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Q: Center of Mass ( No Answer,   1 Comment )
Question  
Subject: Center of Mass
Category: Science > Math
Asked by: ragnorock-ga
List Price: $3.00
Posted: 14 Dec 2004 03:07 PST
Expires: 14 Dec 2004 20:15 PST
Question ID: 442365
Hello,

I need to know the Mass and the Center of mass of a tetrahedron made
of the points (0,0,1),(0,0,0),(1,0,0) and (0,1,0).

The density is X^2 Kg/m^3

Clarification of Question by ragnorock-ga on 14 Dec 2004 03:13 PST
I have the Volume of the Tetrahedron equaling 1/3.
I just do not understand how to get the rest of the question :(

Also this is my first time to use Google Answers and if I am
undercharging please do point it out.   I know this would be easy if I
just knew how to do it :)

Request for Question Clarification by mathtalk-ga on 14 Dec 2004 13:33 PST
Hi, ragnorock-ga:

As fj-ga has pointed out, the volume of your particular tetrahedron is
1/6.  The link posted by fj-ga is quite apt.  It reports, without
proof, that the center of mass of any tetrahedron (aka the centroid)
is the straight average of all four vertices (assuming uniform mass
density).

So, in your case:  (1/4,1/4,1/4)

I'd be happy to post a proof of this (using calculus) for the list
price you've offered, but if you are satisfied with the free Comment
provided by fj-ga, then you might want to Close (expire) the Question
to avoid being charged in the event an Answer is posted.

regards, mathtalk-ga

Clarification of Question by ragnorock-ga on 14 Dec 2004 20:15 PST
Thank you both.
I fianly found some one on campus that explaned it to me
I needed to do a triple intrigral of X^2 to find the mass, Tripple
intrigal of x^3 to find the X cordinat of the center of mass and
Tripple intrigal of Y*X^2 for the y and z cordidnat.

Thank you all again :)
Answer  
There is no answer at this time.

Comments  
Subject: Re: Center of Mass
From: fj-ga on 14 Dec 2004 05:17 PST
 
As a lead, read: http://www.pballew.net/centroid.html 

I also think that you may have the volume worked out incorrectly, see
http://mathworld.wolfram.com/Tetrahedron.html this gives the volume as
1/3 Area x height.

In the tetrahedron you describe, the area of the base triangle is (1/2
base x height) = 1/2, so the volume of the tetrahedron is 1/3 x 1/2 x
1 = 1/6.

You may want to clarify what the 'X' value is. If not given then,
assuming that the tetrahedron units are in metres, the mass would be
1/6(X^2) Kg.

Please note that this comment is free and has come from an unpaid
source and as such is not bound by the quality and guarantee
requirements of
official GA researchers. You can tell who they are as their names are
in bold, blue and underlined!

I'll leave it to an official researcher to provide the full answer if
they find your $3.00 an attractive offer.

Good luck and welcome to GA!

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