The Math Forum

Search All of the Math Forum:

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

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

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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 ]
Red Star

Posts: 136
Registered: 6/28/08
Theory of errors: center of gravity
Posted: Mar 7, 2013 2:48 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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., 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?


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

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.