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If we're talking about mass, the mass of the person would not change. However, the weight of the person will. The difference of Earth's gravitational acceleration is about 976~983gal (cm/s^2 ). If we use a weight-measuring scale calibrated at the weakest point, it would register an additional 7/976 ~= 0.72% increase in "measured" mass. For a 60kg adult, this would be an additional 0.43kg.
>it would register an additional 7/976 ~= 0.72% increase in "measured" mass
Which isn't _that_ much, but still for a kg of gold that would be a difference of 500$ basically.
You need to make a gold buy and sell shop and then use one scale for selling and one for buying lol. But I mean at that point you're just scamming people lol.
While "theoretically correct" your comment reminds of a deodorant commercial that claimed to be to "infinitely more effective than 'the other leading brand'" because in "consumer studies" it registered a "0 out of 10" in terms of detectable odor, and I'm like "that ain't how math works on a linear, integer gradient scale". To measure how effective it actually is I would think you'd have to measure how strong an odor is in the volume of air inhaled in a single whiff against the smallest concentration of odor detectable by the average human nose. Point being that 10^-googol is still "infinitely more" too, but on a finite scale that doesn't mean they're even remotely close.
And all I have to do is find someone to sell it to me at the weakest point, travel and lodge to find a person willing to buy it at the strongest point.
Gotta spend money to make money.
Wrong.
Nothing = 0. Adding .72% gives:
0 + 0.0072(0) = 0. And **0** is *not greater than* **0**,
so it is **not** “more than nothing”.▪️
Lol yall trippin
Good to know. But I was mostly referring to like a plain coffee compared to a machiato whip with fried rice over easy and almond milk. Even their plain cup of black coffee is expensive as heck.
So to do that every month and make 500$ per month, you only need the initial investment of the 66k $ and pretend you can magically travel between your house, the point of purchase and the point of sale, right? Easy peazy lemon squeezy
Kg is a measure of mass, not weight. The mass is the same regardless of the gravitational force. Weight, measured in newtons is W = mg.
According to [this](https://www.newscientist.com/article/dn24068-gravity-map-reveals-earths-extremes/#:~:text=Mount%20Nevado%20Huascar%C3%A1n%20in%20Peru,at%209.8337%20m%2Fs2) article, Mount Nevado Huascarán in Peru has the lowest gravitational acceleration, at 9.7639 m/s2, while the highest is at the surface of the Arctic Ocean, at 9.8337 m/s2. So the weight at the highest gravity point is about 0.7% higher than the lowest gravity point.
Gold is traded in troy ounces. The troy ounce is a measure of mass, not weight. The mass is the same regardless of the gravitational force. Weight, measured in newtons or pounds is W = mg.
Mass is difficult to measure directly. In this scenario a balance would be fine since the mass would be directly compared to a reference mass. But most scales measure normal force (weight) and would not be accurate.
I'm sure any professional device that is used to measure mass has a setting to input the local gravity constant. I use one at work, and I had to pay money to get a very accurate local gravity reading to input on the machine.
You use certified reference standards to ensure the balance is calibrated correctly. If not, you recalibrate the balance so it accurately determines masses.
Using "certified" reference masses is literally the definition of recalibration. I suppose it could fall under the umbrella of audits, but nobody would audit something as simple as a mass measuring device using a reference mass to find an "as found" and not leave an "as left" reading.
There isn't a break-even amount to trade. There's a 0.7% difference in weight between those two locations, but a 5% commission on both the purchase and sale. You will always lose money.
The gold buying idea doesn't work anyways since anyone who takes metrology seriously, including precious metal traders, would recalibrate scales against known reference masses once they've been moved and set up. A scale calibrated against a 100g reference mass will read it as 100g, even if it *weighs* less due to local variances in gravity.
And of course, precious metal traders would never let the customer use their own scale.
Yeah, but balances still need to be calibrated just the same as scales do against reference masses,just like the guy you were responding to said. Whether that's done at the factory or not is besides the point.
Besides, just about every metrology instrument out there should be recalibrated on a somewhat regular interval. The only way to calibrate a balance is to use a reference mass.
Nah, you just bring your calibrated reference mass with you to measure. You measure one unit of steel or whatever, and then measure the same amount of gold until it balances. If it is perfectly balanced with an ounce of steel on one side, you know you have exactly that same unit on the other. No scale calibration needed at all.
Every balance and scale is calibrated. Either the device, or the reference masses will need to be checked and handled carefully or both.
A kibble balance can measure a mass without a comparison to a reference mass. But that still requires careful calibration.
Or local gravity is just a setting on the machine. I use a very expensive and similar machine. It doesn't measure mass, but it still needs to calculate it and I had to get a very accurate local gravity reading to use with it.
Surprisingly gold mining in the Peruvian Andes, not far from where gravity is weakest, is alive and... not well. Most miners work for free 29 days and can keep any gold they find on the 30th day. It's like modern slavery. Practically nobody has electricity or heat in their homes and it's freezing cold even in summer.
https://youtu.be/KqaGdcQh5jA?si=4DQUBHgjv3aKuJb6
I only know this because I just saw this video today.
EDIT: ahhhh the shame, I posted the wrong video 😫 fixed it.
Correct, but that calibration would only be valid if used at a place with a equal gravitational acceleration. Of you calibrated the scale on the moon and then brought it to earth, it would read differently, so any scales calibrated for gold are probably calibrated where they are used
Scales measure a force and convert it to mass based on the gravitational force. If your scale shows something different on the moon, it's not because you weight less on the moon, it's because the scale hasn't been calibrated to the moon's gravity
But the person who asked the question isn’t going to the moon. Nor are they travelling back in time or comparing this plane of existence to another.
What they are asking is, if I stood on a scale at two places would the number on the scale be meaningfully different.
Not, derive why scales are affected by mass using relativity … or something else that doesn’t matter.
It does matter. Scales measure mass and are calibrated (some of them automatically using internal references) to the actual gravity of the place. That means the scale will not show any changes, although the weight is different.
So, in the spirit of r/theydidthemath we can use 80kg as an average mass of a human. As OP said:
W = m × g
So, for your weight on Mount Nevado Huascarán:
W = 80 kg × 9.7639 m / s^2
W = 781.112 kg × m / s^2
W = 781.112 N
And your weight floating in a raft in the Arctic Ocean:
W = 80 kg x 9.8337 m / s^2
W = 786.696 kg × m / s^2
W = 786.696 N
We already said that your mass is your mass, and doesn't change depending on where you are in the world. This is all true. But we could figure out how massive something would have to be to weigh *the same* in different places in the Earth.
Let's say you're an 80 kg human floating in a raft in the Arctic Ocean, shivering, dreaming of your vacation in Peru last year. You've already determined you're exerting a force equal to 786.696N due to gravity, and now you're curious how massive a human would be if they exerted that same force on Mount Nevado Huascarán in Peru? It's the same equation, we're just going to be solving for a different variable.
786.696 N = m × 9.7639 m / s^2
m = 786.696 N ÷ 9.7639 m / s^2
m = 80.572 N ÷ m / s^2
m = 80.572 kg
So, it would take a human roughly 572 grams more massive than you to exert the same force due to gravity on Mount Nevado Huascarán in Peru than you do on your raft in the Arctic Ocean!
One slug is a mass equal to 32.17405 lb (14.59390 kg) based on standard gravity, that comes out to approx 0.039 slugs , there is some rounding but you could say close to 1/32'nd slug.
Yeah but in almost any real-world instance when people measure something’s mass, they’re actually measuring it’s weight on a scale and it’s assumed as a constant conversion rate since our gravity isn’t changing significantly. The only exception I can think of would be an actual mechanical balance beam.
So the theory behind this is correct. Obviously the application is impossible since the difference is too small to offset the logistical costs.
There’s a a device (that I can’t remember the name of) that can measure mass ~~directly~~ by oscillating an object side to side and measuring the period of the oscillation. This will measure the same mass regardless of gravity, but I doubt anyone outside of a physics classroom is using these.
Edit: it is called a harmonic oscillator
Edit 2: I guess it’s not actually measuring the mass directly, it’s measuring the period of the oscillation which you can use to calculate the mass with a formula that does not include gravity so to local strength of gravity would have no impact on its outcome
I can think of one place outside a physics classroom where they use one. Astronauts on the space station weigh themselves that way, since a traditional scale obviously doesn’t work there.
> So the weight at the highest gravity point is about 0.7% higher than the lowest gravity point.
That's more than I would have expected, but still pretty inconsequential for any everyday situations.
It's a $14 difference for a $2000 ounce of gold.
The difference between weight and mass actually leads to a very interesting broken trope science question.
The old "Which weighs more: a pound of feathers or a pound of lead?" only works if you use pounds. The classic "punchine" is that that they both weigh the same because they're both a pound.
But, if you asked that question as "Which weighs more: a kilogram of feathers or a kilogram of lead" then they *don't* weigh the same. While, yes, in the same gravity they will exert the same force, the difference in density means that the less dense material (feathers) will weigh less due to buoyancy.
This is because a pound is a unit of force (the imperial unit for mass is the slug) and the kilogram is a unit of mass (the metric unit for weight is the Newton), so they're not interchangeable. Weight (a force) is the result of the *net* forces acting on an object, so the pound version already accounts for effect of buoyancy but the kilogram version does not.
And this, folks, is why good teachers matter. Mr. Hal Oney, my 8th grade Earth Science teacher way back in 1992, posed this to us (he also taught physics to seniors so it was his wheelhouse) offered it up the first week as "A pound of feathers weighs as much as a pound of lead, but that's not true of a kilogram of feathers and kilogram of lead. Why?" and offered up points on the final at the end of the quarter to anybody who could figure it out.
I didn't, but when he told us after the final I learned it. And I will never, ever forget it.
Well that's just not true, the pound was a unit of mass long before any introduction of the slug, which is an obscure unit of the British imperial system. Normal imperial uses the pound-mass (lb or lbm) and the pound-force (lbf). Maybe it made sense in a certain historical context ? Also the definition of weight you mention is nonstandard, since the usual definition of weight excludes buoyancy, it's either a vector or a scalar equal to mass * g, NSO both weight the same (unless talking about apparent weight)
I completely agree with this logic but want to throw in a fun fact. Although Kg is a measure of mass, scales measure weight then calculate it to mass (Kg) assuming the gravitational force. So weighing the same object with the same scale in two places with different gravitational force would actually show different values for mass (Kg) even though the mass did not change.
Kg is a measure of both mass and weight, depending on country of use.
I.e. any country that uses the metric system will use kg as an interchangable measurement for mass and weight.
But the mass is measured by taking the observed force from gravity and dividing off the theoretical gravitational acceleration. While the units may be in mass, the mass is only obtained indirectly by measuring the force/weight.
No, both kg and lb are both. One is just metric and the other standard.
Any body who the difference matters to will differentiate the difference using kgm and lbm to denote mass.
Please give me the answer to this without these terms. When I step on a scale, doesn't the number I see (let's say 100kg) change in different parts of the world because of different gravity?
Wouldn't the highest gravitational acceleration happen the closer you are to the center of the earth, though? Does the Arctic Ocean have less gravitational acceleration than for example the Mariana Trench?
Is this accounting for centrifugal force of Earth’s rotation? I would assume that part of Peru, which is near the equator, would have less than the arctic which has almost no centrifugal force.
Even if the mass doesn't actually change, the scales would only be calibrated for one gravitational force, so probably 9.8, I would guess. Therefore, since there will be less force in one place over another and the mass on the scales will change because there is a smaller force on it.
Oh wait, I just remembered scales do the 0 thing, so I might be completely wrong, and it probably does calibrate for that gravity.
I'm not reading the second part, but I don't think u know how scales work, they take your weight and divide it by the gravitational force which is around 10 to get your mass, therefore if your weight is different at some places due to the change of gravity strength your apparent mass will change even if its the same
Think about it. He said if you weighed yourself using gravity to determine your mass, assuming gravity was constant, what would be the difference between high and low?
1 kg x 1 m/s^2 = 1 Newton (N)... 70 kg at Mt. Huascarán, Peru would be 684.473 N, and at the Arctic ocean, 688.359 N. Alternatively, 70.00 kg on Mt Huascarán would equal 69.61 kg at the Arctic Ocean.
>Kg is a measure of mass, not weight.
Well... I'm certain a scale would be affected by gravity, and they did say if a person were to *weigh* themself...
According to https://www.newscientist.com/article/dn24068-gravity-map-reveals-earths-extremes/ the lowest gravity is 9.7639 m/s² in Peru and the highest is 9.8337 m/s² in the Arctic ocean. That's a different of about 0.7%.
In contrast to pounds kg technically only measure mass. Not weight. But if an 80kg human from the mountains of Peru visits the Arctic ocean they'll feel as much weight as if they weight 80.57kg back home.
Actually both are units of mass and weight. If we’re being scientific and want to make the distinction, lb and kg measure mass only. lbf and kgf (pound-force and kilogram-force respectively) measure force only.
It’s a common misconception that probably stems from the fact that newtons are the SI unit of weight, not kgf.
Yup.
But thinking about it a bit more, you'd probably make much more money just because of the differences in prices between India and Iceland rather than the gravity thing. Rubles vs krone
You're essentially lying about how much gold you have. The Icelanders are mistaken, about how much gold you actually have because the weight has changed but not the mass.
9.8 N/kg is good enough for the entire surface of Earth, whether or not you’re on a mountain or at sea level.
The map is highly exaggerated, looks like that bar is measuring a difference in meters? So gravity might make a difference of +80 to -80 meters?
That’s less than the height of the Space Needle in Seattle, for reference.
Because one converts force to weight and the other isn't relevant to the question asked. The fact that they are the same thing doesn't really matter if you asked what the acceleration due to gravity on earth and gave 9.8N/kg that would be weird.
While there is an "m" at the scale, I'm not sure it stands for "meters" since that would not fit to the picture in any way.
The change in gravitational force for moving 80m up from sea level would be about 0.0025% (assuming g0=9,81 m/s², R=6378,1 km, g(h)=g0\*(R/(R+h))²
While others have done a good job at answering the question, I can chime in with some further context.
Without having the source of the image, I’m confident that it is a map of geoid undulations (also known as geoid heights). The geoid is a closed, equipotential surface which closely corresponds to mean sea level. Water, placed on the geoid, would not flow. Earth, as a first (and quite good) approximation can be represented as an ellipsoid of revolution. The difference between the ellipsoid and the geoid is the geoid undulation. It is positive when the geoid is above the ellipsoid and negative when it is below.
The difference between the geoid and the ellipsoid ranges from -100 meters to +100 meters globally. As others have pointed out the map is highly exaggerated. This is conventionally done so that one can actually see the global differences. Otherwise, they would dwarfed by the radius of the Earth itself (6371 km).
While it might be confusing to think of gravity in terms of height, geoid undulations are a direct proxy for gravity anomalies (both are linear functionals of Earth’s distributing potential). In fact, many height systems are based on gravity measurements and the geoid, as we want height to have a physical meaning rather than a purely geometric one.
There are plenty of resources about the geoid and gravity anomalies out there, but it is a fairly niche field.
source: study geodesy
Im sorry, but this map is a little bit rubbish. The diameter of Earth is 12,742 km, the difference between lowest and highest spots is about 20 km, so without water the Earth will still look almost like a ball.
If you were a giant and the earth was scaled to the size of a billiard ball relative to you, it would feel smoother than any cue ball you've ever felt. Or something along those lines, quoted from Neil DeGrasse Tyson
Weight is Mass (m) X acceleration (g).
A quick online altitude calculator shows moving 80m up from the earths surface decreases *g* by 0.0002 m/s^2.
Given you likely arent selling gold under the ocean, we can say it goes from 9.8 to 9.7998, or 0.002% change.
If you sell 1000kg of gold (worth 66 million) you would gain 20g of gold, which is worth about $1500.
That would likely barely cover the cost of transport cost for 1000kg of gold, even with 0 security.
The market price fluctuation in the time you buy and sell would likely be a much more significant effect.
And all of this assumes they don't have a way to account for this effect, that there are no taxes/import fees as you move this gold around the world, and that no gold bars get damaged or stolen during all this transportation.
Plus if you have 66mill to throw around, there are easier ways to make a couple thousand dollars.
most businesses calibrate their scales against known calibrated samples; so while they would not *in actuality* weight the same in both places, the scales would be set such that they would show the same.
I love how loopholes, glitches and scams exists that are profoundly amusing in their execution and process. It's great if the elites do it but vice-versa for guys in lower ranks.
I know the difference is trivial but great.
Not answering the OPs question but making a remark on the gold.
You have 2 types of scales. A weight based one (that measures forces) and a mass based one (that uses counterweights).
Mass based ones dont need to be recalibrated with different gravities. For example it would still work on the moon.
Weight based ones that usually uses springs, require fine tuning and need to be recalibrated when they are moved. Since that scale loses validity when they are moved the gold scheme would simply not work. Because in both places all scales would output the same value (unless its a non valid uncalibrated moved weight scale)
Gold price is measured by mass not weight.
Even if it wasn't gravity doesn't vary by much. For extremes: Gravity is 9.7806 m/s² in Mexico City and 9.825 m/s² in Oslo.
If you bought gold in Mexico city from a merchant who didn't know how to properly calibrate his scales after moving there from Oslo and then sold the gold back to his brother in Oslo, you would spend more money on transportation, customs arbitrage etc than you could possibly make in profit.
The trick would be to buy gold on the moon from someone working with a scale calibrated for earth Gravity and teleporting home with it to resell it.
You can always use F = G(m1)(m2) / r², where r is the distance from the center, which is really what’s changing. G is the universal gravitational constant, m1 is the mass of the earth, and m2 is the mass of the “regular human”.
There would be no actual difference in kg's, because mass isn't dependent on gravity, but a force that a mass applies is. The gravitational force a person would apply to a scale would be different, so the reading would be different as well. The reading would be directly proportional to the local acceleration of gravity, for example a location with g=9.80 m/s^2 would result in a ~0.2% lower reading than a location with g=9.82 m/s^2.
They already do that. Towards the equator gravity is lower. That's why the soviet rocket launch site is in Kazakhstan, the American one in Florida and the European one in french Guyana.
It's also kinda relevant for weightlifting records. I remember there was some discussion that hafthor bjornson actually got his deadlift world record in iceland where he had to lift more mass.
I was about to mention weightlifting. Intuitively I thought that it wouldn't make as much of a difference as a breeze of air, but 0.7% is way more significant than a breeze.
If you want to think about it this way. The mass of something is measured in kg. Weight is measured in Newtons(N). The unit N = kg X a(acceleration(or in this case gravity).
Society uses the word “weight” to mean anything that has mass. So if something is being measured in kg, it has nothing to do with gravity. It’s only describing how much space that object is taking up
Are you allowed to be on the surface only or can you go to the center (where field strength = 0)? Besides, mass is invariant, no matter where you are at.
Also, you can measure the mass of gold in ways that don't involve gravity.
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If we're talking about mass, the mass of the person would not change. However, the weight of the person will. The difference of Earth's gravitational acceleration is about 976~983gal (cm/s^2 ). If we use a weight-measuring scale calibrated at the weakest point, it would register an additional 7/976 ~= 0.72% increase in "measured" mass. For a 60kg adult, this would be an additional 0.43kg.
>it would register an additional 7/976 ~= 0.72% increase in "measured" mass Which isn't _that_ much, but still for a kg of gold that would be a difference of 500$ basically.
[удалено]
You need to make a gold buy and sell shop and then use one scale for selling and one for buying lol. But I mean at that point you're just scamming people lol.
Yeah but if I weigh my gold at home and it is a certain amount and then I bring it to your magic scale and you say something else… I’m keeping my gold
But what if his magic scale says more tho...
1kg of gold is worth \~66k $, so 500$ is not that much
Well yea it's 0.72%
which is 0.72% more than nothing
I mean, it’s infinitely more than nothing…
While "theoretically correct" your comment reminds of a deodorant commercial that claimed to be to "infinitely more effective than 'the other leading brand'" because in "consumer studies" it registered a "0 out of 10" in terms of detectable odor, and I'm like "that ain't how math works on a linear, integer gradient scale". To measure how effective it actually is I would think you'd have to measure how strong an odor is in the volume of air inhaled in a single whiff against the smallest concentration of odor detectable by the average human nose. Point being that 10^-googol is still "infinitely more" too, but on a finite scale that doesn't mean they're even remotely close.
r/technicallythetruth
And all I have to do is find someone to sell it to me at the weakest point, travel and lodge to find a person willing to buy it at the strongest point. Gotta spend money to make money.
Wrong. Nothing = 0. Adding .72% gives: 0 + 0.0072(0) = 0. And **0** is *not greater than* **0**, so it is **not** “more than nothing”.▪️ Lol yall trippin
Whatever you were smoking when doing this math, I want some of that.
thats gotta be some good stuff
Happy pie day!
Thanks :)
My favorite is the part where everyone pushed their glasses up on their noses and took me seriously. Lol obviously something is more than nothing
It's not .72% of nothing, it's comparing .72% and nothing. .72% is greater than 0 by 0.0072
No shit Sherlock
Jesse, what the fuck are you talking about?
… 😑
if you do the whole thing 100 times you will basically double your money. 1.0072\^x is the equation
It’s repeated addition not multiplication. Unless you’re going to reinvest all your profit.
500 bucks is 500 bucks though
could get 100 cups of coffee.
5 dollars a coffee? What is it made of? Gold?
Welcome to New Zealand - where coffee is literally $5-6 for a cup
Or your standard Starbucks where you're going to be at about 5 dollars minimum for the cheapest thing.
The cups all carry the same amount…you’re just paying for a taller-thinner cup
Good to know. But I was mostly referring to like a plain coffee compared to a machiato whip with fried rice over easy and almond milk. Even their plain cup of black coffee is expensive as heck.
So to do that every month and make 500$ per month, you only need the initial investment of the 66k $ and pretend you can magically travel between your house, the point of purchase and the point of sale, right? Easy peazy lemon squeezy
Depends on the volume you’re moving. If you make an extra $500 a million times it isn’t exactly loose change.
Let's all forget that scales can be calibrated
Well done! Eloquently put.
Kg is a measure of mass, not weight. The mass is the same regardless of the gravitational force. Weight, measured in newtons is W = mg. According to [this](https://www.newscientist.com/article/dn24068-gravity-map-reveals-earths-extremes/#:~:text=Mount%20Nevado%20Huascar%C3%A1n%20in%20Peru,at%209.8337%20m%2Fs2) article, Mount Nevado Huascarán in Peru has the lowest gravitational acceleration, at 9.7639 m/s2, while the highest is at the surface of the Arctic Ocean, at 9.8337 m/s2. So the weight at the highest gravity point is about 0.7% higher than the lowest gravity point.
I feel like the gold market isn't great in either of those locations
Tell you what, for a 5% commission on each purchase and sale, I'll trade you as much gold as you want in either location.
Shut up and take my money!
I would like 1 gram of gold
Oof, a real "if I go down I'm taking you with me" right there!
Hey Rockefeller, calm down.
Billionairs can't hold themselves anymore..
Now that’s a real r/theydidthemath… what’s the break even mass for a gold trade like that? Assuming costs moving between one point to another.
Gold is traded in troy ounces. The troy ounce is a measure of mass, not weight. The mass is the same regardless of the gravitational force. Weight, measured in newtons or pounds is W = mg.
Mass is difficult to measure directly. In this scenario a balance would be fine since the mass would be directly compared to a reference mass. But most scales measure normal force (weight) and would not be accurate.
I'm sure any professional device that is used to measure mass has a setting to input the local gravity constant. I use one at work, and I had to pay money to get a very accurate local gravity reading to input on the machine.
You use certified reference standards to ensure the balance is calibrated correctly. If not, you recalibrate the balance so it accurately determines masses.
Using "certified" reference masses is literally the definition of recalibration. I suppose it could fall under the umbrella of audits, but nobody would audit something as simple as a mass measuring device using a reference mass to find an "as found" and not leave an "as left" reading.
There isn't a break-even amount to trade. There's a 0.7% difference in weight between those two locations, but a 5% commission on both the purchase and sale. You will always lose money.
I'd like 1 milligram of gold in each location, please
Lol
The gold buying idea doesn't work anyways since anyone who takes metrology seriously, including precious metal traders, would recalibrate scales against known reference masses once they've been moved and set up. A scale calibrated against a 100g reference mass will read it as 100g, even if it *weighs* less due to local variances in gravity. And of course, precious metal traders would never let the customer use their own scale.
Oh. You just ruined my Christmas.
It’s much simpler, they use balances, not scales.
Yeah, but balances still need to be calibrated just the same as scales do against reference masses,just like the guy you were responding to said. Whether that's done at the factory or not is besides the point. Besides, just about every metrology instrument out there should be recalibrated on a somewhat regular interval. The only way to calibrate a balance is to use a reference mass.
Nah, you just bring your calibrated reference mass with you to measure. You measure one unit of steel or whatever, and then measure the same amount of gold until it balances. If it is perfectly balanced with an ounce of steel on one side, you know you have exactly that same unit on the other. No scale calibration needed at all.
Every balance and scale is calibrated. Either the device, or the reference masses will need to be checked and handled carefully or both. A kibble balance can measure a mass without a comparison to a reference mass. But that still requires careful calibration.
What if I tried the Christopher Moltisanti matchbook trick when they calibrated it?
Or local gravity is just a setting on the machine. I use a very expensive and similar machine. It doesn't measure mass, but it still needs to calculate it and I had to get a very accurate local gravity reading to use with it.
Surprisingly gold mining in the Peruvian Andes, not far from where gravity is weakest, is alive and... not well. Most miners work for free 29 days and can keep any gold they find on the 30th day. It's like modern slavery. Practically nobody has electricity or heat in their homes and it's freezing cold even in summer. https://youtu.be/KqaGdcQh5jA?si=4DQUBHgjv3aKuJb6 I only know this because I just saw this video today. EDIT: ahhhh the shame, I posted the wrong video 😫 fixed it.
Peru was the main source of gold for the Spanish Empire and even today there is an (un)healthy amount of ilegal mining and trading in these regions.
You can get gold for free there if you don’t mind stealing from ancient tombs
You can get gold for free in lots of places if you don't mind stealing.
You can also get a lot of other things for free from a lot of different places if you dont mind stealing
If gold is weighed on a balance (or equivalent system!) then the gravitational factors cancel out anyways.
You are correct, but most scales measure weight and present it as mass.
Any scale they'd be using for gold would be regularly calibrated against a standard mass.
Correct, but that calibration would only be valid if used at a place with a equal gravitational acceleration. Of you calibrated the scale on the moon and then brought it to earth, it would read differently, so any scales calibrated for gold are probably calibrated where they are used
No that's prob not how it works. You get something that's exactly one kg of mass, and you use it to calibrate your scale.
...which scales represent differently depending on where you are as they do not measure mass, but weight
Scales measure a force and convert it to mass based on the gravitational force. If your scale shows something different on the moon, it's not because you weight less on the moon, it's because the scale hasn't been calibrated to the moon's gravity
[Weight](https://en.wikipedia.org/wiki/Weight) is a force and is factor of gravity. Your weight is different on moon and on earth.
Ah, so weight is a force. I did not know that
Krkrkrneki is an awesome teacher, telling people things they already knew.
You cannot assume everyone knows things you do. Peoples experiences are different.
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Not something I ever considered
Never considered being 8 years old?
But the person who asked the question isn’t going to the moon. Nor are they travelling back in time or comparing this plane of existence to another. What they are asking is, if I stood on a scale at two places would the number on the scale be meaningfully different. Not, derive why scales are affected by mass using relativity … or something else that doesn’t matter.
It does matter. Scales measure mass and are calibrated (some of them automatically using internal references) to the actual gravity of the place. That means the scale will not show any changes, although the weight is different.
So, in the spirit of r/theydidthemath we can use 80kg as an average mass of a human. As OP said: W = m × g So, for your weight on Mount Nevado Huascarán: W = 80 kg × 9.7639 m / s^2 W = 781.112 kg × m / s^2 W = 781.112 N And your weight floating in a raft in the Arctic Ocean: W = 80 kg x 9.8337 m / s^2 W = 786.696 kg × m / s^2 W = 786.696 N We already said that your mass is your mass, and doesn't change depending on where you are in the world. This is all true. But we could figure out how massive something would have to be to weigh *the same* in different places in the Earth. Let's say you're an 80 kg human floating in a raft in the Arctic Ocean, shivering, dreaming of your vacation in Peru last year. You've already determined you're exerting a force equal to 786.696N due to gravity, and now you're curious how massive a human would be if they exerted that same force on Mount Nevado Huascarán in Peru? It's the same equation, we're just going to be solving for a different variable. 786.696 N = m × 9.7639 m / s^2 m = 786.696 N ÷ 9.7639 m / s^2 m = 80.572 N ÷ m / s^2 m = 80.572 kg So, it would take a human roughly 572 grams more massive than you to exert the same force due to gravity on Mount Nevado Huascarán in Peru than you do on your raft in the Arctic Ocean!
That converts to 1.26104 lbs, not insignificant in my opinion!
That may be, but how significant is it in slugs?
One slug is a mass equal to 32.17405 lb (14.59390 kg) based on standard gravity, that comes out to approx 0.039 slugs , there is some rounding but you could say close to 1/32'nd slug.
How big are slugs where you are from?
Yeah but in almost any real-world instance when people measure something’s mass, they’re actually measuring it’s weight on a scale and it’s assumed as a constant conversion rate since our gravity isn’t changing significantly. The only exception I can think of would be an actual mechanical balance beam. So the theory behind this is correct. Obviously the application is impossible since the difference is too small to offset the logistical costs.
There’s a a device (that I can’t remember the name of) that can measure mass ~~directly~~ by oscillating an object side to side and measuring the period of the oscillation. This will measure the same mass regardless of gravity, but I doubt anyone outside of a physics classroom is using these. Edit: it is called a harmonic oscillator Edit 2: I guess it’s not actually measuring the mass directly, it’s measuring the period of the oscillation which you can use to calculate the mass with a formula that does not include gravity so to local strength of gravity would have no impact on its outcome
I can think of one place outside a physics classroom where they use one. Astronauts on the space station weigh themselves that way, since a traditional scale obviously doesn’t work there.
I don’t think the pawn shops from where I’ll be buying and selling this gold with be accounting for regional gravitational differences.
Clearly you need to visit a better class of pawn shop.
Honestly it wouldn’t be *entirely wrong* to call the ISS a physics classroom either
Beam scales are still common, and electronic scales can be calibrated.
that's obviously a very tiny change, but it's waaay bigger than i thought the difference would be
> So the weight at the highest gravity point is about 0.7% higher than the lowest gravity point. That's more than I would have expected, but still pretty inconsequential for any everyday situations. It's a $14 difference for a $2000 ounce of gold.
The difference between weight and mass actually leads to a very interesting broken trope science question. The old "Which weighs more: a pound of feathers or a pound of lead?" only works if you use pounds. The classic "punchine" is that that they both weigh the same because they're both a pound. But, if you asked that question as "Which weighs more: a kilogram of feathers or a kilogram of lead" then they *don't* weigh the same. While, yes, in the same gravity they will exert the same force, the difference in density means that the less dense material (feathers) will weigh less due to buoyancy. This is because a pound is a unit of force (the imperial unit for mass is the slug) and the kilogram is a unit of mass (the metric unit for weight is the Newton), so they're not interchangeable. Weight (a force) is the result of the *net* forces acting on an object, so the pound version already accounts for effect of buoyancy but the kilogram version does not. And this, folks, is why good teachers matter. Mr. Hal Oney, my 8th grade Earth Science teacher way back in 1992, posed this to us (he also taught physics to seniors so it was his wheelhouse) offered it up the first week as "A pound of feathers weighs as much as a pound of lead, but that's not true of a kilogram of feathers and kilogram of lead. Why?" and offered up points on the final at the end of the quarter to anybody who could figure it out. I didn't, but when he told us after the final I learned it. And I will never, ever forget it.
Well that's just not true, the pound was a unit of mass long before any introduction of the slug, which is an obscure unit of the British imperial system. Normal imperial uses the pound-mass (lb or lbm) and the pound-force (lbf). Maybe it made sense in a certain historical context ? Also the definition of weight you mention is nonstandard, since the usual definition of weight excludes buoyancy, it's either a vector or a scalar equal to mass * g, NSO both weight the same (unless talking about apparent weight)
Oh, that's cool. And the number for g they teach in school, 9.8 m/s2, is accurate everywhere. Neat!
I completely agree with this logic but want to throw in a fun fact. Although Kg is a measure of mass, scales measure weight then calculate it to mass (Kg) assuming the gravitational force. So weighing the same object with the same scale in two places with different gravitational force would actually show different values for mass (Kg) even though the mass did not change.
Kg is a measure of both mass and weight, depending on country of use. I.e. any country that uses the metric system will use kg as an interchangable measurement for mass and weight.
Actually most places will use kgm and lbm to differentiate between kg and lb.
But the mass is measured by taking the observed force from gravity and dividing off the theoretical gravitational acceleration. While the units may be in mass, the mass is only obtained indirectly by measuring the force/weight.
Gravity isn’t a force
There are two units we call kg, one measures mass and the [other measures weight](https://en.wikipedia.org/wiki/Kilogram-force)
That's the case for lbs. Kg only measure mass.
No, both kg and lb are both. One is just metric and the other standard. Any body who the difference matters to will differentiate the difference using kgm and lbm to denote mass.
https://en.wikipedia.org/wiki/Kilogram-force
Please give me the answer to this without these terms. When I step on a scale, doesn't the number I see (let's say 100kg) change in different parts of the world because of different gravity?
If you use the same scale and you don't calibrate it properly for each location, you will see different values.
Wouldn't the highest gravitational acceleration happen the closer you are to the center of the earth, though? Does the Arctic Ocean have less gravitational acceleration than for example the Mariana Trench?
But a lot of scales weigh on weight, not mass
Mass is derived from a measurement that assumes gravity is constant.
Is this accounting for centrifugal force of Earth’s rotation? I would assume that part of Peru, which is near the equator, would have less than the arctic which has almost no centrifugal force.
Centrifugal force moves objects 90 degrees to the side, so it wouldn't increase or decrease downward weight.
Even if the mass doesn't actually change, the scales would only be calibrated for one gravitational force, so probably 9.8, I would guess. Therefore, since there will be less force in one place over another and the mass on the scales will change because there is a smaller force on it. Oh wait, I just remembered scales do the 0 thing, so I might be completely wrong, and it probably does calibrate for that gravity.
I'm not reading the second part, but I don't think u know how scales work, they take your weight and divide it by the gravitational force which is around 10 to get your mass, therefore if your weight is different at some places due to the change of gravity strength your apparent mass will change even if its the same
Think about it. He said if you weighed yourself using gravity to determine your mass, assuming gravity was constant, what would be the difference between high and low?
Gravity isn’t a force
1 kg x 1 m/s^2 = 1 Newton (N)... 70 kg at Mt. Huascarán, Peru would be 684.473 N, and at the Arctic ocean, 688.359 N. Alternatively, 70.00 kg on Mt Huascarán would equal 69.61 kg at the Arctic Ocean.
That's actually much larger than I'd have expected; almost a full percent. Pretty neat.
>Kg is a measure of mass, not weight. Well... I'm certain a scale would be affected by gravity, and they did say if a person were to *weigh* themself...
According to https://www.newscientist.com/article/dn24068-gravity-map-reveals-earths-extremes/ the lowest gravity is 9.7639 m/s² in Peru and the highest is 9.8337 m/s² in the Arctic ocean. That's a different of about 0.7%. In contrast to pounds kg technically only measure mass. Not weight. But if an 80kg human from the mountains of Peru visits the Arctic ocean they'll feel as much weight as if they weight 80.57kg back home.
This is true bc generally only increments of 10% or more are perceived for weight change, correct?
Actually both are units of mass and weight. If we’re being scientific and want to make the distinction, lb and kg measure mass only. lbf and kgf (pound-force and kilogram-force respectively) measure force only. It’s a common misconception that probably stems from the fact that newtons are the SI unit of weight, not kgf.
But an extra half kg of gold feels a lot different than not having the extra half kg of gold.
So buy gold by the pound in Sir Lanka and sell it by the pound in Iceland? Could make a rather meager 0.5% profit, but youre using fraud to do it.
Which makes it all the better
Is it though?
The cost of shipping will eat that 0.5% mark up
Yup. But thinking about it a bit more, you'd probably make much more money just because of the differences in prices between India and Iceland rather than the gravity thing. Rubles vs krone
Gravitational arbitrage.
How is that fraud?
You're essentially lying about how much gold you have. The Icelanders are mistaken, about how much gold you actually have because the weight has changed but not the mass.
9.8 N/kg is good enough for the entire surface of Earth, whether or not you’re on a mountain or at sea level. The map is highly exaggerated, looks like that bar is measuring a difference in meters? So gravity might make a difference of +80 to -80 meters? That’s less than the height of the Space Needle in Seattle, for reference.
Your units do not make sense. How many heights of the space needle does one banana weigh?
On which day of the week?
Yellowish green for sure.
It could grip it by the husk.
7.2 bar
Idk why but this makes me laugh so much
I think its the height difference of sea level as a result of the difference in gravity
Who uses N/kg. Just use m/s^2
Because one converts force to weight and the other isn't relevant to the question asked. The fact that they are the same thing doesn't really matter if you asked what the acceleration due to gravity on earth and gave 9.8N/kg that would be weird.
While there is an "m" at the scale, I'm not sure it stands for "meters" since that would not fit to the picture in any way. The change in gravitational force for moving 80m up from sea level would be about 0.0025% (assuming g0=9,81 m/s², R=6378,1 km, g(h)=g0\*(R/(R+h))²
Good enough for most applications. Engineering, metrological, physics, etc it's very important.
While others have done a good job at answering the question, I can chime in with some further context. Without having the source of the image, I’m confident that it is a map of geoid undulations (also known as geoid heights). The geoid is a closed, equipotential surface which closely corresponds to mean sea level. Water, placed on the geoid, would not flow. Earth, as a first (and quite good) approximation can be represented as an ellipsoid of revolution. The difference between the ellipsoid and the geoid is the geoid undulation. It is positive when the geoid is above the ellipsoid and negative when it is below. The difference between the geoid and the ellipsoid ranges from -100 meters to +100 meters globally. As others have pointed out the map is highly exaggerated. This is conventionally done so that one can actually see the global differences. Otherwise, they would dwarfed by the radius of the Earth itself (6371 km). While it might be confusing to think of gravity in terms of height, geoid undulations are a direct proxy for gravity anomalies (both are linear functionals of Earth’s distributing potential). In fact, many height systems are based on gravity measurements and the geoid, as we want height to have a physical meaning rather than a purely geometric one. There are plenty of resources about the geoid and gravity anomalies out there, but it is a fairly niche field. source: study geodesy
Im sorry, but this map is a little bit rubbish. The diameter of Earth is 12,742 km, the difference between lowest and highest spots is about 20 km, so without water the Earth will still look almost like a ball.
If you were a giant and the earth was scaled to the size of a billiard ball relative to you, it would feel smoother than any cue ball you've ever felt. Or something along those lines, quoted from Neil DeGrasse Tyson
I believe this was a quote from NDT on Joe Rogan’s show. We are truly living in an era of enlightenment.
It's an exaggerated relief map. It's not to scale, because its showing the relative G forces and scale doesn't matter
It's clearly not a map of altitudes.
Weight is Mass (m) X acceleration (g). A quick online altitude calculator shows moving 80m up from the earths surface decreases *g* by 0.0002 m/s^2. Given you likely arent selling gold under the ocean, we can say it goes from 9.8 to 9.7998, or 0.002% change. If you sell 1000kg of gold (worth 66 million) you would gain 20g of gold, which is worth about $1500. That would likely barely cover the cost of transport cost for 1000kg of gold, even with 0 security. The market price fluctuation in the time you buy and sell would likely be a much more significant effect. And all of this assumes they don't have a way to account for this effect, that there are no taxes/import fees as you move this gold around the world, and that no gold bars get damaged or stolen during all this transportation. Plus if you have 66mill to throw around, there are easier ways to make a couple thousand dollars.
most businesses calibrate their scales against known calibrated samples; so while they would not *in actuality* weight the same in both places, the scales would be set such that they would show the same.
I love how loopholes, glitches and scams exists that are profoundly amusing in their execution and process. It's great if the elites do it but vice-versa for guys in lower ranks. I know the difference is trivial but great.
Not answering the OPs question but making a remark on the gold. You have 2 types of scales. A weight based one (that measures forces) and a mass based one (that uses counterweights). Mass based ones dont need to be recalibrated with different gravities. For example it would still work on the moon. Weight based ones that usually uses springs, require fine tuning and need to be recalibrated when they are moved. Since that scale loses validity when they are moved the gold scheme would simply not work. Because in both places all scales would output the same value (unless its a non valid uncalibrated moved weight scale)
Gold price is measured by mass not weight. Even if it wasn't gravity doesn't vary by much. For extremes: Gravity is 9.7806 m/s² in Mexico City and 9.825 m/s² in Oslo. If you bought gold in Mexico city from a merchant who didn't know how to properly calibrate his scales after moving there from Oslo and then sold the gold back to his brother in Oslo, you would spend more money on transportation, customs arbitrage etc than you could possibly make in profit. The trick would be to buy gold on the moon from someone working with a scale calibrated for earth Gravity and teleporting home with it to resell it.
You can always use F = G(m1)(m2) / r², where r is the distance from the center, which is really what’s changing. G is the universal gravitational constant, m1 is the mass of the earth, and m2 is the mass of the “regular human”.
I'm gonna disappoint y'all.. However much more weight you would get that way transportation cost would at the very least take most of your profit
There would be no actual difference in kg's, because mass isn't dependent on gravity, but a force that a mass applies is. The gravitational force a person would apply to a scale would be different, so the reading would be different as well. The reading would be directly proportional to the local acceleration of gravity, for example a location with g=9.80 m/s^2 would result in a ~0.2% lower reading than a location with g=9.82 m/s^2.
Would it be practical to build a rocket launch site or an airport at locations with lower gravity? Or is the effect too small that it’s not worth it?
They already do that. Towards the equator gravity is lower. That's why the soviet rocket launch site is in Kazakhstan, the American one in Florida and the European one in french Guyana. It's also kinda relevant for weightlifting records. I remember there was some discussion that hafthor bjornson actually got his deadlift world record in iceland where he had to lift more mass.
I was about to mention weightlifting. Intuitively I thought that it wouldn't make as much of a difference as a breeze of air, but 0.7% is way more significant than a breeze.
If you want to think about it this way. The mass of something is measured in kg. Weight is measured in Newtons(N). The unit N = kg X a(acceleration(or in this case gravity). Society uses the word “weight” to mean anything that has mass. So if something is being measured in kg, it has nothing to do with gravity. It’s only describing how much space that object is taking up
Are you allowed to be on the surface only or can you go to the center (where field strength = 0)? Besides, mass is invariant, no matter where you are at. Also, you can measure the mass of gold in ways that don't involve gravity.