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.
Well, g is not a real constant, it depends mostly on altitude. The true constant is G. g=9.8 is usually more than enough for your calculations, to the point we often round it to 10 for simplicity, or you remove it completely is the mass is too low. But actual numbers is only the very last step usually. The calculations will be made with letters. The value you use at the end for g depends on the precision you need, so it depends on the precision of the other parameters.
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!
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.
Well yeah. I was just curious if the difference was on the order of millimeters or microns /m².
9.81 in Scotland.
Whoa, thats heavy
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.
Even then, once you figure in a safety factor of 2 or 3 as a minimum, the extra precision really gets lost in the fog anyway.
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. ;-)
Seeing as the British invented gravity, most places just use our gravity rather than making their own.
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)
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.
You round it to 10? Do you also round PI to 3 for simplicity? Kids these days.
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.
yeah :/ in physics class we do round pi to 3
See Wikipedia for this.
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
I learned 9.81 m/s2 and 32.2 ft/s2 with the qualifier being at sea level.
This doesn’t change the issue presented by OP. Sea level is not level across the world. In fact there are much larger differences than most people expect. The Earth is not perfectly round. Earth rotation causes the equator to be affected by a centrifugal force, making it wider there ( more distance to earth core means less gravity ) than at the poles. Overall, gravity at Earth surface level varies by 0.7%, ranging from 9.76 in Peru to 9.83 in the Arctic Ocean, but it’s absolutely not linear. In addition, the Earth is full of gravity anomalies. These cause localized dips and spikes in gravity. Two of the big dogs lips lie in the Indian ocean and the Caribbean. Because water is fluid, sea level is very much affected by local gravity (as well as other factors such as air pressure, salinity, temperature…). Which is also why the moons gravity can cause tides. The permanently lower gravity on these anomalous spots mean that the average sea level here is lower than it would be on a perfect sphere. This difference can be up to two meters in sea level.
I figured they took the best average at sea level across the planet that they could measure.
