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Re: Theory of errors: center of gravity
Posted:
Mar 7, 2013 4:29 PM
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"Allamarein" wrote in message
news:064ba007-b42b-443c-b6ae-1c42a2181449@googlegroups.com...
Let's suppose we have two point masses:
m1 = 4 kg, m2 = 3.5
Their associated standard deviation are:
dm1 = 0.5 kg, dm2 = 0.2 kg
Their distance from the origin of the reference frame are (1D problem):
x1 = 0.7 m, x2 = 0.8 m
Their associated standard deviation is:
dx1 = 0.01 m, dx2 = 0.01 m
I have to find the center of gravity (CoG) of this system and its
uncertainty. The nominal value can be found with the well-known relation:
X = (m1*x1 + m2*x2)/(m1+m2) = 0.7467 m
In order to find the associated uncertainty, I used the relationship for
non-linear combinations (cf.
http://en.wikipedia.org/wiki/Propagation_of_uncertainty), evaluating the
four partial derivatives of the previous relationship.
Hence dX = 0.0079 m
In my opinion is not an intuitive result: in fact the uncertainty of the
center of gravity is less than the uncertainty on the position of each mass.
Are you able to justify this result?
Regards
=================================================================================
Are you?
Suggest you look at the result in the case that there is no uncertainty in
the masses.
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