 #1
 33
 0
Homework Statement
if the black dot is assumed by (0,0).find the center of mass coordinate of this triangle
i'm sorry but since the pic wont show ill attach the link here
https://ibb.co/4Ptw5T7
<Moderator's note: picture added>
Homework Equations
centroid is 2/3 of median [/B]
using vector addition
The Attempt at a Solution
the problem is when i try solve this problem by both method it always give me different answer first I'll use the 2/3 theorem first
~ by seeing the picture it shows us that the length of EF is 2√2(2/sin45) and length from D to midpoint(H) is √2 ,[/B]
EH √2 then the length of center of mass from point D, ⅔DH or ⅔√2 from here i turn this into x axis by multiply it by cos 45(since 90 on point D split into half) so i get ⅔√2.½√2 it become ⅔ this is the length from right side (point D) but the problem demand it from left side (black point) so it become 2⅔=4/3(x axis)
for y axis is using same method and it will give also 4/3result
~and the second method is using vector addition and have form like (x1m1+x2m2)/(m1+m2) in my case (x1l1+x2l2)/(l1+l2) since it doesnt show any mass and just length , and im sure most you already know about this method
so ill straight to my attempt
for x axis (x1l1+x2l2+x3l3)/(l1+l2+l3)
where 1= ED 2=EF 3=DF
(1.2+1.2√2+2.2)/(2+2√2+2)=1.292
and exact same method for y axis
and give same result, and from here the problem is arises , now if we take a look 1.292 is length from left side to right (from black point 0,0) so it length from point D is 21.292=½√2 so for y axis it length from point D is 21.292=½√2 then if we use phytagorean theorem on both result we should able to determine the length from point D to the centrium ( i already calculated it on method 1) so it turned out like this √((½√2)²+(½√2)²)=1 and the answer should be ⅔√2 and if we try further more the length from D to mid point is 1/(2/3)=1,5 and how can there become 1,5??
sorry if i use weird term since im not native english speaker so i'm not familiar with it i , ill really glad if someone can explain this to me since both formula is valid at least so i think
Attachments

13.1 KB Views: 410
Last edited by a moderator: