wouldn't be able to touch them. So I guess I was correct, even if not for the same reason given. No one would make a 4000-mile walking only bridge.
Considering the scale of that bridge would span virtually the entire flight distance from Anchorage, Alaska to Miami, Florida.
solved it! didn't believe the answer at first.
If x is the half-length of the bridge, height h = sqrt(x + 0.25)
Thanks for another great puzzle. But please, don't say your CITY has 4k miles long bridge, I can't imagine that even if I try. 🤪
question is not practical.
distance b/w New Delhi & London is approx 4000 miles.
longest bridge is about 100 miles in the world.
Pre-2016 I'd agree with you, but nowadays we just need to preface it with 'Trump is planning a bridge between his US golf course and his golf course in Scotland...'. Suddenly it sounds legit, still daft, but legit haha! 😁
That's why he said, "imagine that". These puzzles are to check and improve our problem solving skills. Most of the people start counting mistakes in puzzle when they are not able to solve it.
@@kuls43 Lol, when the problem is so out of sync with reality you'd have to take into consideration the curviture of the planet, it's not really unfair of the OP to point out the measurement being used may be an error.
In other news, I just ordered my 4000 mile long handrail and Amazon predicts it will arrive on Tuesday...Wednesday...Thursday...Friday...Saturday...Sunday.... 😁
4,000 miles is just less than a quarter of the earth's circumference.
I'm too lazy to figure out the puzzle with this information included...
Can you, Ammar, or anyone do it for me?!? - Thank you!!! :) :) :)
P.S. miles, inches, feet, blah, blah, blah! Use The Metric System!!! 1,000km bridge and 1cm expansion, for example.
Just for you:
The bridge is 6,437,376 m long and the handrail expands by 0.0254 m.
Happy now?
shouldn't it hang down because of gravity?
Very nice 👌
Can you please use metric as well?
Imagine accidentally merging into this bridge. Next exit: in 4000 miles. Hope you didn't leave your oven on.
(*6437 km in real measurements)
Again a nice puzzle by ammar and this is more than a puzzle it gives some important knowledge too. ❤️❤️❤️
An expansion of only one imch on a 253 400 000 inch handrail is WEEEEELLLLLL under the elasticity limit of any material...
Superb narration 🎉
given that the bridge is 16% of the way around the world, the answer would need to be calculated on an arc, not a straight line. And the handrail might be attached at more than the two ends.
agreed, and specifically a parabola that is nearly a perfect circle. and when comparing 2 circles 1 inch apart at a radius of 3958.8 and 3958.80001578, the length along a 4000 mile section increases by 1 inch. so thats the answer, 1 inch longer equals 1 inch taller in the center.
Brother please help me in solving river crossing game level 14 (horse game) if the pattern was change tell me a method to do this kind of problems
The Earth will have a significant curvature across 4000 miles.
How can my city has this much longer bridge since my country's tip to top length is lesser than 4k miles 🤣
Which country you're
Pls make videos more frequently
WHY GOD, WHY INCHES, FOOTS AND MILES :'(
These are architectural units and are common in this fields
@@abhinavrawat5327 Not outside the USA.
Nonsense. The handrail starts as an arc covering more than 57 degrees of bend.
When it expands, it will not just kink in the middle, the whole arc will lift up by less than 1 part in 126720000 above its previous curvature position, which at the midpoint is only 0.025 inch.
That's a long ass bridge. That's basically the flight distance from Anchorage, Alaska to Miami, Florida. Ignoring the bridge for a moment, no handrail would be that long without being broken up into sections since it would need supports as it would sag otherwise.
Yes, I really enjoyed this tricky puzzle. (But in real life the handrails wouldn't rise that level. This is the beauty of this puzzle. )
And I remember my middle school science teacher explaining the "Tadak Tadak" sound of trains is caused because of this gap in the rail...
The question isn’t whether a person can reach the hand rail. The actual question is whether once they touch the handrail can they tell if it expanded. So… the real answer.. and also my big brain answer is; if the rail is warm to the touch the rail must also have expanded.
4000 mile bridge with a handrail for pedestrians? Who is walking across a 4,000 mile bridge? For that matter, given most countries are less than 4000 miles from side to side, this is a humongous bridge and a humongous city. Russia has a length of 5600 miles, for instance. This is an impossible bridge to exist, and so it's not surprising the answer is impossible as well.
Awesome awesome👍👏😊
The length of this bridge is not suppose to surprise anyone.
This is a bridge from the LAND OF MATHEMATICAL RIDDLES.
I leave there, believe me - It is a really BIG land!!
This bridge connect the city of IMAGINATION to the village of CURIOSITY.
I cross this bridge every day in 5 minutes.
Thanks
Never keep holding on to hand rails
• before I finish the video •
I got around 1/4 of a mile “bump”, so it should be quite visible.
this is so wrong. 0ne inch over 4000 miles would not be noticed, and if anything it would go down ,not up the weight of the handrail alone would cause it to sag
Lmao I guessed the answer would be no since the effect of one inch on all 4 miles would be insignificant smh... My dumb ass thought that all of the handrail just expanded by one inch
WRONG. i was too lazy to solve it correctly. so obviously let down when you solved it the way i did. not only should you be calculating arc length, but 4000 miles is not a straight line either. my intuition leads me to believe not only that increasing by 1 inch wouldnt change much, but also that a 4000 mile handrail is way too short for a 4000 mile bridge if it is 3 feet off the ground. lets check.
a 3 foot tall rail is 4000.00057 miles (3.03 feet longer) long on a 4000 mile bridge. if the rail were to grow by 1 inch, it would get 1 inch taller in the center. i think you are part of that 90% that fail this. well, and to be fair, so am i since i assumed using triangles woul be a close approximation too.
It could be straight, in which case it would be tangential to the earth where one end would be on the earth, the centre 462 miles above the earth and the other 1,659 miles above the earth (watch out for low flying ISS at 250 miles above the earth).
At those heights the effect of the atmosphere and clouds on the weather will affect how hot the handrail gets...
if there is 4000 mile long birdge in my city, dosent that mean my city is bigger than most countries?!
Why would a buckling handrail form a triangle?
Jesus Christ this video is a prime example why metric is far superior to imperial. What a mess.
In what way?
Imperial clumps smaller units together into larger units in a very sensible way.
If you have a field 22 yds (a chain) wide and 220 yards (a furrow long, or furlong) long a team of oxen could plough that in one day. A useful unit is the amount of land a team of oxen could plough: it's called an acre - something easy for a farmer to visualise.
@@cigmorfil4101 whut
@@neliaferreira9983
Just explaining that metric is easier when dealing with abstract things.
The imperial system was built on physical objects and so quite easy to visualise for the non-educated, non-abstract thinkers of its day.
1 ft (12 inches) is the length of my foot - my foot *is* 0.3048 m long!
The distance between my finger tips and elbow *is* near enough 0.4572m, or 18", or as it was known for hundreds of years: 1 cubit.
Stick out my arm to the side and the distance from the fingertips to my nose *is* near enough 0.9144m (or 3 ft, 36 inches), or as it was known for hundreds of years: 1 yard.
Stick out both my arms and the distance between the finger tips *is* near enough 1.8288m, or as it was known for hundreds of years, 1 fathom.
The imperial system was based on measurements people carried about with them wherever they went.
For example, ask someone back them how long a cricket pitch was and they could visualise it as the team of 11 men standing along its length with their arms stretched out just touching at the fingertips with the players are either end just touching the wicket (ie 22 yards, 11 fathoms).
The metric system was based on a fraction of the distance between the north pole and somewhere along a line of longitude (ignoring the undulations caused by hills and valleys, using an average earth radius for it).
Curiously, that was then used to measure the speed of light and was then redefined to be the distance light travels in a fraction of a second...rather a circular definition?
@@cigmorfil4101 Well, yes, ok, but when it comes to science and mathematics, why use imperial at all?
Also, imperial doesn't deal with abstract. It's the opposite: it deals with concrete. Imperial uses everyday household items or circumstances to measure reality. Which is why it is not good for science.
My _city_ has a longest bridge of 4,000 miles??? The *entire* length of the contiguous USA isn't even 4,000 miles... wtf kind of hypothetical 'city' are we talking about here?
I believe there is a false assumption here, in that the planet’s curvature isn’t accounted for.
Why would you do all these calculations in the imperial system? It's as dumb as it gets!
no metric? i dont know and dont care how many inchess are in a mile so...
What is a pedestrian doing in the center of a 4,000 mile bridge? How did he get there?
Brilliant! 👍🏽👍🏽
Wait 🤔 11 inch is less than 1 feet. Human average height is 5 to 6 feet. So he can touch the hand rail
How many countries does a 4000 miles is through ????????
The oversight with this logic problem is that the example it uses. There are far too many pesky details that ruin this as a problem that can be solved in the way shown.
...
The Earth's circumference is only 24, 901 miles (laterally at the equator; only 24,860 miles vertically)-- that bridge 4000 miles long would curve to match the curvature of the Earth, not be a straight line. (Perhaps it is a tunnel bridge that goes under the water and comes back up? The imagery suggests a suspension bridge though.) We can determine the straight line distance from fixed points A and B at the end of the 4000 mile bridge, based on the Earth's circumference. We can determine the radius of a smaller circle, where the same fixed distance between A and B when going around the circumference is 4000 miles plus 1 inch. We can then calculate the high point of the arches away from the straight line from A to B, to see how high the handrail raises.
...
But that isn't the real issue.
...
What is making the handrail go up into the air? Assuming the handrail is periodically attached to the bridge by vertical posts, the extra length would attempt to sag but then be pushed laterally by the posts holding it up. We would see a rail that might curve outward past the edge of the bridge, inward toward the pedestrian walkways of the bridge, or even both in a chaotic zig-zagging pattern. Now we are looking at some complex physics problems. What will the handrail do, based on the bridge's construction? Let's assume that the support posts holding up the handrail are rigid, and are a full 10 feet apart. This means that each section between the posts bows either inward or outward as it expands in the summer heat and seeks to sag due to gravity. There are 5280 feet in a mile, so we are looking at 528 gaps per mile post to post along the 4000 mile long bridge. That's 2,112,000 gaps -- with the extra inch of length divided equally among all of them. There is a 1/2,112,000th of an inch bow inward or outward, between each post as the pedestrian walks along. Safe to say, a pedestrian walking on this bridge would NOT notice an expansion difference of only 1 inch. They will not see it, and they will not feel it.
...
The reality of course is that bridges are typically much smaller than 4000 miles, meaning A to B across the bridge is closer to a flat line. Also, a 4000 mile long metal handrail will expand in length much more than just 1 inch -- the exact degree it will expand depends on the metal used in its construction, which is again information we have not been given. The extreme values used in the puzzle made it impossible to solve logically. We had to make many faulty assumptions to arrive at the demonstrated answer, which is in fact not a real answer to the puzzle.
What this amazing metal is we don't know but that is irrelevant as we're given the required information regarding how it expands between the cold of winter and heat of summer: it expands 1 inch (0.0254 m) over a distance of 4,000 miles (6,437,376 m) over the temperature difference, whatever that is.
What is more relevant is that if the bridge is flat, it will of necessity be tangential to the earth - if one end is on the earth the other will be about 1,659 miles (2,669,900 m)
above the surface of the earth (the centre some 472 miles (759,610 m)). The ISS orbits at about 250 miles (402,336 m) above the surface of the earth.
Great video
Sir, it's not Pythagoras theorem. It's "Goguo theorem"!
Baudhayana *theorem*
@@oktopg well sorry sir no offense. I am not saying that Sir Pythagoras & Rushi Baudhayan didn't recognized this. Sir Goguo was first who invented this. And I believe that one who invented first; should get title for that!
@@ignore5147 while in the first place it is arguable whether one shouldn't consider this theorem being 'discovered' rather than 'invented', anyway no one can tell who really got to it first. It's highly likely that it got discovered independently by several people in the course of history. Maybe it should be called 'unknown humans' theorem' then 😂
I'm sticking with Pythagoras.
Logical people won't use an illogical metric system :)
Well my version has the person holding the rail in the cool of the morning when he is arrested by a cop who gets called away to the other end of the bridge and he doesnt have room in his Cushman to put this criminal (he was drunk and spitting off the bridge, infraction of municipal code of that area), so the cop handcuffed him to the rail ere he drove off. He waited all day, and at the end of the hottest part of the day he saw the cop far down below pulling back up. He spit on the cop as he held the rail. The cop shot him. The End.
P.S. He definitely knew the rail was expanded alright.
@@rogerscottcathey That sounds like a problem fit for a SAW film...wake up to find yourself handcuffed in the middle of the 4000 mile bridge. Obviously there will be an electrical current going through the metal handrail. Which direction do you walk to find the key in time? How long will it take you? How many times will you be electrocuted because you let the metal of the handcuff touch the electrified rail? 😲
@@jessicataylor7174 🤣
Who wants to walk on 4,000 miles long bridge?
Thursday's child perhaps? 😄
'...Thursday's child has far to go...' ~ nursery rhyme reference.
😌😁
Nice😊😊 Thank you!!!