So, I learned in physics class at school in the UK that the value of acceleration due to gravity is a constant called g and that it was 9.81m/s^2. I knew that this value is not a true constant as it is affected by terrain and location. However I didn’t know that it can be so significantly different as to be 9.776 m/s^2 in Kuala Lumpur for example. I’m wondering if a different value is told to children in school that is locally relevant for them? Or do we all use the value I learned?
I just learned ‘about 9.8’ which is true anywhere in the world.
In freshman college physics we had a lab to measure gravity then had to use our lab result for the rest of the course.
Just don’t make the same mistake as one physics lab did. They made a series of measurements and their results showed that gravity quickly increases in fall, falls slowly over winter, and back to about pre-fall levels very slowly in summer. It took quite a while to figure out the reason of this unexpected result. They turned their equipment inside out to find a mistake to no avail. Then they realized that the university stored coal for the central heating and hot water in the basement under the lab…
Could you explain to me why that last part matters?
I’m assuming they’re indicating that the mass below the apparatus increased in fall (when storage was filled) and decreased slowly through the winter, leading them to measure a changed graviational constant. A back of the napkin calculation shows that in order to change the measured gravitational constant by 1 %, by placing a point mass 1 m below the apparatus, that point mass would need to be about 15 000 tons. That’s not a huge number, and it’s not unlikely that their measuring equipment could measure the gravitational acceleration to much better precision than 1 %, I still think it sounds a bit unlikely.
Remember: If we place the point mass (or equivalently, centre of mass of the coal heap) 2 m below the apparatus instead of 1 m, we need 60 000 tons to get the same effect (because gravitational force scales as inverse distance squared). To me this sounds like a fun “wandering story”, that without being impossible definitely sounds unlikely.
For reference: The coal consumption of Luxembourg in 2016 was roughly 90 000 tons. Coal has a density of roughly 1500 kg / m3, so 15 000 tons of coal is about 10 000 m3, or a 21.5 m x 21.5 m x 21.5 m cube, or about four olympic swimming pools.
Edit: The above density calculations use the density of coal, not the (significantly lower) density of a coal heap, which contains a lot of air in-between the coal lumps. My guess on the density of a coal heap is in the range of ≈ 1000 kg / m3 (equivalent to guessing that a coal heap has a void fraction of ≈ 1 / 3.)
Thank you for the very well detailed explanation, as well as the visual. Much appreciated!
À better question is why is a university still using coal heating in the modern age?
This observation further compounds the hypothesis of “fun wandering story that has been told from person to person for a long time”
Fits in with the sinking library and Native American graveyard (though i believe that the exact second one may be regionally locked)
How much was the variation?
Can’t be that big, as the difference in mass close to the instrument only varied in the several tons category, but obviously enough to puzzle the scientists.
9.81 in Scotland.
Whoa, thats heavy
Seeing as the British invented gravity, most places just use our gravity rather than making their own.
This is why you have so many Russians being thrown out of windows in high buildings. They’re testing the local value of g.
Dimitri, come to the window! I have a stopwatch and questions about the local density of the Earth’s crust!
Wow, I also didn’t know it varied so much. I assumed it would be within about 9.81±0.01 worldwide, since I (in UK) was also taught ~=9.81m/s^2
See Wikipedia for this.
We learned 9.82 m/^2. But in the classes I have as an engineering student we use 10 m/s^2. And I wish I was kidding when I say it’s because it easier to do the math in your head. Well obviously for safety critical stuff we use the current value for wherever the math problem is located at
9.8 is close enough to 10 for most human scale calculations. No need to have extra sig figs
Pi = 3
Sin(x) = x
And now, g = 10. Smh.
I have a “pi^2 = g” shirt, and every engineer I know loves it, every friend with a scheme background needs to point out that it’s wrong.
Interesting that I learned 32.2 ft/s, but only 9.8 m/s - one less significant figure, but only a factor of two in precision (32.2 vs 32 = .6%; 9.81 vs 9.8 is only 0.1%). Here’s the fun part - as a practicing engineer for three decades, both in aerospace and in industry, it’s exceedingly rare that precision of 0.1% will lead to a better result. Now, people doing physics and high-accuracy detection based on physical parameters really do use that kind of precision and it matters. But for almost every physical object and mechanism in ordinary life, refining to better than 1% is almost always wasted effort.
Being off by 10/9.81x is usually less than the amount that non-modeled conditions will affect the design of a component. Thermal changes, bolt tensions, humidity, temperature, material imperfections, and input variance all conspire to invalidate my careful calculations. Finding the answer to 4 decimal places is nice, but being about to get an answer within 5% or so in your head, quickly, and on site where a solution is needed quickly makes you look like a genius.
I gotta say, that explanations sounds way better than shrugging and saying “close enough”. But then again our teachers usually say “fanden være med det” meaning “devil be with that” actually meaning “Fu*k it” when it comes to those small deviations
our teachers usually say “fanden være med det”
There’s a lot of wisdom in that. ;-)
Standard gravity is 9.80665 m/s2. That the number defined by the metric people who set all the world’s units. In schools in the united states of america, we used 9.8. I don’t recal using any more precision than that. Gravity at the surface does vary, but you don’t need more presision than that for most academic purposes.
Is that so? I wonder what the story behind that is. Maybe it’s a surface average?
Most people would probably guess this, but meters and seconds are defined independently of Earth’s gravity, so it doesn’t have a true value, just apparently a standard nominal one.
The value of g depends on altitude. You can define it easily at the earth average 0m altitude.
It also depends on latitude, and local geology and…
Maybe it is just weighted by surface area, you’re right, and that’s what I meant by “surface average”.
I’ve learned it as 9.81 but we usually round up to 10 for calculations. (this is for highschool. I haven’t gotten to college yet)
You round it to 10? Do you also round PI to 3 for simplicity? Kids these days.
yeah :/ in physics class we do round pi to 3
Rounding of constants always depends on what you are calculating. Getting a rocket into orbit is a case to use the actual local value of g with a bunch of digits (and the change with height, too). If you build a precision tool, some more digits of PI are no bad idea.
But to calculate the lenght of fence to buy to surround a round pond, I actually used 10/3 for “PI plus safety margin” once.
I was just kidding but good example with the fence.
We just use 9.8 at my high school for calculations. Also its cool to see another young person on the fediverse (Assuming you are still in highschool).
Close enough I graduated last year 2023. I couldn’t get in to the college I wanted so I decided to try it a second time. There’s a countrywide exam that gives you a score. It’s called yks. I’m currently studying for that exam.
