Question

A square plate is produced by welding to- gether four smaller square plates, each of side a. The weight of each of the four plates is shown in the figure.Find the x and y coordinates for the center of gravity.

Answer 1

Coordinates of the center of gravity:

r1= (0.5a,0.5a)

r2=(1.5a,0.5a)

r3=(0.5a,1.5a)

r4=(1.5a,1.5a)

Weighted averages:

$\text{Rcg}=\frac{w\cdot r1+w2\cdot r2+w3\cdot r3+w4\cdot r4}{w1+w2+w3+w4}$

Where:

w1= 50N

w2= 40N

w3= 50N

w4= 70N

Replacing:

$\text{Rcg}=\frac{50(0.5a,0.5a)+40(1.5a,0.5a)+50(0.5a,1.5a)+70(1.5a,1.5a)}{50+40+50+70}$$\text{Rcg}=\frac{5}{21}(0.5a,0.5a)+\frac{4}{21}(1.5a,1.5a)+\frac{5}{21}(0.5a,1.5a)+\frac{1}{3}(1.5a,1.5a)$

Rcg=(x,y)= (43/42a, 53/42a)