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Topic: Theory of errors: center of gravity
Replies: 7   Last Post: Mar 14, 2013 2:40 PM

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David Jones

Posts: 69
Registered: 2/9/12
Re: Theory of errors: center of gravity
Posted: Mar 7, 2013 4:29 PM
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"Allamarein" wrote in message

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?



Are you?

Suggest you look at the result in the case that there is no uncertainty in
the masses.

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