Question

Part 1 of 2

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.
(2a, 2a)
(0,2a)
10 N
30 N
60 N
70 N
(0,0)
(2a, 0)
Find the x-coordinate of the center of gray-
ity (as a multiple of a).
Answer in units of a.
0909
part 2 of 2
Find the y-coordinate of the
ity (as a multiple of a).
Answer in units of a.

Answer 1

(
`(37a)/(34)`,
`(25a)/(34)`)

Explanation:

Given data,

Side of square = a

center of gravity of x,y

`x_(cg)` =
`(w_(1)x_(1) +w_(2)x_(2)+......+w_(n)x_(n) )/(w_(1)+w_(2)+......+w_(n) )`

`y_(cg)` =
`(w_(1)y_(1) +w_(2)y_(2)+......+w_(n)y_(n) )/(w_(1)+w_(2)+......+w_(n) )`

now, find the center of mass of each plate

For plate 1

W = 10N

x- coordinate = a/2

y- coordinate = a+a/2 = 3a/2

For plate 2

W = 30N

x- coordinate = a+a/2=3a/2

y- coordinate = a+a/2 = 3a/2

For plate 3

W = 70N

x- coordinate = a+a/2=3a/2

y- coordinate = a/2

For plate 4

W = 60N

x- coordinate = a/2

y- coordinate = a/2

`x_(cg)` =
`(10*(a)/(2) +30*(3a)/(2)+70*(3a)/(2)+60*(a)/(2))/(10+30+70+60 )` =
`(185a)/(170)` =
`(37a)/(34)`

`y_(cg)` =
`(10*(3a)/(2) +30*(3a)/(2)+70*(a)/(2)+60*(a)/(2))/(10+30+70+60 )` =
`(125a)/(170)` =
`(25a)/(34)`

Therefor (
`(37a)/(34)`,
`(25a)/(34)`) will the center of gravity