Center of Gravity of a Carpenter's Square

AI Thread Summary
The discussion focuses on calculating the center of gravity for a carpenter's square shaped like an L, with specified dimensions. The initial calculations for the coordinates were incorrect due to miscalculations of areas and the positions of the rectangles. A user identified that the x-coordinate for the second rectangle needed to account for its offset from the origin. After recalculating and considering the correct positions, the user successfully determined the correct center of gravity. The final coordinates were confirmed as accurate after addressing the initial confusion.
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Homework Statement



A carpenter's square has the shape of an L, where d1 = 19.0 cm, d2 = 2.00 cm, d3 = 2.00 cm, d4 = 9.0 cm. Locate its center of gravity. (Take (x, y) = (0, 0) at the intersection of d1 and d4.)

Picture ---> http://www.webassign.net/pse/p12-07alt.gif

Answer = (____ , ____) cm


Homework Equations


Xcg=(A1X1+A2X2)/(A1+A2)
Ycg=(A1Y1+A2Y2)/(A1+A2)


The Attempt at a Solution



x1=1cm
x2=3.50cm
y1=9.5cm
y2=1cm

Xcg=(38.8*1+14*3.5)/(38.8+14)=1.66cm
Ycg=(38.8*9.5+14*1)/(38.8+14)=7.47cm

This seems to be the incorrect answer, and I am not sure why...Can anyone help? Thanks.
 
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It seems you have correctly divided the L-shape into two rectangles, one covering d1 and d2 and one covering d4 - d2 and d3. If that is so, then your numbers 38.8 and x2 = 3.5 are wrong.

When you get stuck like this it is often a good idea to track backwards through your work and check all results once more. :-p
 
I recalculated the area to get 38 cm^2 instead of 38.8cm^2, but I am still confused on what the x value should be...why is it not 3.5, which is half of 7, be the correct value. 7 is the length of the second rectangle for (d4-d2) and d3? What should the value of X be then?
 
The x and y coordinates should represent the center of each rectangle as measured from the origin. Since the first rectangle have the origin (0,0) on its lower left corner the center its center is easily found (your x1 and y1). The other rectangle however is offset a bit away from the origin such that the coordinates of its lower left corner is (d2, 0). The number you found (3.5 cm, 1 cm) is "only" the distance from the lower left of this rectangle to its center, so you are missing to include the offset in the coordinates.
 
thank you! I got the right answer now. :)
 

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