Calculating Absolute Gravity Using Relative Measurements for Scientists

[pvpkillerx]

I used a Sodin Gravimeter to measure the relative gravity of a building with 14 floors.
I am wondering on how I use the relative gravity to find absolute gravity?
Information:
Height difference of each floor is 3.95m
Each floor weighs 10⁶kg
For example, on the basement floor, the reading was 62.14mgal, the 1st floor was 61.90mgal, and 3rd floor was 60.18mgal (these converted would be 6.214*10^-4m/s², 6.190*10^-4m/s², 6.018*10^-4m/s², respectively . How do I use this information to find the absolute gravity?



Δg/g = (-2ΔR)/R

g = (G*m)/R²



I found Δg by finding the difference of relative gravity. After that, I don't know what to do. The goal of this lab is to find the radius of earth, but I don't know how. Please help. Just tell me what to do, I don't need an answer. Thank you.

 

[Delphi51]

You could graph Δg vs ΔR and compare the slope with your formula. Knowing g you could find R or vice versa but I don't see how you can find both.

A search for "Sodin Gravitometer" brought this up as the first hit. If you haven't seen it, you will find it very useful.
http://www.physics.utoronto.ca/~phy225h/experiments/gravity/GRAVITY-of-the-EARTH.pdf

 

[pvpkillerx]

ye, that's my experiment, but i don't know what values to plug in.

 

[pvpkillerx]

Okay, let's say i only want to find the radius of earth, how do I do that? What values do I plug in? The slope of Δg vs ΔR is -0.0305 * 10^.4 m/s^2. Please help, thank you. Every time i plug values in, i tried a lot of them, i don't even get a close value to the real value of Earth radius. Any help is appreciated.

 

[Delphi51]

Curious; the slope of Δg vs ΔR should have units of mGal/meter or 1/s^2.
I used the sample values given in the question and got a slope of -.435 mGal/m = .435 x 10^-5 /s^2, which resulted in r = 2 x 10^6 m and is the right order of magnitude anyway. Perhaps you meant to say your slope was -0.0305 * 10^-4 which would also result in an r that is out by a factor of about 2.
The pdf in the link indicates that this raw value may be quite far off due to gravitational attraction of the massive floors in the building. I would attempt to calculate those accelerations and adjust each measurement of Δg before plotting the graph.

 

[Delphi51]

The slope of Δg vs ΔR is -0.0305 * 10^.4 m/s^2.

Curious; the slope of Δg vs ΔR should have units of mGal/meter or 1/s^2.
I used the sample values given in the question and got a slope of -.435 mGal/m = .435 x 10^-5 /s^2, which resulted in r = 2 x 10^6 m and is the right order of magnitude anyway. Perhaps you meant to say your slope was -0.0305 * 10^-4 which would also result in an r that is out by a factor of about 2.
The pdf in the link indicates that this raw value may be quite far off due to gravitational attraction of the massive floors in the building. I would attempt to calculate those accelerations and adjust each measurement of Δg before plotting the graph.[/QUOTE]

 

[pvpkillerx]

I think i might know what my mistake is, cause I converted all of my mGal readings to m/s^2. But I am still wondering what to plug in for the equation. g =9.8, Δg = the value that i get in mGal, what's ΔR and R? What values do I use for those?

 

[D H]

The PDF file that Delphi51 provided in the opening post tells in painstaking detail what you need to do. Did you follow the steps provided in that document?

I doubt that very many physics departments are housed in a 14 story building and let their undergraduate students use a $16,000 Sodin gravimeter to estimate the radius of the Earth based on variations in gravity inside the building. This document that Delphi51 found is exactly what you should be following because this almost certainly is your school.

 

[pvpkillerx]

Of course i followed what it said in the document, seeing as how that is my experiment as i mentioned before. I am just confused with the variables.

 

[Delphi51]

I wouldn't plug values into Δg/g = (-2ΔR)/R. You would end up with multiple values of R and not know which ones were best. Rather, solve it for Δg so it looks like y = mx + b and you can then graph y vs x and know that the slope should be m. The article talks about how the values from some floors will be better than others and likely result in a linear part of your graph; you would use the slope on that part of the graph to compare with the formula. Equating the numerical value of the slope with the slope expression taken from the formula, you would then solve for R.

Okay, what values to use for Δg is complicated and not made very clear in the article. I'm not sure either. I would start with the meter reading for each floor and subtract the reading in the basement to get a Δg for each floor. And the ΔR value corresponding to each is its height above the basement.

It would be interesting to see your table of values and graph. It is quite a fascinating problem. It reminds me of the legend about measuring the height of a tall building with a barometer - a terrific story loved by generations of physics students: http://www.peer.ca/bohr.html

 

[pvpkillerx]

I have figured it out, and i get approximately 6500 to 6800km in radius depending upon which floor i am on. The real value of the radius of Earth is around 6378km, so i am very happy with the results. Thank you very much for all the help, I really appreciate it.

 

[Delphi51]

Super! Good luck with the next one.

 

[xsss]

I am currently doing this experiment as well and I was wondering how you obtained the method of analyzing the results.