Standard deviation in Graviational force, g

In summary: Which is why the equipment I used in undergrad physics labs was not always the newest and most expensive stuff.In summary, the conversation is about a circular motion experiment where the theoretical value for centripetal force and its uncertainty needs to be computed. The mass used in the experiment is measured to a high accuracy, with a standard deviation assumed to be 0. The uncertainty in the acceleration due to gravity, g, is also needed for the calculation. There is a discussion about the accuracy of the scale used for measuring mass and the use of g in the experiment. Ultimately, it is suggested to assume an uncertainty of 0.02 m/s^2 for g and to double check the accuracy of the scale. There is also skepticism about the
  • #1
shyta
56
0
I'm doing a lab report, but I don't need help for it. I just need the standard deviation in g.
I need to compute the theoretical value for centripetal force together with its uncertainty for my circular motion experiment.

That is, since my mass was measured to be 0.208536kg, standard deviation can be assumed to be 0. To compute the theoretical value for centripetal force, F, together with its uncertainty, I need the uncertainty in g.

i.e.
F=mg
dF/F = sqrt( (dm/m)^2 + (dg/g)^2 )

where dm is assumed to be 0

Correct me if I'm wrong. Anyone able to provide dg? I did a Google search and found something like g at equator to be 9.78 and 9.83 at the poles.

can i just assume dg to be 0.02 in this case?


thanks wise ones
 
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  • #2
Why are you assuming that your mass measurement is exact? There will be some error in any mass measurement method. Also, was the way you measured your mass really accurate to 1mg? That seems like a very large number of significant digits in your mass measurement.

As for deviation in g, it should not matter for a circular motion experiment. Why do you use g at all if the lab is about centripetal force?
 
  • #3
From LBL PDG table of constants

standard gravitational accel. g = 9.806 65 m s−2 (exact)

gravitational constant
GN = 6.674 28(67)×10−11 m3 kg−1 s−2 (±0.1%)

Bob S
 
  • #4
Yes, I second the question: How did you get your mass to be measured so accurately?
 
  • #5
The mass is measured by a balance. It's reading is in that amount of sig fig. There was no instructions in the manual to repeat the measurements of m, therefore there will only be 1 value. It's impossible to find a standard deviation for m. If so, should I assume a 0.000001kg uncertainty?

with regards to cgl 2nd question,
As for deviation in g, it should not matter for a circular motion experiment. Why do you use g at all if the lab is about centripetal force?

why doesn't my deviation in g matter? it should theoretically. g is used here because in the experiment we used the weight of a hanging mass to measure the centripetal force. it's hard to describe and i don't really wish to go into details of the experiment.
 
  • #6
You actually have a scale that has that kind of accuracy? I can't imagine that for an academic setting.

I don't think cgl knows the experiment you're talking about but I do. The gravitational acceleration will come in when you try to equalize the force from the spring creating the centripetal acceleration so you do need to find the uncertainty associated with it.

@Bob S: Why does the PDG call it exact?? I'd like to know the reasoning behind that seemingly arbitrary declaration.
 
  • #7
Bob S said:
From LBL PDG table of constants

standard gravitational accel. g = 9.806 65 m s−2 (exact)
Okay, but that's just a conversion factor for acceleration. Like many conversion factors, it is simply defined to be a certain value. It isn't the actual acceleration due to gravity at the OP's location, which is the quantity of interest here.
 
  • #9
Bob is answering an entirely different question. Yes, there is a defined "standard gravity", and depending on where you are on the earth, it's quite close to local gravity or not so close. But using it for local gravity - as it is clearly meant to be by the equation - is a misuse: it's equivalent to assuming you are at STP instead of measuring the temperature.
 
  • #10
hahah I thought so. so anyone? should i assume a 0.000001kg uncertainty for my mass since that is to the accuracy of my balance?

i think i will just be assuming a 0.02m/s^2 uncertainty for my g.
 
  • #11
You have a balance that can weigh half a pound to within a milligram?
 
  • #12
OK, I think I understand the experiment better now. The local deviation in G is fairly small, and 0.02 m/s2. should be a decent estimate (though you could get a lot more accurate than that if necessary).

I'm still surprised that you would have a scale available to measure half a pound to milligram precision. You might want to double check with your teacher/professor or the scale's manual to make sure it's really that accurate, but in the absence of any other information, assuming +/- one of the least significant digits is a decent assumption for scales (so +/- 1mg in this case).
 
  • #13
thanks cjl. I'm pretty sure the scale is to that accuracy so no worries. :)
 
  • #14
shyta said:
thanks cjl. I'm pretty sure the scale is to that accuracy so no worries. :)

You should definitely check. And tell us what kind of scale it is because I'm sure most of the people here are interested in knowing. At that precision, the small changes in air pressure that occur in a normal lab room would have to have some effect on it!
 
  • #15
shyta said:
thanks cjl. I'm pretty sure the scale is to that accuracy so no worries. :)
Just wanted to comment, I think people's skepticism is not so much that such a scale exists; rather that the physics department would budget the huge amount of money required on equipment for a student laboratory.

Equipment in student labs tends to get abused over time. Not by everybody, but when hundreds of untrained people are using that equipment then some of them are not as careful as they ought to be.
 

Related to Standard deviation in Graviational force, g

What is standard deviation in Graviational force, g?

Standard deviation in gravitational force, g, is a measure of how much the values of gravitational force, g, vary from the mean or average value. It tells us how spread out the data points are from the average value and gives us an idea of the degree of variability in the data.

How is standard deviation in Graviational force, g, calculated?

To calculate standard deviation in gravitational force, g, we first find the mean or average value of g. Then, for each data point, we subtract the mean and square the difference. These squared differences are then summed up and divided by the total number of data points minus 1. Finally, we take the square root of this value to get the standard deviation.

What is a high standard deviation in Graviational force, g, indicative of?

A high standard deviation in gravitational force, g, indicates that the values of g are widely spread out from the average value. This could mean that there is a lot of variability in the data or that there are some extreme values that are significantly different from the rest of the data points.

How is standard deviation in Graviational force, g, used in scientific research?

Standard deviation in gravitational force, g, is often used in scientific research to analyze and interpret data. It helps researchers understand the variability in their data and can be used to determine the significance of any differences between groups or conditions. It is also used to calculate confidence intervals and to assess the reliability of data.

What are some factors that can affect the standard deviation in Graviational force, g?

The standard deviation in gravitational force, g, can be affected by a variety of factors. These can include errors in measurement, natural variability in the phenomenon being studied, and the sample size. It can also be influenced by any outliers or extreme values in the data set. It is important for scientists to carefully consider these factors when interpreting the standard deviation in their research.

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