# For the stop bracket shown, locate the x coordinate of the center of gravity.

Question-AnswerCategory: Engineering MechanicsFor the stop bracket shown, locate the x coordinate of the center of gravity.

For the stop bracket shown, locate the x coordinate of the center of gravity.

Step: 1

Divide the stop bracket into sections as follows:

Step: 2

Assume that the bracket is homogeneous. Accordingly, the center of gravity is to coincide with the centroid of the volume.
Write the equation for x-coordinate of center as follows:
……. (1)

Here,  is the x-coordinate centroid of section 1,  is the x-coordinate centroid of section 2,  is the x-coordinate centroid of section 3,  is the x-coordinate centroid of section 4,  is the volume of section 1,  is the volume of section 2, is the volume of section 3 and  is the volume of section 4.

Step: 3

Calculate the x-coordinate centroids of each individual section and corresponding volumes and tabulate the values as follows:

Volume no:

Volume ‘V’

I

5280000

II

6000000?

III

616590

IV

– 1389960

Step: 4

Calculate the x-coordinate of center for the given bracket.
Substitute for and for in equation (1).

Therefore, the x-coordinate of center for the given bracket is .