Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.stat.math.independent

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
David Jones

Posts: 61
Registered: 2/9/12
Re: Theory of errors: center of gravity
Posted: Mar 7, 2013 4:29 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

"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.








Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.