Two identical carpenter\'s squares like the one shown in Figure (a) are fastened

Question

Two identical carpenter's squares like the one shown in Figure (a) are fastened together with light tape to form a U-shaped combination that is open at the top as shown in Figure (b). The dimensions of each square are as follows:

s1 = 15.4 cm,

s2 = s3 = 1.80 cm,

and

s4 = 5.00 cm.

If the bottom of the U has a width

s4,

each side has a length

s1,

and we locate the origin of our coordinate system at the lower left corner of the combination, determine the location of the center of gravity of the combination of the two squares. (Ignore the dimensions of the tape and the thickness of the U-shape.)

Explanation / Answer

We consider the entire combination as 3 pieces of a mass as shown in the figure above                 M1, M2, M3.

Now dimensions of M1 and M2 are (15.4-1.8) x 1.8

Dimension of M3 = 1.8 x 5

Assume d is the density of the material

Mass of each M1 and M2           = (15.4 – 1.8) x 1.8 x d

In case of M3 we assume the bottom parts of the squares are placed one over the other

Mass of M3 = 5 x 1.8 x 2d

c.g of M1 is   0.9, 6.8

c.g of M2 is 4.1, 6.8

c.g of M3 is 2.5, 0.9

c.g of the combined system =

X- co-ordinate of combined c.g                  =   

                                                                                =    = 2.5

Y Co-ordinates of the cobined C.g = =     = 5.2356

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